带有边缘径向裂纹的固支圆板湿模态分析

基于Rayleigh-Ritz法,分析了置于无限大障板中、单面临水、带有边缘径向裂纹的固支圆板的固有频率和振型.引入角函数对裂纹的影响进行描述,采用薄板假设计算裂纹深度等于板半径的边缘径向裂纹圆板振动的最大动能和最大势能;在无旋、无粘、不可压和板微幅振动的假设条件下,采用速度势描述水体运动并获得了由位移基函数表达的附加动能,并通过Rayleigh-Ritz过程获得流固耦合振动系统的特征矩阵,进而求得湿模态对应的固有频率和振型.结果表明,固有频率降低率整体上随模态阶数的增大而减小,而干、湿模态振型的差别则整体上随模态阶数的增大而增大;水体对对称模态和反对称模态的影响有明显的区别.计算结果与ANSYS数值仿真的结果符合的较好.     

考虑非局部应变梯度效应的轴对称压电纳米圆板热-力-电耦合振动EI北大核心CSCD

基于非局部应变梯度理论和Mindlin板理论,研究了热‐力‐电多场耦合下轴对称压电纳米圆板的振动特性。通过Hamilton原理推导了非局部应变梯度本构框架内的运动方程,采用微分求积法数值求解了理论模型微分方程组,分析了压电纳米圆板的振动固有频率受内尺度参数与外场参数的影响。压电纳米圆板的固有频率随着非局部参数的增大而减小,随着应变梯度特征参数的增大而增大。当非局部参数小于应变梯度特征参数时,纳米圆板表现出刚度硬化行为;当非局部参数大于应变梯度特征参数时,表现出刚度软化行为。当非局部参数等于应变梯度特征参数时,纳米圆板的刚度退化为相应的经典连续介质理论结果。此外,固有频率随着径向压力和正电压的增大而减小,随着径向拉力和负电压的增大而增大,随着温差的增加而小幅减小。特别地,研究发现当径向载荷和电压增大到一定程度时,纳米圆板出现了振动失稳现象,并分析了非局部参数与应变梯度特征参数对失稳临界径向载荷及临界电压的影响。     

均布载荷作用下夹层圆板的载荷—频率特征关系

本文讨论了均布载荷作用下夹层圆板在非线性弯曲静平衡构形附近的微幅自由振动，并利用修正迭代法求解，得到了其固有频率—载荷特征关系     

嵌入形状记忆合金圆板在升温场内的自由振动

基于形状记忆合金Brinson一维热力学本构关系和圆板小振幅振动理论,研究了径向嵌入SMA丝的圆板在均匀升温场作用下的自由振动响应,获得了周边不可移简支和夹紧圆板的前三阶固有频率随温度变化的特征关系曲线。结果表明,形状记忆合金丝在从马氏体到奥氏体相变的过程中产生的回复力对板的固有频率具有显著增强作用。由此可见,通过嵌入SMA纤维丝和施加升温载荷可以主动而有效地调节圆板的固有频率。     

轴向运动黏弹性夹层板的多模态耦合横向振动

基于薄板小挠度理论和Kelvin-Voigt黏弹性本构方程, 建立了轴向运动黏弹性夹层板横向振动控制方程, 研究了其横向振动特性。采用一阶和二阶Galerkin截断得到夹层板横向振动的特征方程, 讨论了两种夹心层所占总厚度比率下轴向运动速度对其横向振动特性的影响。研究表明: 在未超过临界速度前, 无论一阶还是二阶截断, 在定性描述系统特征上二者相同, 但一阶截断不适合描述轴向运动速度超过临界速度的情形; 对四边简支黏弹性夹层板, 临界速度和发生耦合模态颤振的速度随着夹心层比率的减少逐渐增大。     

四边简支双曲率蜂窝夹层薄壳自由振动分析

基于Reddy三阶剪切理论,研究了四边简支双曲率蜂窝夹层薄壳的自由振动,以及结构参数对蜂窝夹层薄壳固有频率的影响.将由六边形胞元组成的蜂窝芯层等效为一正交异性层,其等效弹性参数由修正后的Gibson公式得到,应用Reddy三阶剪切理论和Hamilton变分原理推导出四边简支条件下双曲率蜂窝夹层薄壳的频率方程.具体算例表明,采用Reddy三阶剪切理论计算的固有频率精度较高;双曲率蜂窝夹层薄壳的曲率、厚度比及胞元角度对蜂窝夹层壳固有频率有不同程度的影响,其中蜂窝夹层薄壳的固有频率随曲率的增大而增大,随厚度比的增大呈波动变化,随胞元角度的增大而减小.     

