CFRP索斜拉桥的索-浅拱模型及面内自由振动分析

本文针对斜拉桥的受力特点,基于索和浅拱的经典动力学运动方程,结合拉索与浅拱之间的耦合边界条件,并且考虑两者的几何非线性,建立了斜拉桥的多索-浅拱面内自由振动模型。将浅拱分段处理,结合索、浅拱连接处的动态平衡条件,应用分离变量法,建立多索-浅拱模型的面内自由振动理论。以双索浅拱模型为例,求解其特征值问题。同时,建立了相应的有限元模型,有限元计算结果与本文理论分析吻合良好。最后针对CFRP索斜拉桥的关键参数,基于本文的索-浅拱理论,对面内自由振动进一步研究。研究表明：浅拱的矢高在一定范围内变化,仅对某一阶频率产生影响,而其他各阶频率几乎没影响;CFRP拉索能显著改善索-浅拱组合结构的基本动力学特性。     

Stability analysis of a fractional viscoelastic plate strip in supersonic flow under axial loading

The stability of a viscoelastic plate strip, subjected to an axial load with the Kelvin–Voigt fractional order constitutive relationship is studied. Based on the classical plate theory, the structural formulation of the plate is obtained by using the Newton’s second law and the aerodynamic force due to the fluid flow is evaluated by piston theory. The Galerkin method is employed to discretize the equation of motion into a set of ordinary differential equations. To determine the stability margin of plate the obtained set of ordinary differential equations are solved using the Laplace transform method. The effects of variation of the governing parameters such as axial force, retardation time, fractional order and boundary conditions on the stability margin of fractional viscoelastic panel are investigated and finally some conclusions are outlined.     

Nonlinear vibrations of rotating thin circular cylindrical shell

Nonlinear vibrations of thin circular cylindrical shells are investigated in this paper. Based on Love thin shell theory, the governing partial differential equations of motion for the rotating circular cylindrical shell are formulated using Hamilton principle. Taking into account the clamped-free boundary conditions, the partial differential system is truncated by using the Galerkin method. Sequentially, the effects of temperature, geometric parameters, circumferential wave number, axial half wave number and rotating speed on the nature frequency of the rotating circular cylindrical shell are studied. The dynamic responses of the rotating circular cylindrical shell are also investigated in time domain and frequency domain. Then, the effects of nonlinearity, excitation and damping on frequency responses of steady solution are investigated.     

High-order nonlinear contact effects in the dynamic behavior of delaminated sandwich panels with a flexible core

The nonlinear dynamic behavior of delaminated sandwich panels with a flexible core is studied. A general analytical model that accounts for the real contact characteristics of the delaminated interface is developed. The analysis characterizes the influence of the contact phenomenon on the dynamic behavior of the sandwich structure and compares them to simplified models in which the contact conditions at the delaminated interface are assumed a priori. The dynamic model uses the high-order sandwich panel theory (HSAPT) that takes into account the flexibility of the core and considers the geometrically nonlinear effects of the face-sheets as well as the nonlinearity associated with the real contact characteristics of the delaminated surfaces. The dynamic governing equations, boundary conditions, and continuity requirements are derived through the Hamilton principle. The formulation yields a set of coupled nonlinear partial differential equations. The solution in time is based on the Newmark method of integration, and the solution in space uses the Multiple Shooting method combined with a Newton–Raphson iterative scheme. Numerical results that reveal the influence of the contact characteristics on the dynamic response of a sandwich panel are presented. In addition, the results are compared with finite element analysis, and with the simplified models. The study reveals the influence of the real contact phenomenon on the linear and nonlinear response and highlights its role in the dynamic response of the sandwich panel.     

激波主导流动下壁板的热气动弹性稳定性理论分析

针对激波主导流动下弹性壁板的热气动弹性稳定性分析问题,建立了基于当地活塞流理论的分析模型,并用数值仿真方法来验证其正确性. 首先基于Hamilton原理和Von-Karman大变形理论,建立壁板的热气动弹性运动方程,其中假设壁板受热后温度均匀分布,激波前后区域的气动力模型采用当地一阶活塞流理论;利用Galerkin方法将具有连续参数系统的偏微分颤振方程离散为有限个自由度的常微分方程;基于李雅普诺夫间接法将非线性颤振方程组在平衡位置处进行线化,再用Routh-Hurwits判据来判断线性系统的稳定性,从而来推论出非线性颤振系统的气动弹性稳定性. 在时域中采用龙格--库塔法对非线性颤振方程进行数值积分,得到壁板非线性颤振响应的时间历程,与理论分析结果进行对比. 研究结果表明,壁板受到斜激波冲击时,更容易发生颤振失稳,并且激波强度越大,极限环幅值和频率越大;激波主导流场中的壁板失稳边界不同于传统单纯超声速气流中壁板颤振的失稳边界;只有在斜激波前后不同的动压值都满足颤振稳定性边界的条件下,壁板才可能保持其气动弹性稳定性.      

