薄板组合结构动力学特性解析研究

研究薄板组合结构的动力学特性。基于薄板自由振动问题的动态基本解,运用边界元法建立薄板在横向和面内方向的边界控制方程式,为了提高解析建模的精度和效率,根据耦合的思想推导出薄板组合结构的动力学方程,采用频率扫描的方法,准确、快速地求解出薄板组合结构的频率,并得到其相应的振型。数值算例表明本建模方法的可行性和良好的解析计算精度。     

筋板结构动力学特性边界元法解析研究

研究加筋薄板结构动力学特性多域合成的边界元建模解析方法。将矩形板沿梁划分为若干个区域,同时把梁的约束等效为作用在薄板区域上的反力,基于板、梁元件的动态基本解,由边界元法推导出带约束反力的梁和薄板的兰量控制方程,并依据耦合边界上的连续条件,运用多域合成的解析方法快速地建立筋板结构的动力学方程。数值算例表明,文中方法不但节省了计算量,而且具有良好的计算精度。     

螺栓松动边界下纤维增强复合薄板固有特性分析

通过人工弹簧刚度法对螺栓松动边界下纤维增强复合薄板的固有特性进行了分析。首先，为了研究螺栓松动边界的影响，人为地在复合薄板的约束端引入多组弹簧来模拟不同程度的螺栓松动边界，并建立了此类型边界下复合薄板的理论模型。然后，采用正交多项式法建立薄板自由振动的振型函数，并通过Ritz法对方程进行求解，计算此边界下薄板的固有频率和模态振型，给出具体的计算流程。最后，设计并组配了带有预埋压力传感器的螺栓松动边界下复合薄板的振动测试系统，准确测试了螺栓松动不同程度边界下对应的固有频率和模态振型，将实验结果与理论分析结果进行对比，发现两者的振型形态基本一致，其固有频率的误差在0.08%~7.54%之间，属于误差允许的范围，从而验证了所提出方法的可行性。     

Winkler地基上四边自由矩形薄板的亚谐共振与奇异性分析

研究Winkler地基上四边自由矩形薄板的亚谐共振问题.按照弹性力学理论建立Winkler地基上四边自由受简谐激励作用矩形薄板的动力学方程.利用Galerkin方法将其转化为非线性振动方程.应用非线性振动的多尺度法求得系统满足1/3次亚谐共振情况时的一次近似解,并进行数值计算.分析激励、阻尼等对系统响应曲线的影响.应用奇异性理论对1/3次亚谐共振幅频响应方程进行奇异性分析,得到选取不同分岔参数时开折参数平面的转迁集和分岔图.     

加筋薄板的自由振动分析

加筋薄板是航空领域最常见的结构之一,加强筋对薄板振动模态有显著影响。为改善蒙皮加筋薄板的动力学特性,旨在研究板筋连接单元的动力学建模方法以及加强筋对蒙皮薄板振动的影响机制。首先研究加筋薄板铆接、点焊和滚焊连接形式的有限元建模方法,建立铆接、点焊和滚焊薄板构件的有限元动力学模型;然后探讨单向与双向加筋薄板构件的自由振动模态;最后,分析板筋连接形式和加筋安装方向对薄板振动模态的影响机制。结果表明,加强筋的设计对薄板模态影响明显,滚焊加强筋对薄板构件的模态频率影响相对最大。     

任意边界约束下矩形薄板结构振动功率流特性

以矩形薄板结构为研究对象,采用改进傅里叶级数方法(Improved Fourier Series Method,IFSM)对任意边界约束下矩形薄板的振动功率流特性进行计算分析。将矩形薄板结构的横向振动位移容许函数描述为一种改进的三角级数形式,并通过引入正弦级数项来消除位移容许函数及其导数在边界上可能存在的不连续或跳跃现象。应用哈密尔顿原理从能量的角度推导出任意边界约束下矩形薄板结构系统的特征方程,并对矩形薄板结构的振动功率流特性进行了研究分析。通过与有限元法结果进行对比来验证计算方法的有效性。     

基于摄动方法的受损薄板模态分析

将结构的损伤用δ函数进行表达，建立损伤条件下薄板的自由振动方程。利用一阶摄动方法给出摄动项的一般表达式，并结合δ函数的性质，求出受损薄板模态参数的解析表达式。以一个四边简支的受损薄板为数值算例，计算损伤条件下其模态参数的变化。最后分析损伤情况对模态参数的影响，为利用动力学特性对板的损伤监控和检测提供理论依据。     