弹性地基上受压矩形纳米板的自由振动与屈曲特性

基于Eringen非局部弹性理论和经典薄板理论,利用Hamilton原理推导Winkler-Pasternak弹性地基上面内受压正交各向异性矩形纳米板自由振动的控制微分方程并进行无量纲化。采用一种半解析方法—微分变换法(DTM)将无量纲控制微分方程及边界条件变换为等价的代数方程,得到含有无量纲固有频率和屈曲载荷的特征方程。数值给出了不同边界条件下无量纲地基刚度系数、压力强度、载荷参数、长宽比和纳米尺度对正交各向异性矩形纳米板无量纲固有频率的影响以及不同无量纲地基刚度系数、载荷参数和纳米尺度下的屈曲临界载荷值。结果表明:正交各向异性矩形纳米板的无量纲固有频率随无量纲地基刚度系数、载荷参数和长宽比的增大而增大,随纳米尺度的增大而趋向减小;屈曲临界载荷也随无量纲地基刚度系数的增大而增大,随纳米尺度的增大而减小。     

高温与脱粘对复合材料蜂窝板模态特性影响的试验

复合材料蜂窝板是目前航空航天领域中一类非常重要的结构,但此类结构在热环境下的模态特性研究鲜有公开报道。本文针对由碳纤维增强环氧树脂基复合材料层合板和Nomex蜂窝芯层复合而成的夹层板进行了不同温度下的模态试验,在加热过程中结构面板与芯层脱离,向外凸出。损伤发生前,结构固有频率随温度升高而下降,在识别出的前7阶模态中,弯曲振型的下降幅度较大,而扭转振型的降幅较小。对损伤后的结构再次进行常温模态试验,其模态特征发生显著变化,除了固有频率的变化外,模态阻尼比明显提高,而且其中两阶模态振型的顺序发生对调。此外,本文还对该损伤形式的成因进行了分析,所得结论对用于热环境的复合材料蜂窝结构设计具有一定的指导意义。     

四边固支对称蜂窝夹层板主共振非线性动力学计算

应用同伦分析方法(HAM)研究了四边固支对称蜂窝夹层板主共振情况下的非线性动力学特性。将铝基蜂窝芯层等效为一正交异性层, 等效弹性参数由修正后的Gibson方程得出。基于经典叠层板理论(CPT)和几何大变形理论建立了四边固支蜂窝夹层板受横向激振力作用下的受迫振动微分方程, 通过振型正交化将蜂窝夹层板受迫振动微分方程简化成双模态下的动力学控制方程, 得到了主共振情况下的平均方程, 研究了不同结构参数对动力学特性的影响。计算结果表明, 蜂窝夹层板的幅频特性曲线类似单自由度Duffing方程响应曲线, 随着结构参数的增大, 硬特性明显加大并且振幅的峰值明显减小, 所得结论可为蜂窝夹层板的设计和实际应用提供理论依据。     

静载荷作用下夹层圆板大幅度振动的时域特性分析

基于均布载荷作用下夹层圆板大幅度振动的基本方程和四种边界条件,将动挠度设为时间和空间函数的分离形式,利用空间模态假设和变分法,得到用挠度函数表示的应力和转角的表达式,再利用伽辽金法推导出时间模态的控制方程。在此基础上,讨论了初挠度以及夹层板剪切参数对系统振动特性的影响。     

对边简支负泊松比蜂窝夹层板的弯曲自由振动

负泊松比蜂窝夹层板作为一种特殊的复合材料结构,目前对其动态行为尚缺乏认识。应用Reddy剪切板理论分析了对边简支负泊松比蜂窝夹层板的弯曲振动。将内凹六边形胞元的蜂窝芯层等效为一正交异性层,芯层的等效弹性参数由修正后的Gibson公式得出。由具体算例可知经典叠层板理论和一阶剪切板理论不适合用于蜂窝夹层板的振动分析。应用Reddy剪切板理论研究了蜂窝夹层板板厚比、芯层板厚及胞元角度对弯曲振动频率的影响,并绘出相应的曲线图。结果表明:对于对边简支负泊松比蜂窝夹层板,当板厚比小于某一值时,固有频率参数随板厚比的增加而增加;但当板厚比大于该值时,固有频率参数随板厚比的增加呈现复杂的变化形式。本文得到的结果为蜂窝夹层板的设计和实际应用提供了理论依据和数值参考。      

Analytical layerwise free vibration analysis of circular/annular composite sandwich plates with auxetic cores

