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1.
Exact expressions for the frequency equation and mode shapes of composite Timoshenko beams with cantilever end conditions are derived in explicit analytical form by using symbolic computation. The effect of material coupling between the bending and torsional modes of deformation together with the effects of shear deformation and rotatory inertia is taken into account when formulating the theory (and thus it applies to a composite Timoshenko beam). The governing differential equations for the composite Timoshenko beam in free vibration are solved analytically for bending displacements, bending rotation and torsional rotations. The application of boundary conditions for displacement and forces for cantilever end condition of the beam yields the frequency equation in determinantal form. The determinant is expanded algebraically, and simplified in an explicit form by extensive use of symbolic computation. The expressions for the mode shapes are also derived in explicit form using symbolic computation. The method is demonstrated by an illustrative example of a composite Timoshenko beam for which some published results are available. 相似文献
2.
Mesut Şimşek 《International Journal of Engineering Science》2010,48(12):1721-1732
In this study, analytical and numerical solution procedures are proposed for vibration of an embedded microbeam under action of a moving microparticle based on the modified couple stress theory (MCST) within the framework of Euler–Bernoulli beam theory. The governing equation and the related boundary conditions are derived by using Hamilton’s principle. The closed form solution of the transverse deflections of the embedded microbeam is obtained using the finite Fourier sine transformation. In the numerical solution, the dynamic deflections are computed by using the Lagrange’s equations in conjunction with the direct integration method of Newmark. The static deflections are also obtained analytically. A detailed parametric study is conducted to study the influences of the material length scale parameter, the Poisson’s ratio, the velocity of the microparticle and the elastic medium constant as well as the solution procedures on the dynamic responses of the microbeam. For comparison purpose, static deflections and free vibration frequencies of the microbeam are obtained and compared with previously published studies. Good agreement is observed. The results show that the above mentioned effects play an important role on the dynamic behavior of the microbeam. 相似文献
3.
将弹炮发射系统简化为移动质量作用下的轴向运动悬臂梁系统,推导了轴向运动梁的振动方程,采用修正的Galerkin法离散求解该偏微分方程,得到以模态坐标表示的二阶时变常微分方程组,通过Newmark-β法对方程组进行了求解。计算结果表明,移动质量载荷主要使梁的一阶模态受到激励,移动质量的大小和运动速度对悬臂梁的振动响应影响较大,在移动质量作用下梁的伸缩运动都处于不稳定状态;在移动质量脱离悬臂梁后,梁的轴向收缩运动使得梁的瞬时振动频率不断减小,振动位移逐渐衰减,而振动速度逐渐增大,梁的运动处于不稳定状态,伸展时梁的自由振动规律相反。 相似文献
4.
Liao-Liang Ke Yue-Sheng Wang Jie Yang Sritawat Kitipornchai 《International Journal of Engineering Science》2012,50(1):256-267
Nonlinear free vibration of microbeams made of functionally graded materials (FGMs) is investigated in this paper based on the modified couple stress theory and von Kármán geometric nonlinearity. The non-classical beam model is developed within the framework of Timoshenko beam theory which contains a material length scale parameter related to the material microstructures. The material properties of FGMs are assumed to be graded in the thickness direction according to the power law function and are determined by Mori-Tanaka homogenization technique. The higher-order nonlinear governing equations and boundary conditions are derived by using the Hamilton principle. A numerical method that makes use of the differential quadrature method together with an iterative algorithm is employed to determine the nonlinear vibration frequencies of the FGM microbeams with different boundary conditions. The influences of the length scale parameter, material property gradient index, slenderness ratio, and end supports on the nonlinear free vibration characteristics of the FGM microbeams are discussed in detail. It is found that both the linear and nonlinear frequencies increase significantly when the thickness of the FGM microbeam is comparable to the material length scale parameter. 相似文献
5.
Abbas Rastgoo Farzad Ebrahimi Ali Feyz Dizaji 《International Journal of Mechanics and Materials in Design》2006,3(1):29-38
A cantilever beam having arbitrary cross section with a lumped mass attached to its free end while being excited harmonically
at the base is fully investigated. The derived equation of vibrating motion is found to be a non-linear parametric ordinary
differential equation, having no closed form solution for it. We have, therefore, established the sufficient conditions for
the existence of periodic oscillatory behavior of the beam using Green’s function and employing Schauder’s fixed point theorem.
The derived equation of vibration motion is found to be a non-linear parametric ordinary differential equation, having no
closed form solution for it. To formulate a simple, physically correct dynamic model for stability and periodicity analysis,
the general governing equations are truncated to only the first mode of vibration. Using Green’s function and Schauder’s fixed
point theorem, the necessary and sufficient conditions for periodic oscillatory behavior of the beam are established. Consequently,
the phase domain of periodicity and stability for various values of physical characteristics of the beam-mass system and harmonic
base excitation are presented. 相似文献
6.