平板式钻井液叠层筛网自由振动分析

平板式钻井液叠层筛网在钻井液振动筛上得到广泛应用,研究振动筛的结构参数和安装参数对其自由振动的影响可为振动筛和筛网的设计及使用提供依据。提出将使用螺栓绷紧方法安装的筛网模型简化为弹性支承多跨单向连续矩形薄板模型,忽略筛网上的结构非线性特征,整张筛网看作由被底部橡胶支承条划分为k+1块的小矩形板组成。基于弹性矩形薄板振动理论,建立每小块矩形薄板的自由振动方程,提出各跨间薄板的连续性条件,利用传递矩阵方法推导出了整张筛网的传递方程,根据边界条件得到筛网自由振动的频率方程。对某一型号平板式叠层筛网的自由振动特征方程进行数值求解,得到不同螺栓预紧力、不同橡胶支撑条数目及刚度下筛网的固有频率,数据分析表明这三种参数均与筛网的固有频率呈正相关性,并且互相之间有一定影响。     

基于双参数模型的弹性地基薄板自由振动边界元解析

从双参数弹性地基薄板自由振动的微分方程式出发,通过建立双参数弹性地基薄板的动态基本解,运用边界元法(boundary element method,BEM)对双参数弹性地基板弯曲自由振动的动态特性进行解析研究,建立相应的边界积分方程式及动柔度方程式,采用频率扫描法求解其固有频率。算例研究表明,文中的方法计算简便、可行,具有良好的计算精度,同时该方法也适用于文克尔地基板动态特性解析。     

薄板在HASS试验振动载荷下的响应分析

为了从时域角度分析薄板结构在高加速应力筛选(HASS:high accelerated stress screening)试验振动载荷条件的响应,首先采用二次相位调制控制激励峭度的方法进行HASS试验随机振动载荷的仿真模拟,其次建立了薄板在振动载荷条件下的动力学有限元方程,并基于MATLAB对薄板在HASS试验随机振动载荷的响应进行了数值计算分析。得到薄板结构在HASS试验随机振动载荷条件下的位移响应和应力分布,确定薄板结构的薄弱位置,从而为装备结构失效分析及合理制定HASS试验剖面奠定理论基础和依据。     

Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers

In this paper, a free vibration analysis of moderately thick circular functionally graded (FG) plate integrated with two thin piezoelectric (PZT4) layers is presented based on Mindlin plate theory. The material properties of the FG core plate are assumed to be graded in the thickness direction, while the distribution of electric potential field along the thickness of piezoelectric layers is simulated by sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The analytical solution is validated by comparing the obtained resonant frequencies with those of an isotropic host plate. The emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. Good agreement between the results of this paper and those of the finite element analyses validated the presented approach.     

Free vibration analysis of arbitrary shaped thick plates by differential cubature method

In this paper, a new numerical solution technique, the differential cubature method, is applied to solve the free vibration problems of arbitrary shaped thick plates. The basic idea of the differential cubature method is to express a linear differential operation such as a continuous function or any order of partial derivative of a multivariable function, as a weighted linear sum of discrete function values chosen within the overall domain of a problem. By using the differential cubature procedure, the governing differential equations and boundary conditions are transformed into sets of linear homogeneous algebraic equations. This is an eigenvalue problem, of which the eigenvalues can be calculated numerically. The subspace iterative method is employed in search of the free vibration frequency parameters. Detailed formulations are presented, and the method is examined here for its suitability for solving the vibration problems of moderately thick plates governed by Mindlin shear deformation theory. The applicability, efficiency and simplicity of the method are demonstrated through solving some example plate vibration problems of different shapes. The numerical accuracy of the method is ascertained by comparing the vibration frequency solutions with those of existing literatures.     

On the nonlinear vibration of heated corrugated circular plates with shallow sinusoidal corrugations

The large amplitude free vibration of corrugated circular plates with shallow sinusoidal corrugations under uniformly static temperature changes is investigated. Based on the nonlinear bending theory of thin shallow shells, the governing equations for corrugated plates are established from Hamilton's principle. These partial differential equations are reduced to corresponding ordinary ones by elimination of the time variable with Kantorovich averaging method following an assumed harmonic time mode. Then by introducing the Green's function, the resulting dynamic compatible equation and corresponding boundary conditions are converted into equivalent integral equations. Taking the central maximum amplitude of the plate as the perturbation parameter, the perturbation-variation method is used to dynamic equilibrium equation with the aid of Computer Algebra Systems, Maple, from which, the third-order approximate characteristic relation of frequency vs. amplitude for nonlinear vibration of heated corrugated plates is obtained, and the frequency–amplitude characteristic curve is plotted for some specific values of temperature and geometrical parameters. It is found that the rise in temperature will decrease the frequency and vice versa. The nonlinear effect weakens when corrugations become deeper and dense. The present method can easily be expanded for the analysis of nonlinear vibration problem for other heated thin plates and shells.     

