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
Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore th...Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.展开更多
In this paper,the main researches are focused on the horizontal nonlinear vibration characteristics of roll systems for rolling mill,mainly including the study of forced vibration and free vibration of the roller.Firs...In this paper,the main researches are focused on the horizontal nonlinear vibration characteristics of roll systems for rolling mill,mainly including the study of forced vibration and free vibration of the roller.Firstly,the nonlinear damping parameters and nonlinear stiffness parameters within interface of the rolling mill are both considered,and a fractional-order differential term is also introduced to model the horizontal nonlinear vibration.Secondly,the averaging method is introduced to solve the forced vibration system of the mill roll system,and the amplitude-frequency characteristic curves of the system are obtained for different orders,external excitation amplitudes,stiffness and fractional order coefficients.Thirdly,the amplitude-frequency and phasefrequency characteristics of the free vibration of the mill roll system are investigated at different fractional orders.Then,the accuracy of the averaging method for solving the dynamic characteristics of the system is verified by numerical analysis,and the effect of the fractional differential term coefficients and order on the dynamic characteristics of the roll system are investigated.Finally,the time-frequency characteristics and phase-frequency characteristics of free vibration systems at different fractional orders are studied.The validity of the theoretical study is also verified through experiments.展开更多
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is...The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.展开更多
The Green function method (GFM) is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping r...The Green function method (GFM) is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.展开更多
A series of numerical sinmlations about a small scale (aspect ratio: 63.2) flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration (VIV) have been taken into account. The wake hydrodyn...A series of numerical sinmlations about a small scale (aspect ratio: 63.2) flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration (VIV) have been taken into account. The wake hydrodynamics and pipe deformation were accomplished by ANSYS MFX solution strat- egy designed for fluid-structure interaction (FSI) problem with well-performed LES model. The configuration of structured mesh, multi-domain design, different mesh stiffness admeasured by User Fortran ensured that the numerical task was competent to deal with large deformation related to this case. The introduction of instantaneous amplitude definition and modeless component decom- position method (Chen and Kim, 2008) was helpful to reveal much more information from modal analysis. Most results from numerical simulation are generally consistent with those from model test (Choi and Hong, 2000) via the comparison between them. As supplementary to model test, visualization of the vortex wake was also provided. It has been proved that the forced oscillation doesn't only excite a complicated dumbbell-like wake pattern around the outer thimble, but also results in inner flow inside the PVC pipe. The velocity of the inner flow increases with the frequency of forced oscillation.展开更多
This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the...This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.展开更多
A model based on the data from forced vibration experiments is developed for predicting the vortex-induced vibra- tions (VIV) of elastically mounted circular cylinders in flow. The assumptions for free and forced vi...A model based on the data from forced vibration experiments is developed for predicting the vortex-induced vibra- tions (VIV) of elastically mounted circular cylinders in flow. The assumptions for free and forced vibration tests are explored briefly. Energy equilibrium is taken into account to set up the relationship between the dynamic response of selfexcited oscillations and the force coemcients from forced vibration experiments. The gap between these two cases is bridged straightforwardly with careful treatment of key parameters. Given reduced mass m^# and material damping ratio of an elastically mounted circular cylinder in flow, the response characteristics such as amplitude, frequency, lock-in range, added mass coefficient, cross-flow fluid force and the corresponding phase angle can be predicted all at once. In- stances with different combination of reduced mass and material damping ratio are compared to investigate their effects on VIV. The hysteresis phenomenon can be interpreted reasonably. The predictions and the results from recent experiments carried out by Wifliamson' s group are in rather good agreement.展开更多
Numerical simulations of a low-mass-damping circular cylinder which can oscillate freely at transverse and stream- wise directions are presented in this work. The Navier-Stokes equations are solved with finite volume ...Numerical simulations of a low-mass-damping circular cylinder which can oscillate freely at transverse and stream- wise directions are presented in this work. The Navier-Stokes equations are solved with finite volume method, and large eddy simulation of vortex is also performed in the calculation. In order to implement dynamic mesh, overlapping grids are generated to lessen the computation for mesh field itself. Self-excited vibrations are firstly calculated to obtain the average amplitudes and frequencies of the target circular cylinder in the current flow situation, and then forced oscillations are implemented with parameters obtained in vortex-induced vibrations previously. With slight amplitude modulation, time series of displacements in vortex-induced vibrations are essentially harmonic. Regarding the fluid force, which are larger in forced oscillations than those in corresponding self-excited cases because the fluid subtracts energy from the forced cylinders. The phase angles between forces and displacements are 0° and 180° for self-excited ease and forced case respectively. In vortex-induced vibrations, the interactions between fluid and structure produce some weakly energetic vortices which induce the modulations of amplitude and frequency.展开更多
The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-...The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.展开更多
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear...The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.展开更多
In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates w...In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.展开更多
The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved....The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.展开更多
