Vibration analysis of size-dependent flexoelectric nanoplates incorporating surface and thermal effects

This article is concerned with the thermo-mechanical vibration behavior of flexoelectric nanoplates under uniform and linear temperature distributions. Flexoelectric nanoplates have higher natural frequencies than conventional piezoelectric nanoplates, especially at lower thicknesses. Both nonlocal and surface effects are considered in the analysis of flexoelectric nanoplates for the first time. Hamilton's principle is employed to derive the governing equations and the related boundary conditions, which are solved applying the Galerkin-based solution. A comparison study is also performed to verify the present formulation with those of previous data. Numerical results are presented to investigate the influences of the flexoelectricity, nonlocal parameters, surface elasticity, temperature rise, plate thickness, and various boundary conditions on the vibration frequencies of thermally affected flexoelectric nanoplate.     

Determination of elastic constants from measured natural frequencies of specially orthotropic cantilever plates

Abstract

The present paper examines the possibility of evaluating the elastic constants of specially orthotropic rectangular thin plates from the measured natural frequencies of cantilever plates. An expression is developed for orthotropic rectangular thin cantilever plates to determine natural frequencies, and its validity is demonstrated through finite element analysis as well as using published test results.     

Vibration analysis of orthotropic cantilever cylindrical shells with axial thickness variation

A semi-analytical finite element method is used to determine the free vibration characteristics of thin orthotropic cantilever circular cylindrical shells. Love's first approximation shell theory is used for the formulation. The effect of the variation of thickness along the axial direction on natural frequencies, especially on the lowest frequency, has been studied with a constraint on the total mass of the shell for a particular length to middle surface radius ratio. Studies have been conducted for different degrees of orthotropy and various values of length to radius ratio.     

An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position

In this article, an analytical method is presented for thermo-mechanical vibration analysis of functionally graded (FG) nanoplates with different boundary conditions under various thermal loadings including uniform, linear, and nonlinear temperature rise via a four-variable plate theory considering neutral surface position. The temperature-dependent material properties of FG nanoplate vary gradually along the thickness according to the Mori-Tanaka homogenization scheme. The exactness of solution is confirmed by comparing obtained results with those provided in the literature. A parametric study is performed investigating the effects of nonlocal parameter, temperature fields, gradient index, and boundary conditions on vibration behavior of FG nanoplates.     

Thermo-mechanical vibration analysis of rotating nonlocal nanoplates applying generalized differential quadrature method

In this study, thermal and small-scale effects on the flapwise bending vibrations of a rotating nanoplate, which can be the basis of nano-turbine design, have been analyzed. The nano-turbine is made of an orthotropic nanoplate with a setting angle that is modeled based on the classical plate theory (CPT) with cantilever boundary conditions. The axial forces are also included in the model as the true spatial variation due to the rotation and temperature change. The governing equations and boundary conditions are derived according to Hamilton's principle and the governing equations are solved with the aid of the generalized differential quadrature method. The effects of small-scale parameter, nondimensional angular velocity, temperature change, and setting angles in the first four nondimensional frequencies are discussed. Due to the consideration of the rotating effects, results of this study are applicable in nano-machines, such as nano-motors, nano-rotor, and other rotating nano-structures. Also, by considering the effect of thermal loading on rotation of a nanoplate, the results are useful in the design of nano-turbines.     

Nonlocal free vibration of orthotropic non-prismatic skew nanoplates

The free vibration of orthotropic non-prismatic skew nanoplate based on the first-order shear deformation theory (FSDT) in conjunction with Eringen’s nonlocal elasticity theory is presented. As a simple, accurate and low computational effort numerical method, the differential quadrature method (DQM) is employed to solve the related differential equations. For this purpose, after deriving the equations of motion and the related boundary conditions, they are transformed from skewed physical domain to rectangular computational domain of DQM and accordingly discretized. After validating the formulation and method of solution, the effects of nonlocal parameter in combination with geometrical parameters and boundary conditions on the natural frequencies of the orthotropic skew nanoplates are investigated.     

