A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping ...A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping matrix is decomposed into the sum of a proportional-and a nonproportional-damping parts, and the solutions of the real modal eigenproblem with the proportional dampings are determined, which are a set of initial approximate solutions of the complex modal eigenproblem. Second, by taking the nonproportional-damping part as a small modification to the proportional one and using the matrix perturbation analysis method, a set of approximate solutions of the complex modal eigenvalue problem can be obtained analytically. The result is quite simple. The new method is applicable to the systems with viscous dampings-which do not deviate far away from the proportional-damping case. It is particularly important that the solution technique be also effective to the systems with heavy, but not over, dampings. The solution formulas of complex modal eigenvlaues and eigenvectors are derived up to second-order perturbation terms. The effectiveness of the perturbation algorithm is illustrated by an exemplar numerical problem with heavy dampings. In addition, the practicability of approximately estimating the complex modal eigenvalues, under the proportional-damping hypothesis, of damped vibration systems is discussed by several numerical examples.展开更多
Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight s...Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.展开更多
A kind of inverse eigenvalue problem in structural dynamics design is considered. The problem is formulated as an optimization problem. The properties of this problem are analyzed, and the existence of the optimum sol...A kind of inverse eigenvalue problem in structural dynamics design is considered. The problem is formulated as an optimization problem. The properties of this problem are analyzed, and the existence of the optimum solution is proved. The directional derivative of the objective function is obtained and a necessary condition for a point to be a local minimum point is given. Then a numerical algorithm for solving the problem is presented and a plane-truss problem is discussed to show the applications of the theories and the algorithm.展开更多
In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by...In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving algebraic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients,which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.展开更多
<span style="font-family:Verdana;">In this paper, for the initial and boundary value problem of beams with</span> <span style="font-family:Verdana;">structural damping, by introdu...<span style="font-family:Verdana;">In this paper, for the initial and boundary value problem of beams with</span> <span style="font-family:Verdana;">structural damping, by introducing intermediate variables, the original </span><span style="font-family:Verdana;">fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span><span><span style="font-family:Verdana;"> Numerical examples are provided to confirm the theoretical results. In the end, we test the value of <em>δ</em></span><span style="font-family:Verdana;"> to observe its influence on the model.</span></span></span>展开更多
Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompress...Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual (GMRES) method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GiViRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.展开更多
A novel infinite element method(IEM)is presented for solving plate vibration problems in this paper.In the proposed IEM,the substructure domain is partitioned into multiple layers of geometrically similar finite eleme...A novel infinite element method(IEM)is presented for solving plate vibration problems in this paper.In the proposed IEM,the substructure domain is partitioned into multiple layers of geometrically similar finite elements which use only the data of the boundary nodes.A convergence criterion based on the trace of the mass matrix is used to determine the number of layers in the IE model partitioning process.Furthermore,in implementing the Craig-Bampton(CB)reduction method,the inversion of the global stiffness matrix is calculated using only the stiffness matrix of the first element layer.The validity and performance of the proposed method are investigated by means of four illustrative problems.The first example considers the case of a simple clamped rectangular plate.It is observed that the IEM results are consistent with the theoretical results for first six natural frequencies.The second example considers the frequency response of a clamped rectangular plate with a crack.The main feature of IEM is that a very fine and good quality virtual mesh can be created around the crack tip.The third and fourth examples consider the natural frequency of a multiple point supported plate and a perforated plate,respectively.The results are obtained just need to adjust the reference point or boundary nodes.The parametric analyses for various geometric profiles are easy to be conducted using these numerical techniques.In general,the results presented in this study have shown that the proposed method provides a direct,convenient and accurate tool for eigenvalue analysis of thin plate structure with complicated shapes.展开更多
