Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) u...Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) unifies near-field and farfield models, alleviating the thresholding effect. Current localization methods in MPR based on the angle of arrival (AOA) and time difference of arrival (TDOA) measurements resort to semidefinite relaxation (SDR) and Gauss-Newton iteration, which are computationally complex and face the possible diverge problem. This paper formulates a pseudo linear equation between the measurements and the unknown MPR position,which leads to a closed-form solution for the hybrid TDOA-AOA localization problem, namely hybrid constrained optimization(HCO). HCO attains Cramér-Rao bound (CRB)-level accuracy for mild Gaussian noise. Compared with the existing closed-form solutions for the hybrid TDOA-AOA case, HCO provides comparable performance to the hybrid generalized trust region subproblem (HGTRS) solution and is better than the hybrid successive unconstrained minimization (HSUM) solution in large noise region. Its computational complexity is lower than that of HGTRS. Simulations validate the performance of HCO achieves the CRB that the maximum likelihood estimator (MLE) attains if the noise is small, but the MLE deviates from CRB earlier.展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or pa...Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or particle scale mechanical analyses of these systems. The electrostatic repulsive force depends on the mid-plane potential between two charged particles. Previous analytical solutions of the mid-plane potential, including those based on simplified assumptions and modern mathematic methods, are reviewed. It is shown that none of these solutions applies to wide ranges of interparticle distance from 0 to 10 and surface potential from 1 to 10. Three previous analytical solutions are chosen to develop a semi-analytical solution which is proven to have more extensive applications. Furthermore, an empirical closed-form expression of mid-plane potential is proposed based on plenty of numerical solutions. This empirical solution has extensive applications, as well as high computational efficiency.展开更多
The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different metho...The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different methods. It is found that the deflection can be expressed by means of the four characteristic roots and the two rotations should be expressed by all the six characteristic roots,which is the particularity of Mindlin plate theory. And the closed-form solutions,which satisfy two of the three governing equations and all boundary conditions and are accurate for rectangular plates with moderate thickness,are derived for any combinations of simply supported and clamped edges. The free edges can also be dealt with if the other pair of opposite edges is simply supported. The present results agree well with results published previously by other methods for different aspect ratios and relative thickness.展开更多
In this paper,a nonlinear strength criterion is proposed using the average of intermediate(σ2)and minor(σ3)principal stresses in place of σ3 in Ramamurthy(1994)’s strength criterion.The proposed criterion has the ...In this paper,a nonlinear strength criterion is proposed using the average of intermediate(σ2)and minor(σ3)principal stresses in place of σ3 in Ramamurthy(1994)’s strength criterion.The proposed criterion has the main advantages of negligible variation of strength parameters with confining stress and ability to link with conventional strength parameters.Additionally,a new closed-form solution based on the proposed criterion is derived and validated for Chhibro Khodri tunnel.Further,analytical solutions including Singh’s elastoplastic theory,Scussel’s approach,and closed-form solutions based on conventional and modified Ramamurthy(2007)criteria are compared with the results of proposed approach.It is shown that the in situ squeezing pressure predictions made by the proposed approach are more accurate.Also,a parametric study of the present analytical solution is carried out,which displays explicit dependency of tunnel stability on internal support pressure and tunnel depth.The influence of tunnel geometry is observed to be dependent on the applied support pressure.展开更多
A closed-form numerical algorithm (CFNA) is analyzed in detail. CFNA iswidely used in mechanical dynamics for periodic solution of second-order original differentialequations (SODE) with periodic time-variant coeffici...A closed-form numerical algorithm (CFNA) is analyzed in detail. CFNA iswidely used in mechanical dynamics for periodic solution of second-order original differentialequations (SODE) with periodic time-variant coefficients. The principle of the algorithm is todiscretize the motion period into many short time intervals, so the coefficient matrices of theequation set are regarded as constant in a time interval. Defects are found in the originalalgorithm in treating the modal coordinates at the two end-nodes and important modifications to thedefects is made for the algorithm. The modified algorithm is finally used to solve the dynamicproblem of a three-ring planetary gear transmission.展开更多