The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutio...The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutions obtained in a previous paper. The vibration shows a strong coupling between the membrane and bending solutions: either the membrane drive or the bending drive causes motions of both the membrane type and bending type. Three interesting effects characteristic of the forced vibration emerge from the coupling nature: the non-bending effect, the inner-quiescent effect and the inner-membrane-motion-and-outer-bending-motion effect. These effects may have potential applications in engineering.展开更多
In this paper, reciprocal theorem method (RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory. The paper derives the dynamic basic solution...In this paper, reciprocal theorem method (RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory. The paper derives the dynamic basic solution of thick rectangular; and the exact analytical solution of the steady-state responses of thick rectangular plates with three clamped edges and one free edge under harmonic uniformly distributed disturbing forces is found by RTM. It is regarded as a simple, convenient and general method for calculating the steady-stare responses of forced vibration of thick rectangular plates.展开更多
In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed...In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.展开更多
In this paper, applying the method of the reciprocal theorem, we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmon...In this paper, applying the method of the reciprocal theorem, we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates, the figures and tables of number value of bending moment and the deflection amplitudes as well.展开更多
In this paper, applying the method of reciprocal theorem, we give the distributions of the amplitude of bending moments along clamped edges and the amplitude of deflections along free edges of rectangular plates with ...In this paper, applying the method of reciprocal theorem, we give the distributions of the amplitude of bending moments along clamped edges and the amplitude of deflections along free edges of rectangular plates with two adjacent clamped edges under harmonic distributed and concentrated loads.展开更多
In this study, free and forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by carbon nanotubes (CNTs) under magnetic field based on modify couple stress theory (MCST) with temper...In this study, free and forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by carbon nanotubes (CNTs) under magnetic field based on modify couple stress theory (MCST) with temperature-variable material propertiesis presented. Also, the boundary conditions at two ends of nano-composite rotating pressurized microbeam reinforced by CNTs are considered as simply supported. The governing equations are obtained based on the Hamilton's principle and then computed these equations by using Navier's solution. The magnetic field is inserted in the thickness direction of the nano-composite microbeam. The effects of various parameters such as angular velocity, temperature changes, and pressure between of the inside and outside, the magnetic field, material length scale parameter, and volume fraction of nanocomposite microbeam on the natural frequency and response systemare studied. The results show that with increasing volume fraction of nano-composite microbeam, thickness, material length scale parameter, and magnetic fields, the natural frequency increases. The results of this research can be used for optimization of micro-structures and manufacturing sensors, displacement fluid, and drug delivery.展开更多
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the National Natural Science Foundation of China(Nos.12302007,12372006,and 12202109)the Specific Research Project of Guangxi for Research Bases and Talents(No.AD23026051)。
文摘Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.
基金supported by the National Key Research and Development Program of China (No.2018YFA0707300)the National Natural Science Foundation of China (Nos.51905372, 51804215)+1 种基金the State Key Laboratory of Metal Extrusion and Forging Equipment Technology Open-end FundsChengdu Technological University Laboratory Open Fund.
文摘In this paper,the main researches are focused on the horizontal nonlinear vibration characteristics of roll systems for rolling mill,mainly including the study of forced vibration and free vibration of the roller.Firstly,the nonlinear damping parameters and nonlinear stiffness parameters within interface of the rolling mill are both considered,and a fractional-order differential term is also introduced to model the horizontal nonlinear vibration.Secondly,the averaging method is introduced to solve the forced vibration system of the mill roll system,and the amplitude-frequency characteristic curves of the system are obtained for different orders,external excitation amplitudes,stiffness and fractional order coefficients.Thirdly,the amplitude-frequency and phasefrequency characteristics of the free vibration of the mill roll system are investigated at different fractional orders.Then,the accuracy of the averaging method for solving the dynamic characteristics of the system is verified by numerical analysis,and the effect of the fractional differential term coefficients and order on the dynamic characteristics of the roll system are investigated.Finally,the time-frequency characteristics and phase-frequency characteristics of free vibration systems at different fractional orders are studied.The validity of the theoretical study is also verified through experiments.
基金Project supported by the National Natural Science Foundation of China (No. 10472060)Natural Science Founda-tion of Shanghai Municipality (No. 04ZR14058)Doctor Start-up Foundation of Shenyang Institute of Aeronautical Engineering (No. 05YB04).
文摘The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
基金Project supported by the National Science and Technology Major Project(NMP)of China(No.2013ZX04011-011)
文摘The Green function method (GFM) is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.
基金Korea Research Foundation Grant funded by the Korean Government (MOEHRD,Basic Research Promotion Fund) (KRF-2008-D00556)Mokpo National University RIC for Midisize Shipbuilding
文摘A series of numerical sinmlations about a small scale (aspect ratio: 63.2) flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration (VIV) have been taken into account. The wake hydrodynamics and pipe deformation were accomplished by ANSYS MFX solution strat- egy designed for fluid-structure interaction (FSI) problem with well-performed LES model. The configuration of structured mesh, multi-domain design, different mesh stiffness admeasured by User Fortran ensured that the numerical task was competent to deal with large deformation related to this case. The introduction of instantaneous amplitude definition and modeless component decom- position method (Chen and Kim, 2008) was helpful to reveal much more information from modal analysis. Most results from numerical simulation are generally consistent with those from model test (Choi and Hong, 2000) via the comparison between them. As supplementary to model test, visualization of the vortex wake was also provided. It has been proved that the forced oscillation doesn't only excite a complicated dumbbell-like wake pattern around the outer thimble, but also results in inner flow inside the PVC pipe. The velocity of the inner flow increases with the frequency of forced oscillation.