蜂窝层芯夹层板结构振动与传声特性研究

蜂窝层芯夹层板应用于飞行器、高速列车等交通工具的主体及底板结构时需要考虑其振动及隔声特性. 针对声压激励下的四边简支蜂窝层芯夹层板结构,应用基于Reissner夹层板理论的结构振动方程建立了的声振耦合理论模型(声压以简支模态双级数的形式引入振动控制方程),结合流固耦合条件求解了声振耦合系统控制方程,应用有限元模拟对理论预测进行了验证. 基于理论模型的数值计算结果,系统研究了蜂窝层芯夹层板结构的振动特性和传声特性,刻画了层芯厚度、蜂窝壁厚、夹层板面内尺寸和声压入射角度等关键系统参数对夹层板振动和传声特性的影响,为此类结构的工程优化设计提供了必要的理论参考.     

弹性地基上转动FGM梁自由振动的DTM分析

基于Euler-Bernoulli梁理论,利用广义Hamilton原理推导得到弹性地基上转动功能梯度材料(FGM)梁横向自由振动的运动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,计算了弹性地基上转动FGM梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种边界条件下横向自由振动的无量纲固有频率,再将控制微分方程退化到无转动和地基时的FGM梁,计算其不同梯度指数时第一阶无量纲固有频率值,并和已有文献的FEM和Lagrange乘子法计算结果进行比较,数值完全吻合。计算结果表明,三种边界条件下FGM梁的无量纲固有频率随无量纲转速和无量纲弹性地基模量的增大而增大;在一定无量纲转速和无量纲弹性地基模量下,FGM梁的无量纲固有频率随着FGM梯度指数的增大而减小;但在夹紧-简支和夹紧-自由边界条件下,一阶无量纲固有频率几乎不变。     

Meshfree modeling of dynamic response of mechanical structures

Transient nature of the loading conditions applied to the structural components makes dynamic analysis one of the important components in the design-analysis cycle. Time-varying forces and accelerations can substantially change stress distributions and cause a premature failure of the mechanical structures. In addition, it is also important to determine dynamic response of the structural elements to the frequency of the applied loads. In this paper we describe the first application of the meshfree Solution Structure Method (SSM) to the structural dynamics problems. SSM is a meshfree method which enables construction of the solutions to the engineering problems that satisfy exactly all prescribed boundary conditions. This method is capable of using spatial meshes that do not conform to the shape of a geometric model. Instead of using the grid nodes to enforce boundary conditions, it employs distance fields to the geometric boundaries and combines them with the basis functions and prescribed boundary conditions at run time. This defines unprecedented geometric flexibility of the SSM as well as the complete automation of the solution procedure. In the proposed approach we will use SSM to enforce initial and boundary conditions, while transient behavior is enforced by time marching schemes used to solve systems of ordinary differential equations. In the paper we will explain the key points of the SSM as well as investigate the accuracy and convergence of the proposed approach by comparing our results with the ones obtained using traditional finite element analysis. Despite in this paper we are dealing with 2D in-plane vibrations, the proposed approach has a straightforward application to model vibrations of 3D structures.     

The Flow Analysis of Viscoelastic Fluid with Fractional Order Derivative in Horizontal Well

The fractional calculus approach is introduced into the seepage mechanics. A three-dimensional relaxation model of viscoelastic fluid is built. The models based on four boundary conditions of exact solution in Laplace space for some unsteady flows in an infinite reservoir is obtained by using the Laplace transform and Fourier sine and cosine integral transform. The pressure transient behavior of non-Newtonian viscoelastic fluid is studied by using Stehfest method of the numerical Laplace transform inversion and Gauss–Laguerre numerical integral formulae. The viscoelastic fluid is very sensitive to the order of the fractional derivative. The change rules of pressure are discussed when the parameters of the models change. The plots of type pressure curves are given, and the results can be provided to theoretical basis and well-test method for oil field.     