In this paper, free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness and finite element methods. To determine the governing equations of motion by the present theory, the core density has been taken into consideration. The governing partial differential equations of motion for one element contained three layers are derived using Hamilton’s principle. This formulation leads to two partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are combined to form one ordinary differential equation. Closed form analytical solution for this equation is determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. They are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the known Wittrick–Williams algorithm. After validation of the present model, the effect of various parameters such as density, thickness and shear modulus of the core for various boundary conditions on the first natural frequency is studied. 相似文献
7.
研究非线性轴向运动黏弹性Rayleigh梁因速度周期变化产生的亚谐波共振。轴向运动速度在平均速度附近做简谐周期性脉动。通过取物质导数的Kelvin本构关系描述Rayleigh梁的黏弹性。运用多尺度近似解析方法,构建轴向运动Rayleigh梁的非线性偏微分方程的可解性条件,分析参数振动稳态响应的振幅与扰动速度频率关系。并运用微分求积方法直接离散非线性Rayleigh梁的控制方程,以验证近似解析方法分析。通过数值算例,分析了系统参数对稳态响应曲线的影响。 相似文献
8.
Sonia Ahangar Ghader Rezazadeh Rasool Shabani Goodarz Ahmadi Alireza Toloei 《International Journal of Mechanics and Materials in Design》2011,7(4):327-342
In this paper, the size-dependent vibrational behavior of a microbeam conveying fluid was investigated using the Modified
Couple Stress Theory. For cantilever and clamped-clamped microbeams, the small amplitude vibration equation of the micro-beams
was solved using a Galerkin based reduced order model and the effects of material length-scale parameter on its natural frequencies
were evaluated. It was found that for the both cantilever and clamped-clamped conditions, the critical fluid velocities predicted
by the modified couple stress theory are higher than those predicted by the classical beam theory. In addition, the differences
between the eigen-frequencies and the critical fluid velocities predicted by the modified couple stress theory and classical
beam theory depends on the ratio of the material length-scale parameter to the beam height. In addition an unexpected result
in the difference between the first eigen-frequency of the cantilever micro-beam obtained by the classical and the modified
couple stress theory has been achieved. 相似文献
9.
10.
In this article, the vibration frequency of an orthotropic nanoplate under the effect of temperature change is investigated. Using nonlocal elasticity theory, governing equations are derived. Based on the generalized differential quadrature method for cantilever and propped cantilever boundary conditions, the frequencies of orthotropic nanoplates are considered and the obtained results are compared with valid reported results in the literature. The effects of temperature variation, small scale, different boundary conditions, aspect ratio, and length on natural nondimensional frequencies are studied. The present analysis is applicable for the design of rotating and nonrotating nano-devices that make use of thermo-mechanical vibration characteristics of nanoplates. 相似文献
11.
基于Timoshenko梁理论研究两端夹紧、一端夹紧一端简支、两端简支三种不同边界条件下的轴向运动功能梯度材料(FGM)梁在热冲击载荷作用下的自由振动响应。利用Hamilton原理推导热冲击下轴向运动FGM梁的自由振动控制微分方程,并采用分离变量法求解一维热传导方程。通过微分求积法(DQM)在梁的长度方向进行离散,将原方程转化为四阶广义特征值问题,求解FGM梁自由振动的无量纲固有频率并进行特性分析。考虑了不同热冲击载荷,不同梯度指数和不同轴向运动无量纲速度对FGM梁自振频率的影响。结果表明:热冲击载荷越大,对降低FGM梁的固有频率的效果越明显;在轴向运动速度和热流输入不改变的情况下,逐渐增大材料梯度指数会使FGM梁的固有频率随之减小;FGM梁对热冲击短时间内有减缓作用,相对于均匀材料一阶失稳所需时间更长,受到热冲击的FGM梁在轴向运动时也更快达到失稳状态。 相似文献
12.
基于经典薄板理论和Hamilton原理研究温度影响下Winkler-Pasternak弹性地基上多孔功能梯度材料(FGM)矩形板的自由振动特性。采用Voigt混合幂率模型和孔隙任意分布模型来表征多孔FGM矩形板的材料属性,并考虑多孔FGM矩形板内部均匀温升和材料具有温度依赖特性;应用物理中面推导弹性地基上多孔FGM矩形板自由振动的控制微分方程并进行无量纲化;采用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,引入典型的六种边界在MATLAB统一编程且保证计算精度一致,经过迭代收敛,求解出无量纲固有频率;通过算例研究了边界条件、梯度指数、升温、孔隙率、长宽比、边厚比、无量纲弹性刚度系数和无量纲剪切刚度系数对多孔FGM矩形板振动特性的影响。 相似文献
13.