加载频率对悬臂梁振动疲劳特性的影响

研究了加载频率对悬臂梁振动疲劳特性的影响。首先,给三组相同的悬臂梁结构分别施加三种不同频率（悬臂梁的固有频率,略大于固有频率和略小于固有频率）的正弦激励,使其具有相同的初始应力,试验测得应力随循环次数的变化规律;其次,在试验测得应力历程的基础上,计算悬臂梁的疲劳损伤量,研究在相同初始应力下不同加载频率对同一悬臂梁振动疲劳特性的影响;最后,将预估结果与试验测得的固有频率下降量作了对比。结果表明：加载频率对振动疲劳寿命有较大的影响,文中给出的预估结果与试验结果比较吻合     

正交异性矩形薄板自由振动的一般解析解

本文建立了正交异性矩形薄板自由振动横向位移函数微分方程的一般解。可用来求解任意边界矩形板的振动问题。作为例题,计算了复合材料悬臂层合板的频率。其结果与试验值基本吻合。     

Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates

As a first endeavor, the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates is investigated using the nonlocal elasticity theory. The formulation is derived based on the first order shear deformation theory (FSDT). The solution procedure is based on the transformation of the governing equations from physical domain to computational domain and then discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. The formulation and the method of the solution are firstly validated by carrying out the comparison studies for the isotropic and orthotropic rectangular plates against existing results in literature. Then, the effects of nonlocal parameter in combination with the geometrical shape parameters, thickness-to-length ratio and the boundary conditions on the frequency parameters of the nanoplates are investigated.     

Experimental and numerical investigations for the free vibration of cantilever trapezoidal plates

Abstract

Based on the advantages of non‐contact and full field measurement, the optical technique called amplitude‐fluctuation electronic speckle pattern interferometry (AFESPI) with an out‐of‐plane setup is employed to investigate the free vibration of cantilever trapezoidal plates with various taper ratios and sweep‐back angles. Twenty different plate configurations are analyzed, including triangular and trapezoidal plates, and the first seven vibration modes of each plate are measured. The AF‐ESPI method is very convenient for measuring vibrating objects because no contact is required in contrast to classical modal analysis using accelerometers. Based on the fact that clear fringe patterns will appear only in resonance, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present technique. Numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Excellent agreements are obtained for both results of resonant frequencies and mode shapes. The influences of taper ratios and sweep‐back angles on the vibration behavior of cantilever trapezoidal plates are also demonstrated in terms of the dimensionless frequency parameter.     

Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics

Buckling response of orthotropic single layered graphene sheet (SLGS) is investigated using the nonlocal elasticity theory. Two opposite edges of the plate are subjected to linearly varying normal stresses. Small scale effects are taken into consideration. The nonlocal theory of Eringen and the equilibrium equations of a rectangular plate are employed to derive the governing equations. Differential quadrature method (DQM) has been used to solve the governing equations for various boundary conditions. To verify the accuracy of the present results, a power series (PS) solution is also developed. DQM results are successfully verified with those of the PS method. It is shown that the nonlocal effects play a prominent role in the stability behavior of orthotropic nanoplates. Furthermore, for the case of pure in-plane bending, the nonlocal effects are relatively more than other cases (other load factors) and the difference in the effect of small scale between this case and other cases is significant even for larger lengths.     

Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium

An analytical approach for free vibration analysis of all edges simply-supported double-orthotropic nanoplates is presented. The two nanoplates are assumed to be bonded by an internal elastic medium and surrounded by external elastic foundation. The governing equations are derived based on the nonlocal theory and the expressions of the natural frequencies are proposed in an explicit form. The suggested model is justified by a good agreement between the results given by present model and available data in literature. The model is used to study the vibration of double-orthotropic nanoplates for three typical deformation modes. The influences of small scale coefficient, stiffness of the external and internal mediums and aspect ratio on the frequencies of the double-orthotropic nanoplates are also elucidated.     

Stress analysis of thick orthotropic cantilever tubes under transverse loading

In this work, a new high-order displacement-based method is proposed to investigate stresses and strains in thick arbitrary laminated orthotropic cantilever straight tubes under transverse loading. The most general displacement field of elasticity for an arbitrary thick laminated orthotropic straight tube is developed. A layer-wise method is employed to analytically determine the local displacement functions and stresses under transverse loading. The accuracy of the proposed method is subsequently verified by comparing the theoretical results with experimental data, finite-element method (FEM), and Lekhnitskii solution. The results show good agreement. In addition, high efficiency in terms of computational time is shown when the proposed method is used as compared with FEM. Finally, several numerical examples for stress and strain distributions in various thick cantilever composite straight tubes subjected to transverse loading are discussed.     

Modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam

This paper presents a detailed investigation on the modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam with hollow circular cross-section. To consider multiple crack effects, a cantilever beam including cracks is considered for six damage scenarios. Finite element models are constituted in ANSYS software for numerical solutions. The results are validated by experimental measurements. Ambient vibration tests are performed to extract the dynamic characteristics using Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI) methods. Calculated and measured natural frequencies and mode shapes for undamaged and damaged beams are compared with each other. Automated model updating is carried out using the modal sensitivity method based on Bayesian parameter estimation to minimize the differences for damage detection. In addition, modal assurance criterion (MAC) and coordinated modal assurance criterion (COMAC) factors are obtained from the mode shapes and two set of measurements to establish the correlation between the measured and calculated values for damage location identification.     

复合材料封闭变截面薄壁梁自由振动分析

摘要：基于拉格朗日方程建立了复合材料封闭变截面薄壁梁的自由振动微分方程,给出了两种刚度配置下的变矩形截面悬臂直梁的自由振动方程简化形式及其相应的迦辽金法求解的固有频率。基于大型通用有限元软件ANSYS,计算了薄壁变截面悬臂梁的固有频率,并且与迦辽金法的求解结果进行了对比。分析了复合材料的弹性耦合,铺层角度和截面变化对薄壁梁的自由振动的影响。     

悬臂梁结构裂纹参数识别的实验研究

实验研究了悬臂梁结构裂纹位置和深度参数的辨识,裂纹试件采用线切割加工而成,在靠近悬臂梁的自由端利用脉冲力锤激振,通过PXI测试系统获取测试信号;采用细化快速傅立叶变换提高瞬态响应信号分析的频率分辨率,从而获得比较准确的系统固有频率.测试分析获得系统前三阶固有频率,利用基于小波有限元的裂纹故障诊断算法,绘制裂纹等效刚度与位置曲线,三条曲线的交点预测出裂纹的位置和深度.实验结果验证了通过振动测试诊断裂纹参数的有效性和实用性.     

磁致伸缩层合悬臂梁式作动器的振动分析

为了分析磁致伸缩薄膜型层合悬臂梁式作动器的振动问题,应用磁致伸缩材料的非线性本构关系,由哈密尔顿原理导出了双层悬臂梁的振动微分方程。采用分离变量方法和常微分方程组的解析解法对磁致伸缩薄膜型层合悬臂梁的自由振动和受迫振动进行了理论分析。数值算例表明本文计算结果与有限元结果吻合较好,从而佐证了本文理论模型和求解方法的正确性,并讨论了几何参数、材料参数对层合梁固有频率的影响。还分析了在周期输入磁场激励下悬臂梁的挠度响应,且挠度响应呈现出倍频效应的动态特性。      

轴向运动变长度悬臂梁的振动控制

研究具有轴向运动速度、变长度悬臂梁的横向振动控制,提出了两种主动控制方案.采用Hamilton原理得到了端部带主动振子或跨内含有主动控制力的轴向运动悬臂梁的振动方程和边界条件.运用修正的伽辽金法得到了求解系统响应的近似方程.运用LQR法设计了主动振子和主动力的控制器,其中采用加权系数法选择Q,R矩阵.用数值计算仿真了两种控制方案的效果.结果表明采用主动振子或主动力都能够有效地控制轴向运动悬臂梁的横向振动.在相同的初始条件下,主动力控制的效果比主动振子要好,但主动振子的物理可实现性要优于主动力.     

Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method

The small scale effect on the vibration analysis of orthotropic single layered graphene sheets (SLGS) is studied. Elastic theory of the graphene sheets is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived for the graphene sheets. Differential quadrature method (DQM) is employed to solve the governing differential equations for various boundary conditions. Nonlocal theories are employed to bring out the small scale effect of the nonlocal parameter on the natural frequencies of the orthotropic graphene sheets. Further, effects of (i) nonlocal parameter, (ii) size of the graphene sheets, (iii) material properties and (iv) boundary conditions on nondimensional vibration frequencies are investigated.     

On the determination of natural frequencies of a cantilever beam in free bending vibration: a rigid multibody approach

A new approximate method for the determination of natural frequencies of a cantilever beam in free bending vibration by a rigid multibody system is proposed. Uniform Euler-Bernoulli cantilever beams with and without a lumped mass at the tips are considered. The modelling method consists of two steps. In the first step, the cantilever beam is replaced by lumped masses interconnected by massless flexible beams. In the second step, the massless flexible beams are replaced by massless rigid beams connected through revolute and prismatic joints with corresponding springs in them. Elastic properties of the massless flexible beams are modelled by the springs introduced. The method proposed is compared with similar ones in the literature.