Vibration analysis of piezoelectric FGM sensors using an accurate method

In this study, free vibration analysis of moderately thick smart FG annular/circular plates with different boundary conditions is presented on the basis of the Mindlin plate theory. This structure comprised a host FG plate and two bonded piezoelectric layers. Piezoelectric layers are open circuit therefore this plate can be used as a sensor. According to power-law distribution of the volume fraction of the constituents, material properties vary continuously through the thickness of host plate while Poisson's ratio is set to be constant. Using Hamilton's principle and Maxwell electrostatic equation yields six complex coupled equations which are solved via an exact closed-form method. The accuracy of the frequencies is verified by the available literature, finite element method (FEM) and the Kirchhoff theory. The effects of plate parameters like boundary condition and gradient index are investigated and significance of coupling between in-plane and transverse displacements on the resonant frequency is proved.     

3-D vibration analysis of skew thick plates using Chebyshev–Ritz method

The free vibration characteristics of skew thick plates with arbitrary boundary conditions have been studied based on the three-dimensional, linear and small strain elasticity theory. The actual skew plate domain is mapped onto a basic cubic domain and the eigenvalue equation is then derived from the energy functional of the plate by using the Ritz method. A set of triplicate Chebyshev polynomial series multiplied by a boundary function chosen to satisfy the essential geometric boundary conditions of the plate is developed as the trial functions of the displacement components. The vibration modes are divided into antisymmetric and symmetric ones in the thickness direction and can be studied individually. The convergence and comparison studies show that rather accurate results can be obtained by using this approach. Parametric investigations on rhombic plates with fully clamped edges and completely free edges are performed in detail, with respect to the thickness-span ratio and skew angle. Some results known for the first time are reported, which may serve as the benchmark values for future numerical technique research.     

Vibration of circular Mindlin plates with concentric elastic ring supports

This paper studies the vibration behaviour of circular Mindlin plates with multiple concentric elastic ring supports. Utilizing the domain decomposition technique, a circular plate is divided into several annular segments and one core circular segment at the locations of the elastic ring supports. The governing differential equations and the solutions of these equations are presented for the annular and circular segments based on the Mindlin-plate theory. A homogenous equation system that governs the vibration of circular Mindlin plates with elastic ring supports is derived by imposing the essential and natural boundary and segment interface conditions. The first-known exact vibration frequencies for circular Mindlin plates with multiple concentric elastic ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented. The influence of the elastic ring support stiffness, locations, plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed.     

Free vibration analysis of orthotropic plates with variable thickness resting on non-uniform elastic foundation by element free Galerkin method

This study intends to investigate the vibration behavior of a thin square orthotropic plate resting on non-uniform elastic foundation and its thickness varying in one or two directions. By using the classical plate theory and employing element free Galerkin method, it is shown that the fundamental frequency coefficients obtained are in good agreement with available results in the literature. The effects of thickness variation, foundation parameter and boundary conditions on frequency are investigated. The results show that the method converges very fast regardless of parameters involved.     

Vibrations characteristics of joined cylindrical-spherical shell with elastic-support boundary conditions

Based on the Reissner-Naghdi’s thin shell theory, this paper concentrates on the free vibration of a joined cylindrical-spherical shell with elastic-support boundary conditions by a domain decomposition method. The joined shell is first separated from the elastic-support boundary and then subdivided into some cylindrical and spherical shell segments along the axis of revolution. The elastic-support boundary is regarded as a combination of distributed linear springs and can be treated as a special interface as well as the interface between two adjacent shell segments. Through the variational operation of the whole energy functional, the discretized equations of motion are derived by the expansions of the displacement field for each shell segment with Fourier series and Chebyshev orthogonal polynomials in the circumferential and longitudinal direction, respectively. To analyze the numerical convergence and precision of the present method, a number of case studies have been conducted and the solutions are compared with those derived by ANSYS and those presented in the previous literature to confirm the reliability and accuracy.