Generally speaking, the background shear current U(z) must be taken into account in eigenvalue problems of nonlinear internal waves in ocean, as is different from those of linear internal waves. A numerical calculat...Generally speaking, the background shear current U(z) must be taken into account in eigenvalue problems of nonlinear internal waves in ocean, as is different from those of linear internal waves. A numerical calculation method for eigenvalue problems of nonlinear internal waves is presented in this paper on the basis of the Thompson-Haskell's calculation method. As an application of this method, at a station (21°N, 117°15′E) in the South China Sea, a modal structure and parameters of nonlinear internal waves are calculated, and the results closely agree with the calculated results based on observation by Yang et al..展开更多
In this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matrices M,D and K for the quadratic pencil Q(λ)=λ^(2)M+λD+K,so that Q(λ)has a prescribed subset of...In this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matrices M,D and K for the quadratic pencil Q(λ)=λ^(2)M+λD+K,so that Q(λ)has a prescribed subset of eigenvalues and eigenvectors.This method can determine the solvability of the inverse eigenvalue problem automatically.We then consider the least squares model for updating a quadratic pencil Q(λ).More precisely,we update the model coefficient matrices M,C and K so that(i)the updated model reproduces the measured data,(ii)the symmetry of the original model is preserved,and(iii)the difference between the analytical triplet(M,D,K)and the updated triplet(M_(new),D_(new),K_(new))is minimized.In this paper a computationally efficient method is provided for such model updating and numerical examples are given to illustrate the effectiveness of the proposed method.展开更多
针对传统调谐质量阻尼器(TMD)的不足,本文研究了粘弹性碰撞调谐质量阻尼器(viscoelastic pounding tuned mass damper,PTMD)对高层钢结构的减振问题,采用数值仿真对PTMD进行了参数研究和优化。碰撞材料和预留间隙对PTMD的减振效果至关重...针对传统调谐质量阻尼器(TMD)的不足,本文研究了粘弹性碰撞调谐质量阻尼器(viscoelastic pounding tuned mass damper,PTMD)对高层钢结构的减振问题,采用数值仿真对PTMD进行了参数研究和优化。碰撞材料和预留间隙对PTMD的减振效果至关重要,若碰撞材料等效弹性模量较低,减振率将随着间隙的增大而减小,最后趋于恒定;碰撞材料等效弹性模量较高,减振率随预留间隙的增大,先上升后下降,最后稳定在一个定值。PTMD在不同地震强度和不同地震作用下,对高层钢结构均有较好的减振效果。从减振效果、空间要求和附加质量块重量三方面对比了TMD与PTMD,结果表明:PTMD可以大幅降低阻尼的功率要求、安装空间限制和质量块重量,比TMD更加经济有效。展开更多
文摘A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping matrix is decomposed into the sum of a proportional-and a nonproportional-damping parts, and the solutions of the real modal eigenproblem with the proportional dampings are determined, which are a set of initial approximate solutions of the complex modal eigenproblem. Second, by taking the nonproportional-damping part as a small modification to the proportional one and using the matrix perturbation analysis method, a set of approximate solutions of the complex modal eigenvalue problem can be obtained analytically. The result is quite simple. The new method is applicable to the systems with viscous dampings-which do not deviate far away from the proportional-damping case. It is particularly important that the solution technique be also effective to the systems with heavy, but not over, dampings. The solution formulas of complex modal eigenvlaues and eigenvectors are derived up to second-order perturbation terms. The effectiveness of the perturbation algorithm is illustrated by an exemplar numerical problem with heavy dampings. In addition, the practicability of approximately estimating the complex modal eigenvalues, under the proportional-damping hypothesis, of damped vibration systems is discussed by several numerical examples.
基金supported by the National Natural Science Foundation of China(Grants Nos.51978150 and 52050410334)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grants No.SJCX23_0069)the Fundamental Research Funds for the Central Universities.
文摘Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.
基金This research is partially supported by the National Natural Science Foundation of China (No. 10271055).
文摘A kind of inverse eigenvalue problem in structural dynamics design is considered. The problem is formulated as an optimization problem. The properties of this problem are analyzed, and the existence of the optimum solution is proved. The directional derivative of the objective function is obtained and a necessary condition for a point to be a local minimum point is given. Then a numerical algorithm for solving the problem is presented and a plane-truss problem is discussed to show the applications of the theories and the algorithm.
基金Supported by Liu Hui Applied Mathematics Center of Nankai University-Tianjin University( No. H10124).
文摘In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving algebraic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients,which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.