Dynamic response of composite sandwich plates subjected to time-dependent pressure pulses

The dynamic response of orthotropic sandwich composite plates impacted by time-dependent external blast pulses is studied by use of numerical techniques. The theory is based on classical sandwich plate theory including the large deformation effects, such as geometric non-linearities, in-plane stiffness and inertias, and shear deformation. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solutions are assumed for the space domain and substituted into the equations of motion. Then the Galerkin Method is used to obtain the non-linear differential equations in the time domain. The finite difference method is applied to solve the system of coupled non-linear equations. The results of theoretical analyses are obtained and compared with ANSYS results. Effects of the face sheet number, as well as those related to the ply-thickness, core thickness, geometrical non-linearities, and of the aspect ratio are investigated. Detailed analyses of the influence of different type of pressure pulses on dynamic response are carried out.     

Chaotic Analysis of Nonlinear Viscoelastic Panel Flutter in Supersonic Flow

In this paper chaotic behavior of nonlinear viscoelastic panels in asupersonic flow is investigated. The governing equations, based on vonKàarmàn's large deflection theory of isotropic flat plates, areconsidered with viscoelastic structural damping of Kelvin's modelincluded. Quasi-steady aerodynamic panel loadings are determined usingpiston theory. The effect of constant axial loading in the panel middlesurface and static pressure differential have also been included in thegoverning equation. The panel nonlinear partial differential equation istransformed into a set of nonlinear ordinary differential equationsthrough a Galerkin approach. The resulting system of equations is solvedthrough the fourth and fifth-order Runge–Kutta–Fehlberg (RKF-45)integration method. Static (divergence) and Hopf (flutter) bifurcationboundaries are presented for various levels of viscoelastic structuraldamping. Despite the deterministic nature of the system of equations,the dynamic panel response can become random-like. Chaotic analysis isperformed using several conventional criteria. Results are indicative ofthe important influence of structural damping on the domain of chaoticregion.     

TORSIONAL VIBRATIONS OF A RIGID CIRCULAR PLATE ON SATURATED STRATUM OVERLAYING BEDROCK

The torsional vibration of a rigid plate resting on saturated stratum overlaying bedrock has been analysed for the first time. The dynamic governing differential equations for saturated poroelastic medium are solved by employing the technology of Hankel transform. By taking into account the boundary conditions, the dual integral equations of torsional vibration of a rigid circular plate are established, which are further converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficients of the foundation on saturated stratum, the contact shear stress under the foundation and the angular amplitude of the foundation are evaluated. Numerical results indicate that, when the dimensionless height is bigger than 5, saturated stratum overlaying bedrock can be treated as saturated half space approximately. When the dimensionless frequency is low, the permeability of the soil must be taken into account. Furthermore, when the vibration frequency is a constant, the height of the saturated stratum has a slight effect on the dimensionless contact shear stress under the foundation.     

压电压磁圆柱壳的自由振动分析

本文基于三维弹性理论，结合状态空间理论和离散奇异卷积算法分析了压电压磁圆柱壳的自由振动问题．圆柱壳的厚度方向被作为状态空间理论的传递方向，同时应用离散奇异卷积算法对面内域进行离散．因此，初始的偏微分运动方程被转化为由一阶常微分方程构成的状态方程．离散奇异卷积算法的引入使得本方法可以处理不同边界条件，从而扩展了常规状态空间方法的应用范围．本文对数值算例的计算验证了此方法的有效性和精确度．     

初始纵横向荷载效应对薄板自振频率的影响分析The analysis for the effect of both initial in-plane and transverse loads on the natural frequency of plates

首先基于能量变分原理,给出了同时考虑初始纵向、横向荷载效应情况下板的应变能表达、动力平衡微分方程及单元刚度矩阵。再以动力平衡微分方程为基础,运用伽辽金法解得四种典型板同时考虑初始纵向、横向荷载效应的基频近似解,并运用瑞利法解得简支矩形板考虑初始纵向、横向荷载效应的前三阶频率近似解。然后相互验证了考虑初始纵向、横向荷载效应的板单元刚度矩阵和频率近似解的正确性,并进一步分析了初始纵向、横向荷载及相关因素对板自振频率的影响。结果表明,考虑初始纵向、横向荷载效应后,板的自振频率主要受初始纵向荷载、初始横向荷载、板的厚度及边界条件等因素的影响;初始纵向、横向荷载效应对板的基频影响明显于高阶频率;初始纵向、横向荷载对板的自振频率影响分别呈线性和抛物线规律。     

Transient dynamic responses of a cracked solid subjected to in-plane loadings

Transient dynamic responses of an elastic cracked solid subjected to in-plane surface loadings are investigated in this study. Two vertical cracks, a surface-breaking crack and a sub-surface crack, are considered. The frequency responses of the plane strain problem are calculated by the computational mechanics combining the finite element method with the boundary integral equation. The finite element method is used for the near-field enclosing the crack, while the boundary integral equation is applied for the far-field to satisfy the Sommerfeld radiation condition. The transient responses are then obtained using fast Fourier transform. Surface displacements, crack opening displacements, and dynamic stress intensity factors are presented to show the significant effects of the cracks. The interaction between the elastic waves and the cracks as well as the mode conversion phenomena can be observed and understood through the numerical simulations.     

