横观各向同性热电材料简支矩形板的自由振动

从耦合的三维压电热弹性理论出发分析了横观各向同性热电材料简支矩板的自由振动,证明其存在两类振动,即解耦的第一类振动和耦合的第二类振动,如果板的结构和上下表面边界条件关于中面对称,则第二类振动又可进一步分解为对称振和反对称振动,给出了热电材料简支矩形板自由振动的三维精确解,采用Ｍｏｎｔｅ Ｃａｒｌｏ法克服了超越方程求复根的困难。对于ＰＺＴ－４矩形板给出了数值结果,分析了耦合效应对振动频率的影响,计算     

夹层圆板的振动

本文讨论了夹层圆板的自由振动问题,利用修正迭代法得到了确定具有固定边界条件夹层圆板振动基频的解析表达式,并给出了数值计算结果.     

石英晶体板高频振动模态的有限元分析

厚度剪切振动是石英晶体谐振器的工作模态,精确了解厚度剪切振动模态的分布对于谐振器的设计有着十分重要的意义.目前,由直行波假设计算得到的频率和模态并不完全符合石英晶体板实际的精确振动模式,也不能精确满足工程设计的需要.本文基于Mindlin高阶板理论,采用有限元法来分析石英晶体板的高频振动模态,并在Linux并行集群上进行计算来解决大规模的线性方程组的特征值计算问题.通过计算得到了振动频率随长厚比变化的频谱图,其结果与已知文献中的结果比较,符合得较好,验证了有限元结果的可靠性.同时给出了厚度剪切振动在板中线处的位移分布,分析了金属电极的不同质量比对于厚度剪切振动模态的影响,解释了石英晶体板内的复杂的振动模式.本文的分析结果对石英晶体谐振器的设计具有指导意义.     

基于非局部弹性理论的纳米板横向振动

本文利用非局部弹性理论研究了单层石墨烯的纳米板的横向自由振动响应.通过迭代法推导了非局部应力表达,进一步通过哈密顿原理推导了纳米板的控制方程,应用纳维解法得到四边简支纳米板振动固有频率的数值解,并将本文研究结果与已有文献结果进行对比,进一步讨论了小尺寸效应,以及纳米板的三维尺寸和半波数对振动频率的影响.结果表明:非局部效应的存在使得纳米板的等效刚度和固有频率降低;半波数的增加则使得纳米板的固有频率提高.相关分析结果对基于二维纳米材料的新设备的设计和优化具有重要意义.     

双层加筋圆柱壳在不同舷间连接形式下的声辐射性能分析

论文用解析法推导得出了双层加筋圆柱壳的两种舷间连接形式-实肋板和托板的反力表达式,其中实肋板的振动形式分别采用三种振动方程近似表示-考虑板的面内面外振动、仅考虑板的面内振动、仅考虑板的面内准纵波振动,托板的振动形式也分别采用三种振动方程近似表示-考虑板的面内振动、仅考虑板的面内准纵波振动、近似成杆的纵向振动,数值分析对...     

饱和地基上弹性圆板的动力响应

研究弹性圆板在饱和地基上的垂直振动特性,即首先应用Hankel变换方法求解饱和土波动方程,然后按混合边值条件建立饱和地基上圆板垂直振动的对偶积分方程,用一种简便的方法,对偶积分方程可化为易于数值计算的第二类Fredholm积分方程。文末的数值分析得出了板振动的一些规律性,由此表明当板的挠曲刚度D趋于无穷大且不计板的质量时,其结果和无质量刚性圆盘在饱和地基上的振动特性完全一致。     

基于应变梯度中厚板单元的石墨烯振动研究

基于应变梯度理论建立了单层石墨烯等效明德林(Mindlin) 板动力学方程,推导了四边简支明德林中厚板自由振动固有频率的解析解. 提出了一种考虑应变梯度的4 节点36 自由度明德林板单元,利用虚功原理建立了单层石墨烯的等效非局部板有限元模型. 通过对石墨烯振动问题的研究,验证了应变梯度有限元计算结果的收敛性. 运用该有限元法研究了尺寸、振动模态阶数以及非局部参数对石墨烯振动特性的影响. 研究表明,这种单元能够较好地适用于研究考虑复杂边界条件石墨烯的尺度效应问题. 基于应变梯度理论的明德林板所获得石墨烯的固有频率小于基于经典明德林板理论得到的结果. 尺寸较小、模态阶数较高的石墨烯振动尺度效应更加明显. 无论采用应变梯度理论还是经典弹性本构关系,考虑一阶剪切变形的明德林板模型预测的固有频率低于基尔霍夫(Kirchho) 板所预测的固有频率.     

