功能梯度材料圆板的非线性热振动及屈曲

采用弹性理论建立了功能梯度材料板的静力平衡方程,利用静力平衡方程确定了功能梯度材料板的中性面位置,在此基础上推导出了功能梯度材料板在均匀温度场中的非线性振动及屈曲微分方程组,求得了功能梯度材料圆板的非线性振动及屈曲的近似解,讨论分析了中性面位置、梯度指数、温度等因素对功能梯度材料圆板非线性振动及屈曲的影响.把该方法计算结果与有限元计算结果进行了比较,验证了该方法的计算结果是可靠的.算例分析表明,中性面位置对均匀温度场中功能梯度材料圆板的非线性振动及屈曲有一定影响.     

用Timoshenko修正理论研究有梯度界面层双材料梁的振动特性

采用Timoshenko梁修正理论研究了有梯度界面层双材料梁的振动问题,利用静力方程确定了有梯度界面层双材料梁的中性轴位置,在此基础上应用Timoshenko梁修正理论建立了有梯度界面层双材料梁的振动方程,求得其自振频率表达式及其在简谐荷载作用下强迫振动的解析解.讨论分析了梯度界面层高度等因素对有梯度界面层双材料梁的振动影响,并用有限元法验证了Timoshenko梁修正理论.通过实例计算,得到了梯度界面层高度等因素对有梯度界面层双材料梁振动特性有较大影响的结论.     

功能梯度薄壁圆柱壳的自由振动

研究了由功能梯度材料制成的薄壁圆柱壳的自由振动.采用幂律分布规律描述功能梯度材料沿厚度的梯度性质,根据Donnell壳体理论,导出了功能梯度材料薄壁圆柱壳线性振动的简化控制方程.基于此理论分析了功能梯度圆柱壳的自由振动特性,给出了两端简支功能梯度材料薄壁圆柱壳小挠度固有振动的频率公式.以简支圆柱壳作为算例,与前人结果及有限元法对比验证了该简化功能梯度薄壁圆柱壳理论的正确性,同时讨论了周向波数及梯度指数对其频率的影响.     

作大范围运动FGM矩形薄板的动力学特性研究

对作大范围运动功能梯度材料矩形薄板的刚柔耦合动力学问题进行了研究.以连续介质力学为基础,在柔性薄板面内变形中考虑了传统建模方法忽略的二次耦合变形量,采用假设模态法对薄板变形位移进行离散,运用拉格朗日方程推导了大范围运动功能梯度材料板的刚柔耦合动力学方程.对旋转运动下取不同功能梯度指数的悬臂功能梯度板的动力学行为进行仿真,比较了本文建立的一次近似耦合模型和传统不计耦合变形项的零次近似模型.结果表明,随着转速的提高,传统零次模型发散,而本文模型收敛,能够较好地描述系统动力学行为.利用本文建立的一次近似模型,研究了功能梯度指数对转动功能梯度板变形的影响,研究表明,随着功能梯度指数的增大,板的横向变形也增大.通过求解旋转FGM板在恒定转速下的固有频率,进一步分析了功能梯度板材料组分变化对板振动特性的影响.     

粘弹性板的非线性动力稳定性分析方法

将微分-积分型参数振动方程组转化成微分型,且基于增量谐波平衡法的一般应用途径,分析了受面内周期激励的粘弹性板的非线性动力稳定特性,揭示了主要动力不稳定区域的整体下移以及缩小和标准线性固体材料的粘性参数、板的振动频率之间的关系．同时给出了增量谐波平衡法直接应用于非线性微分-积分型参数振动方程的简化途径,并通过两种应用途径所得结果的对比,检验了这种简化途径的有效性．     

复合材料层合板非线性热振动分析

采用有限元方法研究复合材料层合板结构在线性温度场作用下非线性热振动特性．采用特征值屈曲分析方法,判断了结构在线性温度场作用下的临界屈曲分歧点,计算了结构的一阶弯曲固有频率,分析了铺层角度及铺层层数对结构临界屈曲温度分布和结构固有频率的影响,总结了其对复合材料层合板结构热振动特性影响的一般规律．这些结论对复合材料结构设计、抗热设计有一定的指导意义．     

基于无网格法考虑热效应及剪切效应FGM梁的动力学建模与仿真

将无网格点插值法和无网格径向基点插值法用于温度场中旋转柔性功能梯度材料梁的动力学分析.在考虑剪切效应的基础上,在梁本构关系中计及热应变,采用4种离散方法描述梁的变形场,运用第二类Lagrange方程,推导出大范围运动功能梯度材料梁的一次近似刚柔耦合动力学方程,研究不同温度变化下梁的动力学响应.通过动力学仿真得出以下结论：温度场对沿横向对称分布的功能梯度材料梁的横向变形影响较小,对纵向变形的影响较大,且在计算温度荷载作用下的梁末端变形时不应忽略轴向变形影响.     