In this paper,an exact closed-form solution for a curved sandwich panel with two piezoelectric layers as actuator and sensor that are inserted in the top and bottom facings is presented.The core is made from functiona...In this paper,an exact closed-form solution for a curved sandwich panel with two piezoelectric layers as actuator and sensor that are inserted in the top and bottom facings is presented.The core is made from functionally graded(FG)material that has heterogeneous power-law distribution through the radial coordinate.It is assumed that the core is subjected to a magnetic field whereas the core is covered by two insulated composite layers.To determine the exact solution,first characteristic equations are derived for different material types in a polar coordinate system,namely,magneto-elastic,elastic,and electro-elastic for the FG,orthotropic,and piezoelectric materials,respectively.The displacement-based method is used instead of the stress-based method to derive a set of closed-form real-valued solutions for both real and complex roots.Based on the elasticity theory,exact solutions for the governing equations are determined layer-by-layer that are considerably more accurate than typical simplified theories.The accuracy of the presented method is compared and validated with the available literature and the finite element simulation.The effects of geometrical and material parameters such as FG index,angular span along with external conditions such as magnetic field,mechanical pressure,and electrical difference are investigated in detail through numerical examples.展开更多
A closed-form solution to the linear matrix equation AX-EXF = BY with X and Y unknown and matrix F being in a companion form is proposed, and two equivalent forms of this solution are also presented. The results provi...A closed-form solution to the linear matrix equation AX-EXF = BY with X and Y unknown and matrix F being in a companion form is proposed, and two equivalent forms of this solution are also presented. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems in descriptor system theory. The results proposed here are parallel to and more general than our early work about the linear matrix equation AX-XF = BY .展开更多
Density-graded cellular materials have tremendous potential in structural applications where impact resistance is required.Cellular materials subjected to high impact loading result in a compaction type deformation,us...Density-graded cellular materials have tremendous potential in structural applications where impact resistance is required.Cellular materials subjected to high impact loading result in a compaction type deformation,usually modeled using continuum-based shock theory.The resulting governing differential equation of the shock model is nonlinear,and the density gradient further complicates the problem.Earlier studies have employed numerical methods to obtain the solution.In this study,an analytical closed-form solution is proposed to predict the response of density-graded cellular materials subjected to a rigid body impact.Solutions for the velocity of the impinging rigid body mass,energy absorption capacity of the cellular material,and the incident stress are obtained for a single shock propagation.The results obtained are in excellent agreement with the existing numerical solutions found in the literature.The proposed analytical solution can be potentially used for parametric studies and for effectively designing graded structures to mitigate impact.展开更多
Based on the complex effective conductivity method, a closed-form expression for the internal impedance of mixed carbon nanotube (CNT) bundles, in which the number of CNTs for a given diameter follows a Gaussian dis...Based on the complex effective conductivity method, a closed-form expression for the internal impedance of mixed carbon nanotube (CNT) bundles, in which the number of CNTs for a given diameter follows a Gaussian distribution, is proposed in this paper. It can appropriately capture the skin effect as well as the temperature effect of mixed CNT bundles. The results of the closed-form expression and the numerical calculation are compared with various mean diameters, standard deviations, and temperatures. It is shown that the proposed model has very high accuracy in the whole frequency range considered, with maximum errors of 1% and 2.3% for the resistance and the internal inductance, respectively. Moreover, by using the proposed model, the high-frequency electrical characteristics of mixed CNT bundles are deeply analyzed to provide helpful design guidelines for their application in future high-performance three-dimensional integrated circuits.展开更多
This study proposed an analytical model for the tunnel supported with a tangentially yielding liner in viscoelastic ground.The efficiency of the developed analytical model was verified by comparing the calculated resu...This study proposed an analytical model for the tunnel supported with a tangentially yielding liner in viscoelastic ground.The efficiency of the developed analytical model was verified by comparing the calculated results with associated numerical simulation results.Using the analytical model,a comprehensive parameter sensitivity analysis was performed to examine the effects of the rate of tunnel face advancement,concrete liner thickness,installation time of liner,and strength and thickness of yielding elements on the tunnel responses.The results highlight the significant benefit of the tangentially yielding liner to relieve overstress in the tunnel liner and improve the stability of the tunnel.The yield efficiency of the tangentially yielding liner depends highly on the yielding strength and deformable capacity of the yielding elements and less on the installation time.展开更多
We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing therma...We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.展开更多