旋转运动导电圆板电磁弹性耦合振动方程

针对磁场环境中旋转运动导电圆板的电磁弹性耦合振动理论建模问题进行研究。在考虑几何非线性效应下,给出了旋转运动圆板的形变势能、动能及变分表达式。应用哈密顿变分原理,推得磁场中旋转运动导电圆板的磁弹性耦合非线性振动方程。根据麦克斯威尔电磁场方程及相应的电磁本构关系,并基于磁弹性基本假设,推得磁场环境中旋转运动圆板所受的电磁力表达式和磁弹性二维电动力学方程。通过算例,分析了横向磁场中旋转运动圆板的轴对称振动问题,得到了圆板的固有振动频率随转速、磁感应强度的变化规律,并对结果进行了分析。     

基于应变梯度有限元的单层石墨烯振动研究

建立了单层石墨烯等效非局部薄板的一种新的有限元模型,并运用有限元法分析不同边界条件下单层石墨烯振动的小尺度效应。给出了基于弹性应变梯度理论下Kirchhoff板的振动方程。发展了一种4节点24自由度的板单元,用于离散化求解考虑微纳结构尺度效应的高阶微分方程。在研究四边简支板振动时,考虑应变梯度的非局部弹性有限元数值计算结果与理论分析结果相一致。用有限元方法研究了不同尺寸、振动波长、振动模态阶数、边界条件类型以及非局部参数的单层石墨烯振动。     

考虑辐射散热叠层板热诱发振动的有限元分析

通过在叠层板单层厚度方向上布置温度线的方法,求解了考虑辐射散热边界条件下的叠层板的瞬态温度场;在此基础上利用考虑剪切效应的高阶板位移场建立板振动的有限元方程,分析了叠层板的热诱发振动问题;通过算例与ANSYS三维耦合单元(Solid5)结果的对比表明,提出的计算模型和方法具有很好的计算效率和精度.     

计算圆板大振幅非线性振动频率的平均刚度法

本文用平均刚度法研究圆板大振幅非线性振动的频率问题，导出了相应的非线性广义特征值方程，构造了一种避免发散并能加速收敛的加权平均迭代法，计算结果与Ｋａｎｔｏｒｏｖｉｃｈ时间平均法的解十分吻合。     

Large amplitude free flexural vibrations of laminated composite skew plates

Here, the large amplitude free flexural vibration behaviors of thin laminated composite skew plates are investigated using finite element approach. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The non-linear governing equations obtained employing Lagrange's equations of motion are solved using the direct iteration technique. The variation of non-linear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, number of layers, fiber orientation, boundary condition and aspect ratio. The influence of higher vibration modes on the non-linear dynamic behavior of laminated skew plates is also highlighted. The present study reveals the redistribution of vibrating mode shape at certain amplitude of vibration depending on geometric and lamination parameters of the plate. Also, the degree of hardening behavior increases with the skew angle and its rate of change depends on the level of amplitude of vibration.     

NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS

The non-linear forced vibration of axially moving viscoelastic beams excited bythe vibration of the supporting foundation is investigated. A non-linear partial-differential equa-tion governing the transverse motion is derived from the dynamical, constitutive equations andgeometrical relations. By referring to the quasi-static stretch assumption, the partial-differentialnon-linearity is reduced to an integro-partial-differential one. The method of multiple scales isdirectly applied to the governing equations with the two types of non-linearity, respectively. Theamplitude of near- and exact-resonant, steady state is analyzed by use of the solvability conditionof eliminating secular terms. Numerical results are presented to show the contributions of foun-dation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude forthe first and the second mode.     

Non-linear vibration of variable speed rotating viscoelastic beams

Non-linear vibration of a variable speed rotating beam is analyzed in this paper. The coupled longitudinal and bending vibration of a beam is studied and the governing equations of motion, using Hamilton’s principle, are derived. The solutions of the non-linear partial differential equations of motion are discretized to the time and position functions using the Galerkin method. The multiple scales method is then utilized to obtain the first-order approximate solution. The exact first-order solution is determined for both the stationary and non-stationary rotating speeds. A very close agreement is achieved between the simulation results obtained by the numerical integration method and the first-order exact solution one. The parameter sensitivity study is carried out and the effect of different parameters including the hub radius, structural damping, acceleration, and the deceleration rates on the vibration amplitude is investigated.     