三维实体转子系统热-结构耦合响应分析

以某型航空发动机高压转子系统为研究对象,基于不均匀分布稳态温度场,建立了某高压转子系统三维实体单元有限元模型以及稳态温度场下转子系统热-结构耦合振动方程,利用热-结构-动力学耦合理论,采用间接耦合法,通过稳态温度场分析和静力分析生成热应力,然后进行预应力模态分析,最后利用模态叠加法进行不平衡量和热弯曲耦合响应分析,实现热-结构-动力学耦合计算.通过稳态温度场对典型级盘稳态响应影响的分析以及不平衡量与热弯曲耦合稳态响应分析,发现耦合响应对转子系统各级盘的振动响应有较大影响.     

石墨烯树脂复合材料板1∶3内共振非线性动力学分析

石墨烯是一种新型的碳纳米材料,将石墨烯添加到不同基体中可达到增强基体力学性能,并优化结构的效果.本文主要研究了在悬臂边界条件下石墨烯复合材料板的非线性动力学行为,通过Halpin-Tsai模型计算了复合材料板的等效杨氏模量,运用一阶剪切板理论和Hamilton原理得到复合材料板的非线性动力学方程.通过模态缩聚,得到复合材料板横向位移的运动控制方程.应用Rayleigh-Ritz法计算出复合材料板的固有频率,发现第二阶与第四阶固有频率间存在1:3的关系.利用多尺度法研究了复合材料板在1:3内共振情况下的非线性振动响应,通过数值模拟分析了外激励对板结构非线性振动响应的影响.结果表明:横向外激励对复合材料板的非线性动力学行为影响较大,对实际工程具有一定的指导意义.     

复合边界条件下功能梯度板1:1内共振的周期与混沌运动

以两对边简支另两对边自由的功能梯度材料板为研究对象,首先建立了考虑材料物性参数与温度相关的、在热/机械载荷共同作用下的几何非线性动力学方程,采用渐进摄动法对系统在1:1内共振-主参数共振-1/2亚谐共振情况下的非线性动力学行为进行了摄动分析,得到系统的四自由度平均方程,并对平均方程进行数值计算,分析外激励对系统非线性动...     

Buckling and post-buckling of magneto-electro-thermo-elastic functionally graded porous nanobeams

The problem of the nonlinear thermal buckling and post-buckling of magneto-electro-thermo-elastic functionally graded porous nanobeams is analyzed based on Eringen’s nonlocal elasticity theory and by using a refined beam model. The beams with immovable clamped ends are exposed to the external electric voltages, magnetic potentials, a uniform transverse load and uniform temperature change. For the first time, the four types of porosity distribution in the nanobeam are considered and compared in complex electric–magnetic fields. Besides, the new formula of the effective material properties is proposed in this paper to simultaneously estimate the material distribution and porosity distribution in the thickness direction. The generalized variation principle is used to induce the governing equations, then the approximate analytical solution of the METE-FG nanobeams based on physical neutral surface is obtained by using a two-step perturbation technique. Finally, detailed parametric analyses are performed to get an insight into the effects of different physical parameters, including the slenderness ratio, small-scale parameter, volume fraction index, external electric voltages, magnetic potentials, porosity coefficient and different porosity distributions, for providing an effective way to improve post-buckling strength of porous beams.

     

Thermal buckling analysis of temperature-dependent FG-CNTRC quadrilateral plates

The main objective of the present study is to analyze the thermal buckling of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) quadrilateral plates. Functionally graded patterns are introduced for the distribution of the carbon nanotubes (CNTs) through the thickness direction of the plate. The effective material properties of nanocomposite plate reinforced by CNTs are considered to be temperature-dependent (TD) and estimated using the micromechanical model. By the use of minimum total potential energy principle and based on the first-order shear deformation theory of plates, the stability equations are obtained. In order to use the generalized differential quadrature (GDQ) method and solve the stability equations, the irregular domain of quadrilateral plate is transformed into regular computational domain employing the mapping technique. The efficiency and accuracy of the proposed approach are first validated. Then, a comprehensive parametric study is presented to examine the effects of model parameters on the thermal buckling of FG-CNTRC quadrilateral plates. The results indicate that considering temperature dependency of the material properties plays an important role in the stability of the FG-CNTRC quadrilateral plates subjected to thermal loading.     