Dynamic programming(DP)is frequently used to obtain the optimal solution to the hybrid electric vehicle(HEV)energy management.The trade-off between the accuracy and the computational effort is the biggest problem for ...Dynamic programming(DP)is frequently used to obtain the optimal solution to the hybrid electric vehicle(HEV)energy management.The trade-off between the accuracy and the computational effort is the biggest problem for the DP method.The closed-form solution to the DP is proposed to solve this problem.Firstly,the affine linear model of the engine fuel rate is obtained based on engine test data.The piecewise linear approximation of the motor power demand is obtained considering the different energy flows in the charging and discharging stages of the battery.Then,the second-order Taylor expansion for the cost matrix at each time and state grid point is introduced to get the closed-form solution of the optimal torque split.The results show that this method can greatly reduce the computing burden by 93%while ensuring near-optimal fuel economy compared with the conventional DP method.展开更多
This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement res...This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.展开更多
A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is pr...A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is presented. This research generalizes the previous solution by Trifunac in 1972, which tackled only the semi-circular foundation, to arbitrary shallow circular-arc foundation cases, and is thus comparatively more realistic. Ground surface displacement spectra at higher frequencies are also obtained. As an analytical series solution, the accuracy and error analysis of the numerical results are also discussed. It was observed from the results that the rise-to-span ratio of the foundation profi le, frequency of incident waves, and mass ratios of different media(foundation-structure-soil) are the three primary factors that may affect the surface ground motion amplitudes near the structure.展开更多
Highly accurate closed-form eigensolutions for flutter of three-dimensional(3D)panel with arbitrary combinations of simply supported(S),glide(G),clamped(C)and free(F)boundary conditions(BCs),such as cantilever panels,...Highly accurate closed-form eigensolutions for flutter of three-dimensional(3D)panel with arbitrary combinations of simply supported(S),glide(G),clamped(C)and free(F)boundary conditions(BCs),such as cantilever panels,are achieved according to the linear thin plate theory and the first-order piston theory as well as the complex modal analysis,and all solutions are in a simple and explicit form.The iterative Separation-of-Variable(iSOV)method proposed by the pre-sent authors is employed to obtain the highly accurate eigensolutions.The flutter mechanism is studied with the benefit of eigenvalue properties from mathematical senses.The effects of boundary conditions,chord-thickness ratios,aerodynamic damping,aspect ratios and in-plane loads on flut-ter properties are examined.The results are compared with those of Kantorovich method and Galerkin method,and also coincide well with analytical solutions in literature,verifying the accu-racy of the present closed-form results.It is revealed that,(A)the flutter characteristics are domi-nated by the cross section properties of panels in the direction of stream flow;(B)two types of flutter,called coupled-mode flutter and zero-frequency flutter which includes zero-frequency single-mode flutter and buckling,are observed;(C)boundary conditions and in-plane loads can affect both flutter boundary and flutter type;(D)the flutter behavior of 3D panel is similar to that of the two-dimensional(2D)panel if the aspect ratio is up to a certain value;(E)four to six modes should be used in the Galerkin method for accurate eigensolutions,and the results converge to that of Kantorovich method which uses the same mode functions in the direction perpendicular to the stream flow.The present analysis method can be used as a reference for other stability issues characterized by complex eigenvalues,and the highly closed-form solutions are useful in parameter designs and can also be taken as benchmarks for the validation of numerical methods.展开更多
Earthquake engineers have made a lot of efforts to derive a comprehensive set of closed form expressions for performance evaluation of frames, which are already presented in guidelines such as SAC/FEMA. These analytic...Earthquake engineers have made a lot of efforts to derive a comprehensive set of closed form expressions for performance evaluation of frames, which are already presented in guidelines such as SAC/FEMA. These analytical expressions have been developed to estimate the annual probability of exceeding a limit state. In the process of such seismic assessments, some essential assumptions are adopted to simplify the process. One of these fundamental assumptions declares that drift demand at any seismic intensity level follows a lognormal distribution around its median. To investigate the validity of this assumption, this paper describes a case study of the types of errors that could be produced by using the sample median as the central tendency. Based on the Maximum Likelihood Estimation method as well as other statistical evidence, this paper proposes the use of the sample geometric mean instead of the sample median for the central tendency. Further, the results of seismic reliability evaluations of 4 sample frames are compared based on utilizing both the geometric mean and the sample median. In this process, both first and second order power law fits of the hazard curve are implemented to compare the effects of hazard estimation and the selection of the central tendency on the final results. It is observed in the application example that the sample geometric mean could lead to more accurate results.展开更多