Non-linear longitudinal vibrations of piezoceramics excited by weak electric fields

Typical non-linear effects, e.g. dependence of the resonance frequency on the amplitude, superharmonics in spectra and a non-linear relationship between excitation voltage and vibration amplitude as well as jump phenomena are observed in experiments with piezoceramics excited at resonance by weak electric fields. These non-linear effects can be observed for both the piezoelectric 31- and the 33-effect. In contrast to the well-known non-linear effects exhibited by piezoceramics in the presence of strong electric fields, these effects are not described in detail in the literature.In this paper, we attempt to model these phenomena using an electric enthalpy density to capture the cubic-like effects observed in the experiments. The equations of motion for the system under consideration are derived via the Ritz method using Hamilton's principle. The ‘non-linear’ parameters are identified and the numerical results are compared to those obtained experimentally. The effects described herein may have a significant influence in structures excited close to resonance frequencies via piezoelectric elements.     

Low-Dimensional Galerkin Models for Nonlinear Vibration and Instability Analysis of Cylindrical Shells

This paper discusses the derivation of discrete low-dimensional models for the non-linear vibration analysis of thin shells. In order to understand the peculiarities inherent to this class of structural problems, the non-linear vibrations and dynamic stability of a circular cylindrical shell subjected to dynamic axial loads are analyzed. This choice is based on the fact that cylindrical shells exhibit a highly non-linear behavior under both static and dynamic axial loads. Geometric non-linearities due to finite-amplitude shell motions are considered by using Donnell’s nonlinear shallow shell theory. A perturbation procedure, validated in previous studies, is used to derive a general expression for the non-linear vibration modes and the discretized equations of motion are obtained by the Galerkin method. The responses of several low-dimensional models are compared. These are used to study the influence of the modelling on the convergence of critical loads, bifurcation diagrams, attractors and large amplitude responses of the shell. It is shown that rather low-dimensional and properly selected models can describe with good accuracy the response of the shell up to very large vibration amplitudes.     

Non-linear dynamics of a soft magneto-elastic Cartesian manipulator

This paper studies the non-linear dynamics of a soft magneto-elastic Cartesian manipulator with large transverse deflection. The system has been subjected to a time varying magnetic field and a harmonic base excitation at the roller-supported end. Unlike elastic and viscoelastic manipulators, here the governing temporal equation of motion contains additional two frequency forced, and linear and non-linear parametric excitation terms. Method of multiple scales has been used to solve the temporal equation of motion. The influences of various system parameters such as amplitude and frequency of magnetic field strength, amplitude and frequency of support motion, and the payload on the frequency response curves have been investigated for three different resonance conditions. With the help of numerical results, it has been shown that by using suitable amplitude and frequency of magnetic field, the vibration of the manipulator can be significantly controlled. The developed results and expressions can find extensive applications in the feed-forward vibration control of the flexible Cartesian manipulator using magnetic field.     

Non-linear dynamics of a flexible single link Cartesian manipulator

The present work deals with the non-linear vibration of a harmonically excited single link roller-supported flexible Cartesian manipulator with a payload. The governing equation of motion of this system is developed using extended Hamilton's principle, which is reduced to the second-order temporal differential equation of motion, by using generalized Galerkin's method. This equation of motion contains both cubic non-linearities of geometric and inertial type in addition to linear forced and non-linear parametric excitation terms. Method of multiple scales is used to solve this non-linear equation and study the stability and bifurcations of the system. Influence of amplitude of the base excitation and mass ratio on the steady state response of the system is investigated for both simple and subharmonic resonance conditions. Critical bifurcation points are determined from the fixed-point responses and periodic, quasi-periodic responses are also found for different system parameters. The results obtained using the perturbation analysis are compared with the previously published experimental work and are found to be in good agreement. This work will be useful for the designer of a flexible manipulator.     

Nonlinear vibration of symmetrically laminated composite skew plates by finite element method

Here, the large amplitude free flexural vibration behavior of symmetrically laminated composite skew plates is investigated using the finite element method. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Kármán's assumptions is introduced. The nonlinear matrix amplitude equation obtained by employing Galerkin's method is solved by direct iteration technique. Time history for the nonlinear free vibration of composite skew plate is also obtained using Newmark's time integration technique to examine the accuracy of matrix amplitude equation. The variation of nonlinear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, fiber orientation and boundary condition.     

Non-linear vibrations of transversely isotropic rectangular'' plates

The large amplitude free flexural vibration of transversely isotropic rectangular plate, incorporating the effects of transverse shear and rotatory inertia, is studied using the von Karman field equations. A mode shape, consisting of three generalised-coordinates together with the Galerkin technique, results in a system of three non-linear simultaneous ordinary differential equations which govern the motion of the plate. These equations are integrated using a fourth-order Runge-Kutta method to obtain the period for each amplitude of vibration. The non-linear period vs amplitude behaviour is of the hardening type and it is also found that transverse shear and rotary inertia effects increase the period and that this increase is quite significant even for thin transversely isotropic plates. The results are compared with earlier results which were based on a one-term or one generalised coordinate solution and using the Berger approximation or the von Karman field equations.