文摘This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.
基金This project was financially supported bythe National Natural Science Foundation of China ( Grant No50323004)a grant fromthe Science and Technology Commission of Shanghai Municipality (No05DJ14001)
文摘A model based on the data from forced vibration experiments is developed for predicting the vortex-induced vibra- tions (VIV) of elastically mounted circular cylinders in flow. The assumptions for free and forced vibration tests are explored briefly. Energy equilibrium is taken into account to set up the relationship between the dynamic response of selfexcited oscillations and the force coemcients from forced vibration experiments. The gap between these two cases is bridged straightforwardly with careful treatment of key parameters. Given reduced mass m^# and material damping ratio of an elastically mounted circular cylinder in flow, the response characteristics such as amplitude, frequency, lock-in range, added mass coefficient, cross-flow fluid force and the corresponding phase angle can be predicted all at once. In- stances with different combination of reduced mass and material damping ratio are compared to investigate their effects on VIV. The hysteresis phenomenon can be interpreted reasonably. The predictions and the results from recent experiments carried out by Wifliamson' s group are in rather good agreement.
基金supported by the National Natural Science Foundation of China(Grant No.50538050)
文摘Numerical simulations of a low-mass-damping circular cylinder which can oscillate freely at transverse and stream- wise directions are presented in this work. The Navier-Stokes equations are solved with finite volume method, and large eddy simulation of vortex is also performed in the calculation. In order to implement dynamic mesh, overlapping grids are generated to lessen the computation for mesh field itself. Self-excited vibrations are firstly calculated to obtain the average amplitudes and frequencies of the target circular cylinder in the current flow situation, and then forced oscillations are implemented with parameters obtained in vortex-induced vibrations previously. With slight amplitude modulation, time series of displacements in vortex-induced vibrations are essentially harmonic. Regarding the fluid force, which are larger in forced oscillations than those in corresponding self-excited cases because the fluid subtracts energy from the forced cylinders. The phase angles between forces and displacements are 0° and 180° for self-excited ease and forced case respectively. In vortex-induced vibrations, the interactions between fluid and structure produce some weakly energetic vortices which induce the modulations of amplitude and frequency.
文摘The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.
文摘The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
文摘In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.
基金Project supported by the National Natural Science Foundation of China (No.10972143)the Shanghai Municipal Education Commission (No.YYY11040)+2 种基金the Shanghai Leading Academic Discipline Project (No.J51501)the Leading Academic Discipline Project of Shanghai Institute of Technology(No.1020Q121001)the Start Foundation for Introducing Talents of Shanghai Institute of Technology (No.YJ2011-26)
文摘The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.
基金Project supported by the Shanghai Leading Academic Discipline Project(No.Y0103)the Natural Science Foundation of Zhejiang Province of China(No.100039)
文摘The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutions obtained in a previous paper. The vibration shows a strong coupling between the membrane and bending solutions: either the membrane drive or the bending drive causes motions of both the membrane type and bending type. Three interesting effects characteristic of the forced vibration emerge from the coupling nature: the non-bending effect, the inner-quiescent effect and the inner-membrane-motion-and-outer-bending-motion effect. These effects may have potential applications in engineering.
文摘In this paper, reciprocal theorem method (RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory. The paper derives the dynamic basic solution of thick rectangular; and the exact analytical solution of the steady-state responses of thick rectangular plates with three clamped edges and one free edge under harmonic uniformly distributed disturbing forces is found by RTM. It is regarded as a simple, convenient and general method for calculating the steady-stare responses of forced vibration of thick rectangular plates.
文摘In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.
文摘In this paper, applying the method of the reciprocal theorem, we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates, the figures and tables of number value of bending moment and the deflection amplitudes as well.
文摘In this paper, applying the method of reciprocal theorem, we give the distributions of the amplitude of bending moments along clamped edges and the amplitude of deflections along free edges of rectangular plates with two adjacent clamped edges under harmonic distributed and concentrated loads.
基金the Iranian Nanotechnology Development Committee for their financial supportthe University of Kashan (463855/7)
文摘In this study, free and forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by carbon nanotubes (CNTs) under magnetic field based on modify couple stress theory (MCST) with temperature-variable material propertiesis presented. Also, the boundary conditions at two ends of nano-composite rotating pressurized microbeam reinforced by CNTs are considered as simply supported. The governing equations are obtained based on the Hamilton's principle and then computed these equations by using Navier's solution. The magnetic field is inserted in the thickness direction of the nano-composite microbeam. The effects of various parameters such as angular velocity, temperature changes, and pressure between of the inside and outside, the magnetic field, material length scale parameter, and volume fraction of nanocomposite microbeam on the natural frequency and response systemare studied. The results show that with increasing volume fraction of nano-composite microbeam, thickness, material length scale parameter, and magnetic fields, the natural frequency increases. The results of this research can be used for optimization of micro-structures and manufacturing sensors, displacement fluid, and drug delivery.