基金supported by the National Natural Science Foundation of China (62101359)Sichuan University and Yibin Municipal People’s Government University and City Strategic Cooperation Special Fund Project (2020CDYB-29)+1 种基金the Science and Technology Plan Transfer Payment Project of Sichuan Province (2021ZYSF007)the Key Research and Development Program of Science and Technology Department of Sichuan Province (2020YFS0575,2021KJT0012-2 021YFS-0067)。
文摘Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) unifies near-field and farfield models, alleviating the thresholding effect. Current localization methods in MPR based on the angle of arrival (AOA) and time difference of arrival (TDOA) measurements resort to semidefinite relaxation (SDR) and Gauss-Newton iteration, which are computationally complex and face the possible diverge problem. This paper formulates a pseudo linear equation between the measurements and the unknown MPR position,which leads to a closed-form solution for the hybrid TDOA-AOA localization problem, namely hybrid constrained optimization(HCO). HCO attains Cramér-Rao bound (CRB)-level accuracy for mild Gaussian noise. Compared with the existing closed-form solutions for the hybrid TDOA-AOA case, HCO provides comparable performance to the hybrid generalized trust region subproblem (HGTRS) solution and is better than the hybrid successive unconstrained minimization (HSUM) solution in large noise region. Its computational complexity is lower than that of HGTRS. Simulations validate the performance of HCO achieves the CRB that the maximum likelihood estimator (MLE) attains if the noise is small, but the MLE deviates from CRB earlier.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
基金Project supported by the National Key Basic Research Program of China(Grant No.2012CB026103)the National Natural Science Foundation of China(Grant No.51009136)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2011212)
文摘Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or particle scale mechanical analyses of these systems. The electrostatic repulsive force depends on the mid-plane potential between two charged particles. Previous analytical solutions of the mid-plane potential, including those based on simplified assumptions and modern mathematic methods, are reviewed. It is shown that none of these solutions applies to wide ranges of interparticle distance from 0 to 10 and surface potential from 1 to 10. Three previous analytical solutions are chosen to develop a semi-analytical solution which is proven to have more extensive applications. Furthermore, an empirical closed-form expression of mid-plane potential is proposed based on plenty of numerical solutions. This empirical solution has extensive applications, as well as high computational efficiency.
基金supported by the National Natural Science Foundation of China (No. 10772014)
文摘The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different methods. It is found that the deflection can be expressed by means of the four characteristic roots and the two rotations should be expressed by all the six characteristic roots,which is the particularity of Mindlin plate theory. And the closed-form solutions,which satisfy two of the three governing equations and all boundary conditions and are accurate for rectangular plates with moderate thickness,are derived for any combinations of simply supported and clamped edges. The free edges can also be dealt with if the other pair of opposite edges is simply supported. The present results agree well with results published previously by other methods for different aspect ratios and relative thickness.
文摘In this paper,a nonlinear strength criterion is proposed using the average of intermediate(σ2)and minor(σ3)principal stresses in place of σ3 in Ramamurthy(1994)’s strength criterion.The proposed criterion has the main advantages of negligible variation of strength parameters with confining stress and ability to link with conventional strength parameters.Additionally,a new closed-form solution based on the proposed criterion is derived and validated for Chhibro Khodri tunnel.Further,analytical solutions including Singh’s elastoplastic theory,Scussel’s approach,and closed-form solutions based on conventional and modified Ramamurthy(2007)criteria are compared with the results of proposed approach.It is shown that the in situ squeezing pressure predictions made by the proposed approach are more accurate.Also,a parametric study of the present analytical solution is carried out,which displays explicit dependency of tunnel stability on internal support pressure and tunnel depth.The influence of tunnel geometry is observed to be dependent on the applied support pressure.
基金This project is supported by National Natural Science Foundation of China (No.50205019) Development Foundation of Shanghai Municipal Commission of Education, China (No.04EB03).
文摘A closed-form numerical algorithm (CFNA) is analyzed in detail. CFNA iswidely used in mechanical dynamics for periodic solution of second-order original differentialequations (SODE) with periodic time-variant coefficients. The principle of the algorithm is todiscretize the motion period into many short time intervals, so the coefficient matrices of theequation set are regarded as constant in a time interval. Defects are found in the originalalgorithm in treating the modal coordinates at the two end-nodes and important modifications to thedefects is made for the algorithm. The modified algorithm is finally used to solve the dynamicproblem of a three-ring planetary gear transmission.