文摘<span style="font-family:Verdana;">In this paper, for the initial and boundary value problem of beams with</span> <span style="font-family:Verdana;">structural damping, by introducing intermediate variables, the original </span><span style="font-family:Verdana;">fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span><span><span style="font-family:Verdana;"> Numerical examples are provided to confirm the theoretical results. In the end, we test the value of <em>δ</em></span><span style="font-family:Verdana;"> to observe its influence on the model.</span></span></span>
基金supported by the National Natural Science Foundation of China (No. 50839003)the Natural Science Foundation of Yunnan Province (No. 2008GA027)
文摘Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual (GMRES) method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GiViRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.
文摘A novel infinite element method(IEM)is presented for solving plate vibration problems in this paper.In the proposed IEM,the substructure domain is partitioned into multiple layers of geometrically similar finite elements which use only the data of the boundary nodes.A convergence criterion based on the trace of the mass matrix is used to determine the number of layers in the IE model partitioning process.Furthermore,in implementing the Craig-Bampton(CB)reduction method,the inversion of the global stiffness matrix is calculated using only the stiffness matrix of the first element layer.The validity and performance of the proposed method are investigated by means of four illustrative problems.The first example considers the case of a simple clamped rectangular plate.It is observed that the IEM results are consistent with the theoretical results for first six natural frequencies.The second example considers the frequency response of a clamped rectangular plate with a crack.The main feature of IEM is that a very fine and good quality virtual mesh can be created around the crack tip.The third and fourth examples consider the natural frequency of a multiple point supported plate and a perforated plate,respectively.The results are obtained just need to adjust the reference point or boundary nodes.The parametric analyses for various geometric profiles are easy to be conducted using these numerical techniques.In general,the results presented in this study have shown that the proposed method provides a direct,convenient and accurate tool for eigenvalue analysis of thin plate structure with complicated shapes.
基金supported by the National Natural Science Foundation of China (Grant No. 40706055)
文摘Generally speaking, the background shear current U(z) must be taken into account in eigenvalue problems of nonlinear internal waves in ocean, as is different from those of linear internal waves. A numerical calculation method for eigenvalue problems of nonlinear internal waves is presented in this paper on the basis of the Thompson-Haskell's calculation method. As an application of this method, at a station (21°N, 117°15′E) in the South China Sea, a modal structure and parameters of nonlinear internal waves are calculated, and the results closely agree with the calculated results based on observation by Yang et al..
基金Research supported by National Natural Science Foundation of China(10571047 and 10861005)Provincial Natural Science Foundation of Guangxi(0991238)。
文摘In this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matrices M,D and K for the quadratic pencil Q(λ)=λ^(2)M+λD+K,so that Q(λ)has a prescribed subset of eigenvalues and eigenvectors.This method can determine the solvability of the inverse eigenvalue problem automatically.We then consider the least squares model for updating a quadratic pencil Q(λ).More precisely,we update the model coefficient matrices M,C and K so that(i)the updated model reproduces the measured data,(ii)the symmetry of the original model is preserved,and(iii)the difference between the analytical triplet(M,D,K)and the updated triplet(M_(new),D_(new),K_(new))is minimized.In this paper a computationally efficient method is provided for such model updating and numerical examples are given to illustrate the effectiveness of the proposed method.
文摘针对传统调谐质量阻尼器(TMD)的不足,本文研究了粘弹性碰撞调谐质量阻尼器(viscoelastic pounding tuned mass damper,PTMD)对高层钢结构的减振问题,采用数值仿真对PTMD进行了参数研究和优化。碰撞材料和预留间隙对PTMD的减振效果至关重要,若碰撞材料等效弹性模量较低,减振率将随着间隙的增大而减小,最后趋于恒定;碰撞材料等效弹性模量较高,减振率随预留间隙的增大,先上升后下降,最后稳定在一个定值。PTMD在不同地震强度和不同地震作用下,对高层钢结构均有较好的减振效果。从减振效果、空间要求和附加质量块重量三方面对比了TMD与PTMD,结果表明:PTMD可以大幅降低阻尼的功率要求、安装空间限制和质量块重量,比TMD更加经济有效。