非线性地基上正交异性矩形板的非线性热振动

研究了非线性地基上正交异性矩形板的非线性固有热振动.采用常规的L-P法分析非线性地基上正交异性矩形板的非线性热振动难以得到高精度的近似解,为此,先对该强非线性振动系统进行参数变换,将该强非线性振动系统转化为弱非线性振动系统.然后采用改进的L-P法进行求解,得到了强非线性振动系统的高精度近似解.此外,讨论了温度、地基特征参数、长宽比等因素对非线性地基上正交异性矩形板非线性热振动固有频率的影响,得到了非线性地基上正交异性矩形板热振动频率随温度下降、地基特征参数变大、长宽比变大而增大的结论.     

Vibrational investigation of the spinning bi-dimensional functionally graded (2-FGM) micro plate subjected to thermal load in thermal environment

Microsystem Technologies - This article presented a numerical method for discovering the free vibration of a spinning bi-dimensional functionally graded materials (FGM) micro circular plate exposed...     

Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell

In this research, thermal buckling and forced vibration characteristics of the imperfect composite cylindrical nanoshell reinforced with graphene nanoplatelets (GNP) in thermal environments are presented. Halpin–Tsai nanomechanical model is used to determine the material properties of each layer. The size-dependent effects of GNPRC nanoshell is analyzed using modified couple stress theory. For the first time, in the present study, porous functionally graded multilayer couple stress (FMCS) parameter which changes along the thickness is considered. The novelty of the current study is to consider the effects of porosity, GNPRC, FMCS and thermal environment on the resonance frequencies, thermal buckling and dynamic deflections of a nanoshell using FMCS parameter. The governing equations and boundary conditions are developed using Hamilton’s principle and solved by an analytical method. The results show that, porosity, GNP distribution pattern, modified couple stress parameter, length to radius ratio, mode number and the effect of thermal environment have an important role on the resonance frequencies, relative frequency change, thermal buckling, and dynamic deflections of the porous GNPRC cylindrical nanoshell using FMCS parameter. The results of current study can be useful in the field of materials science, micro-electro-mechanical systems and nano electromechanical systems such as microactuators and microsensors.

     

Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method

This paper presents the free vibration and buckling analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) laminated non-rectangular plates, i.e., quadrilateral and skew plates, using a four-nodded straight-sided transformation method. At first, the related equations of motion and buckling of quadrilateral plate have been given, and then, these equations are transformed from the irregular physical domain into a square computational domain using the geometric transformation formulation via discrete singular convolution (DSC). The discretization of these equations is obtained via two-different regularized kernel, i.e., regularized Shannon’s delta (RSD) and Lagrange-delta sequence (LDS) kernels in conjunctions with the discrete singular convolution numerical integration. Convergence and accuracy of the present DSC transformation are verified via existing literature results for different cases. Detailed numerical solutions are performed, and obtained parametric results are presented to show the effects of carbon nanotube (CNT) volume fraction, CNT distribution pattern, geometry of skew and quadrilateral plate, lamination layup, skew and corner angle, thickness-to-length ratio on the vibration, and buckling analyses of FG-CNTR-laminated composite non-rectangular plates with different boundary conditions. Some detailed results related to critical buckling and frequency of FG-CNTR non-rectangular plates have been reported which can serve as benchmark solutions for future investigations.

     

Asymmetric thermal buckling of temperature dependent annular FGM plates on a partial elastic foundation

In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on partial Winkler-type elastic foundation under uniform temperature elevation is investigated. Material properties of the plate are assumed to be temperature dependent. Each property of the plate is graded across the thickness direction using a power law function. First order shear deformation plate theory and von Kármán type of geometrical nonlinearity are used to obtain the equilibrium equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained considering the deflection-less conditions. Only plates which are clamped on both inner and outer edges are considered. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region and the second set which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalised differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved iteratively to obtain the critical conditions of the plate, the associated circumferential mode number and buckled shape of the plate. Benchmark results are given in tabular and graphical presentations dealing with critical buckling temperature and buckled shape of the plate. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and power law index of the graded plate. It is shown that, stiffness foundation, and radius of foundation may change the buckled shape of the plate in both circumferential and radial directions. Furthermore, as the stiffness of the foundation or radius of foundation increases, critical buckling temperature of the plate enhances.