热环境下壁板非线性颤振分析

基于一阶活塞气动力理论,采用Von Karman大变形应变-位移关系建立了无限展长壁板热环境下颤振方程,采用伽辽金方法对方程进行离散处理.取温度为分叉参数,研究壁板颤振时的分叉及混沌等复杂动力学特性.结果表明:温度载荷降低了系统的颤振临界动压,改变了颤振特性.在整个分岔参数范围内,系统呈现出较为复杂的变化,包括衰减振动、极限环振动、拟周期振动和混沌型振动.当考虑材料热效应时,系统的颤振动压将进一步降低,其响应也表现出更为丰富的非线性动态力学行为.     

Diffusion in a generalized thermoelastic solid in an infinite body with a cylindrical cavity

A dynamic problem of an infinite isotropic cylinder of radius r subjected to boundary conditions of the radial stress, temperature, or concentration of the diffusing substance is studied by using the equations of state of a elastothermodiffusive solid with one relaxation time and the Laplace transform technique. The distributions of the displacement, temperature, and concentration are displayed graphically and analytically.     

An alternative procedure for the non-linear vibration analysis of fluid-filled cylindrical shells

Using Donnell non-linear shallow shell equations in terms of the displacements and the potential flow theory, this work presents a qualitatively accurate low dimensional model to study the non-linear dynamic behavior and stability of a fluid-filled cylindrical shell under lateral pressure and axial loading. First, the reduced order model is derived taking into account the influence of the driven and companion modes. For this, a modal solution is obtained by a perturbation technique which satisfies exactly the in-plane equilibrium equations and all boundary, continuity, and symmetry conditions. Finally, the equation of motion in the transversal direction is discretized by the Galerkin method. The importance of each mode in the proposed modal expansion is studied using the proper orthogonal decomposition. The quality of the proposed model is corroborated by studying the convergence of frequency–amplitude relations, resonance curves, bifurcation diagrams, and time responses. The parametric analysis clarifies the influence of the lateral and axial loads on the non-linear vibrations and stability of the liquid-filled shell. Finally, the global response of the system is investigated in order to quantify the degree of safety of the shell in the presence of external perturbations through the use of bifurcation diagrams and basins of attraction. This allows one to evaluate the safety and dynamic integrity of the cylindrical shell in a dynamic environment.     

Vibration of fluid-conveying pipe with nonlinear supports at both ends

The axial fluid-induced vibration of pipes is very widespread in engineering applications. The nonlinear forced vibration of a viscoelastic fluid-conveying pipe with nonlinear supports at both ends is investigated. The multi-scale method combined with the modal revision method is formulated for the fluid-conveying pipe system with nonlinear boundary conditions. The governing equations and the nonlinear boundary conditions are rescaled simultaneously as linear inhomogeneous equations and linear inhomogeneous boundary conditions on different time-scales. The modal revision method is used to transform the linear inhomogeneous boundary problem into a linear homogeneous boundary problem. The differential quadrature element method (DQEM) is used to verify the approximate analytical results. The results show good agreement between these two methods. A detailed analysis of the boundary nonlinearity is also presented. The obtained results demonstrate that the boundary nonlinearities have a significant effect on the dynamic characteristics of the fluid-conveying pipe, and can lead to significant differences in the dynamic responses of the pipe system.

     

Non-linear global dynamics of an axially moving plate

In the present study, the geometrically non-linear dynamics of an axially moving plate is examined by constructing the bifurcation diagrams of Poincaré maps for the system in the sub and supercritical regimes. The von Kármán plate theory is employed to model the system by retaining in-plane displacements and inertia. The governing equations of motion of this gyroscopic system are obtained based on an energy method by means of the Lagrange equations which yields a set of second-order non-linear ordinary differential equations with coupled terms. A change of variables is employed to transform this set into a set of first-order non-linear ordinary differential equations. The resulting equations are solved using direct time integration, yielding time-varying generalized coordinates for the in-plane and out-of-plane motions. From these time histories, the bifurcation diagrams of Poincaré maps, phase-plane portraits, and Poincaré sections are constructed at points of interest in the parameter space for both the axial speed regimes.