A dynamic analysis is presented for an axially translating cantilever beam simulating the spacecraft antenna featuring time-variant velocity. The extended Hamilton’s principle is employed to formulate the governing partial differential equations of motion for an axially translating Bernoulli–Euler beam. Further, the assumed modes method and the separation of variables are utilized to solve the resulting equation of motion. Attention is focused on assessing the coupling effects between the axial translation motion and the flexural deformation during the beam extension or retraction operations upon the vibratory motion of a beam with an arbitrarily varying length under a prescribed time-variant velocity field. A number of numerical simulations are also presented to illustrate the qualitative features of the underlying mechanical vibration of an axially extending or contracting flexible beam. In general, the transverse beam vibration is stabilized during extension and unstabilized during retraction. The axial acceleration of a translating beam does not affect the transverse vibratory system stabilization. 相似文献
14.
The vibration analysis of rotating, functionally graded Timoshenko nano-beams under an in-plane nonlinear thermal loading is studied for the first time. The formulation is based on Eringen's nonlocal elasticity theory. Hamilton's principle is used for the derivation of the equations. The governing equations are solved by the differential quadrature method. The nano-beam is under axial load due to the rotation and thermal effects, and the boundary conditions are considered as cantilever and propped cantilever. The thermal distribution is considered to be nonlinear and material properties are temperature-dependent and are changing continuously through the thickness according to the power-law form. 相似文献
15.
通过数值方法研究超临界速度下,两端固定边界的轴向运动梁平面耦合非线性振动固有频率。发展有限差分法,确定在超临界范围轴向运动梁的径向与横向耦合平面内非平凡静平衡位形。基于非平凡静平衡位形,经坐标变换,建立超临界轴向运动梁连续陀螺系统的标准控制方程。运用高阶Galerkin截断,研究超临界运动状态下梁平面振动的固有频率;并研究Galerkin截断阶数对计算结果的影响。 相似文献
16.
In the present work, a generalized solution for the vibration of functionally graded microbeam is studied. A vibrational response is presented for a microbeam subjected to a ramp-type heating and which has functionally varying material properties through its thickness. The governing equations of the generalized thermoelasticity without energy dissipation proposed by Green and Naghdi are presented. An analytical technique based on Laplace transform is used to calculate the vibration of deflection and the temperature. The inverses of Laplace transforms are computed numerically using Fourier expansion techniques. The effect of the ramping time parameter is studied on the lateral vibration, the temperature, the displacement, the stress, the bending thermal moment, and the strain energy of the functionally graded microbeam. The influence of the thickness of the beam is also analyzed. 相似文献
17.
Farshid Allahkarami Mansour Nikkhah-bahrami Maryam Ghassabzadeh Saryazdi 《International Journal of Mechanics and Materials in Design》2018,14(2):243-261
In this article, dynamic buckling analysis of an embedded curved microbeam reinforced by functionally graded carbon nanotubes is carried out. The structure is subjected to thermal, magnetic and harmonic mechanical loads. Timoshenko beam theory is employed to simulate the structure. Furthermore, the temperature-dependent surrounding elastic foundation is modeled by normal springs and a shear layer. Using strain gradient theory, the small scale effects are taken into account. The extended rule of mixture is employed to estimate the equivalent properties of the composite material. The governing equations and different boundary conditions are derived based on the energy method and Hamilton’s principle. Dynamic stability regions of the system are obtained using differential quadrature method. The aim of this paper is to investigate the influence of different parameters such as small scale effect, boundary conditions, elastic foundation, volume fraction and distribution types of carbon nanotubes, magnetic field, temperature and central angle of the curved microbeam on the dynamic stability region of the system. The results indicate that by increasing the volume fraction of CNTs, the frequency of the system increases and thus the dynamic stability region occurs at higher frequencies. 相似文献
18.
端部约束悬臂输流管道的动力学特性 总被引:1,自引:0,他引:1
根据梁模型横向弯曲振动模态函数一般表达式,由边界约束条件确定其模态函数的一般表达式,采用Galerkin法将运动方程在模态空间内展开,利用动力学分析方法,分析端部受线性弹簧支承和扭转弹簧约束的端部约束悬臂管道从非保守系统逐渐变为保守系统过程中的固有特性和稳定性。数值仿真结果表明,这种特殊边界输流管道具有复杂变化的动力学特性,支承和约束刚度系数的变化对系统固有特性和稳定性产生很大的影响:随着弹簧刚度的增大,系统的固有频率上升,管道失稳方式从颤振变为屈曲,并且影响系统其他参数对管道动力学特性的作用。 相似文献
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20.
为了实现对主系统的宽频振动抑制,研发了一种可调的双稳态非线性能量阱(BNES)。介绍了BNES的结构和工作原理;其次分析了BNES的刚度构成以及其非线性动力学特性,并建立了悬臂梁-BNES系统动力学微分方程;采用数值方法探究了不同磁铁间距时的BNES对悬臂梁瞬态时域振动抑制效果和稳态频域的宽频抑振能力;对两组不同的悬臂梁系统进行了实验,验证了不同磁铁间距时的双稳态非线性能量阱的宽频振动抑制能力。研究结果表明,该BNES对悬臂梁的瞬态时域响应和稳态频域响应都有很好的振动抑制能力。 相似文献