文摘In this paper,an exact closed-form solution for a curved sandwich panel with two piezoelectric layers as actuator and sensor that are inserted in the top and bottom facings is presented.The core is made from functionally graded(FG)material that has heterogeneous power-law distribution through the radial coordinate.It is assumed that the core is subjected to a magnetic field whereas the core is covered by two insulated composite layers.To determine the exact solution,first characteristic equations are derived for different material types in a polar coordinate system,namely,magneto-elastic,elastic,and electro-elastic for the FG,orthotropic,and piezoelectric materials,respectively.The displacement-based method is used instead of the stress-based method to derive a set of closed-form real-valued solutions for both real and complex roots.Based on the elasticity theory,exact solutions for the governing equations are determined layer-by-layer that are considerably more accurate than typical simplified theories.The accuracy of the presented method is compared and validated with the available literature and the finite element simulation.The effects of geometrical and material parameters such as FG index,angular span along with external conditions such as magnetic field,mechanical pressure,and electrical difference are investigated in detail through numerical examples.
基金supported by the Major Program of National Nat-ural Science Foundation of China (No. 60710002) Program for Changjiang Scholars and Innovative Research Team in University
文摘A closed-form solution to the linear matrix equation AX-EXF = BY with X and Y unknown and matrix F being in a companion form is proposed, and two equivalent forms of this solution are also presented. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems in descriptor system theory. The results proposed here are parallel to and more general than our early work about the linear matrix equation AX-XF = BY .
基金the financial support provided by the US Army Research Office under grant number W911NF-18-1-0023.
文摘Density-graded cellular materials have tremendous potential in structural applications where impact resistance is required.Cellular materials subjected to high impact loading result in a compaction type deformation,usually modeled using continuum-based shock theory.The resulting governing differential equation of the shock model is nonlinear,and the density gradient further complicates the problem.Earlier studies have employed numerical methods to obtain the solution.In this study,an analytical closed-form solution is proposed to predict the response of density-graded cellular materials subjected to a rigid body impact.Solutions for the velocity of the impinging rigid body mass,energy absorption capacity of the cellular material,and the incident stress are obtained for a single shock propagation.The results obtained are in excellent agreement with the existing numerical solutions found in the literature.The proposed analytical solution can be potentially used for parametric studies and for effectively designing graded structures to mitigate impact.
基金Project supported by the National Science and Technology Major Project of China(Grant No.2015ZX03001004)the National Natural Science Foundation of China(Grant Nos.61604113,61625403,61334003,61376039,61574104,and 61474088)
文摘Based on the complex effective conductivity method, a closed-form expression for the internal impedance of mixed carbon nanotube (CNT) bundles, in which the number of CNTs for a given diameter follows a Gaussian distribution, is proposed in this paper. It can appropriately capture the skin effect as well as the temperature effect of mixed CNT bundles. The results of the closed-form expression and the numerical calculation are compared with various mean diameters, standard deviations, and temperatures. It is shown that the proposed model has very high accuracy in the whole frequency range considered, with maximum errors of 1% and 2.3% for the resistance and the internal inductance, respectively. Moreover, by using the proposed model, the high-frequency electrical characteristics of mixed CNT bundles are deeply analyzed to provide helpful design guidelines for their application in future high-performance three-dimensional integrated circuits.
基金We acknowledge the funding support from the University Transportation Center for Underground Transportation Infrastructure(UTC-UTI)at the Colorado School of Mines and the U.S.Department of Transportation(DOT)(Grant No.69A3551747118).
文摘This study proposed an analytical model for the tunnel supported with a tangentially yielding liner in viscoelastic ground.The efficiency of the developed analytical model was verified by comparing the calculated results with associated numerical simulation results.Using the analytical model,a comprehensive parameter sensitivity analysis was performed to examine the effects of the rate of tunnel face advancement,concrete liner thickness,installation time of liner,and strength and thickness of yielding elements on the tunnel responses.The results highlight the significant benefit of the tangentially yielding liner to relieve overstress in the tunnel liner and improve the stability of the tunnel.The yield efficiency of the tangentially yielding liner depends highly on the yielding strength and deformable capacity of the yielding elements and less on the installation time.
文摘We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.
基金National Natural Science Foundation of China:[Grant Number 52077217].
文摘Dynamic programming(DP)is frequently used to obtain the optimal solution to the hybrid electric vehicle(HEV)energy management.The trade-off between the accuracy and the computational effort is the biggest problem for the DP method.The closed-form solution to the DP is proposed to solve this problem.Firstly,the affine linear model of the engine fuel rate is obtained based on engine test data.The piecewise linear approximation of the motor power demand is obtained considering the different energy flows in the charging and discharging stages of the battery.Then,the second-order Taylor expansion for the cost matrix at each time and state grid point is introduced to get the closed-form solution of the optimal torque split.The results show that this method can greatly reduce the computing burden by 93%while ensuring near-optimal fuel economy compared with the conventional DP method.
基金supported by National Natural Science Foundation of China (No. 50978183)Tianjin Natural Science Foundation (No. 07JCZDJC10100)
文摘This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.
文摘A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is presented. This research generalizes the previous solution by Trifunac in 1972, which tackled only the semi-circular foundation, to arbitrary shallow circular-arc foundation cases, and is thus comparatively more realistic. Ground surface displacement spectra at higher frequencies are also obtained. As an analytical series solution, the accuracy and error analysis of the numerical results are also discussed. It was observed from the results that the rise-to-span ratio of the foundation profi le, frequency of incident waves, and mass ratios of different media(foundation-structure-soil) are the three primary factors that may affect the surface ground motion amplitudes near the structure.
基金supported by the National Natural Science Foundation of China(Nos.11872090,11672019,11472035)。
文摘Highly accurate closed-form eigensolutions for flutter of three-dimensional(3D)panel with arbitrary combinations of simply supported(S),glide(G),clamped(C)and free(F)boundary conditions(BCs),such as cantilever panels,are achieved according to the linear thin plate theory and the first-order piston theory as well as the complex modal analysis,and all solutions are in a simple and explicit form.The iterative Separation-of-Variable(iSOV)method proposed by the pre-sent authors is employed to obtain the highly accurate eigensolutions.The flutter mechanism is studied with the benefit of eigenvalue properties from mathematical senses.The effects of boundary conditions,chord-thickness ratios,aerodynamic damping,aspect ratios and in-plane loads on flut-ter properties are examined.The results are compared with those of Kantorovich method and Galerkin method,and also coincide well with analytical solutions in literature,verifying the accu-racy of the present closed-form results.It is revealed that,(A)the flutter characteristics are domi-nated by the cross section properties of panels in the direction of stream flow;(B)two types of flutter,called coupled-mode flutter and zero-frequency flutter which includes zero-frequency single-mode flutter and buckling,are observed;(C)boundary conditions and in-plane loads can affect both flutter boundary and flutter type;(D)the flutter behavior of 3D panel is similar to that of the two-dimensional(2D)panel if the aspect ratio is up to a certain value;(E)four to six modes should be used in the Galerkin method for accurate eigensolutions,and the results converge to that of Kantorovich method which uses the same mode functions in the direction perpendicular to the stream flow.The present analysis method can be used as a reference for other stability issues characterized by complex eigenvalues,and the highly closed-form solutions are useful in parameter designs and can also be taken as benchmarks for the validation of numerical methods.
文摘Earthquake engineers have made a lot of efforts to derive a comprehensive set of closed form expressions for performance evaluation of frames, which are already presented in guidelines such as SAC/FEMA. These analytical expressions have been developed to estimate the annual probability of exceeding a limit state. In the process of such seismic assessments, some essential assumptions are adopted to simplify the process. One of these fundamental assumptions declares that drift demand at any seismic intensity level follows a lognormal distribution around its median. To investigate the validity of this assumption, this paper describes a case study of the types of errors that could be produced by using the sample median as the central tendency. Based on the Maximum Likelihood Estimation method as well as other statistical evidence, this paper proposes the use of the sample geometric mean instead of the sample median for the central tendency. Further, the results of seismic reliability evaluations of 4 sample frames are compared based on utilizing both the geometric mean and the sample median. In this process, both first and second order power law fits of the hazard curve are implemented to compare the effects of hazard estimation and the selection of the central tendency on the final results. It is observed in the application example that the sample geometric mean could lead to more accurate results.