In the present research, free vibration of circular and annular sandwich plates with auxetic (negative Poisson’s ratio) cores and isotropic/orthotropic face sheets is investigated for different combinations of the boundary conditions. To ensure that the results are accurate and reliable, a global–local layerwise plate theory is employed instead of the traditional equivalent single-layer theories. The governing equations are derived based on Hamilton’s principle and solved using a Taylor transform whose center is located at the outer radius of the plate. Due to this hint, the resulting semi-analytical solution can be employed for both circular and annular sandwich plates. After investigation of vibration behavior of a single-layer annular auxetic plate, a comprehensive parametric study including evaluation of effects of the auxeticity for sandwich plates with isotropic and orthotropic face sheets, symmetric and asymmetric layups, different core to sheet thickness, radius to thickness, and inner to outer radius ratios, and various boundary conditions, is carried out. Results show that unlike the single-layer auxetic plates that exhibit a transition state, the auxeticity may considerably increase the natural frequencies and rigidities of the circular/annular sandwich plates, especially when the boundary conditions induce higher rigidity in the plate or when the fibers are along the radial direction. Accuracy of results of the employed layerwise theory and the proposed semi-analytical solution is verified by comparing the results with those of the three-dimensional theory of elasticity extracted from the ABAQUS software.     

Free vibration analysis of composite sandwich plates with different truss cores

The free vibration of composite truss core sandwich plates is investigated. The natural frequencies of the sandwich plate are calculated by using the classic laminated plate theory, the first-order shear deformation theory, Reddy's third-order shear deformation theory, and a Zig-Zag theory. The differences between the natural frequencies, obtained from the four theories, are compared. The influences of structural parameters on the natural frequencies and the ratios of natural frequency to equivalent density of the sandwich plates with pyramidal core, tetrahedral core, and 3D-Kagome core are studied with the aid of the Zig-Zag theory.     

Mode shapes and frequencies of radially symmetric vibrations of annular sandwich plates of variable thickness

An analysis and numerical results of radially symmetric vibrations of annular sandwich plates with core of linearly varying thickness are presented. The face sheets are treated as membranes of constant thickness, and the core is assumed to be solid as well as moderately thick. Due to linear thickness variation in the core, the face sheets take the shape of a truncated conical shell and because of this the face sheets membrane forces contribute to the bending and transverse shear of the core of the sandwich plate. Keeping this in view, the equations of motion for such a plate are developed by Hamilton’s energy principle. The frequency equations for three different combinations of boundary conditions, namely clamped at the inner edge and clamped or simply supported or free at the outer edge, are obtained by employing the differential quadrature method. The lowest three roots of these frequency equations have been reported as the frequencies for the first three modes of vibration. The effect of various plate parameters such as taper parameter, thickness of the core at the center, face thickness, and radii ratio on the natural frequencies has been analyzed. Three-dimensional mode shapes for a specified plate for all the three boundary conditions are illustrated. A comparison of results is presented.     

Frequency spectra of extensional vibration in isotropic shortcolumns and thick circular disks

A simple analytical method based on the equivalent elastic theory is presented for predicting the natural frequencies of a short column or a thick circular disk of axially symmetrical coupled vibration in which the longitudinal, the radial and the thickness extensional vibrations are considered. A critical value of thickness/diameter ratio is given that defines a boundary between a short column and a thick disk. Theoretical analyses show that the longitudinal and radial vibrations in infinite length rods, the radial and thickness extensional vibrations in thin plate are the special vibrating modes of a short column or a thick disk. The calculated frequencies for an isotropic column or a disk are in good agreement with the measured results     

纵振激励频率对圆盘弯曲振动特性的影响

利用有限元方法,计算并分析了具有一定大小的激励面积、频率不同的纵向夹心式换能器激励圆盘中心时,产生一阶弯曲振动的规律.结果表明:随着激励源频率的逐渐提高,圆盘弯曲振动的基频在不断增大,节圆半径也在增大,圆盘圆心处的位移振幅先增大后减小.实验测试与有限元计算结果基本吻合.该研究为此类复合纵弯振动系统的设计和实际应用提供了一定的参考.     

纸蜂窝夹层板主共振频率的影响因素

目的 研究芯层结构因素和静应力因素对纸蜂窝夹层板-质量系统主共振频率的影响。方法 采用正弦振动试验测试纸蜂窝夹层板-质量系统的振动传递特性,分析不同静应力作用下不同蜂窝芯的纸蜂窝夹层板-质量系统的主共振频率变化规律。结果 纸蜂窝夹层板-质量系统的主共振频率在150~350 Hz之间;蜂窝芯结构及芯层材料影响纸蜂窝夹层板的刚性,从而影响系统的主共振频率;载荷质量变化引起静应力的变化,也会影响系统的主共振频率。主共振频率均随蜂窝胞元边长、纸板厚度、芯纸定量及静应力的增大而降低。结论 可为纸蜂窝夹层板的振动传递特性研究提供基础,有助于不同材质蜂窝夹层板的优化设计。     

Vibration analysis of sandwich plates with lattice truss core

An effective methodology is developed to investigate the vibration of the sandwich plate with pyramidal lattice core. Equation of motion of lattice sandwich plate is established by Hamilton's principle. Displacement fields are expressed with a simple method, and the natural frequencies of the lattice sandwich plate are conveniently calculated. The correctness of the analytical method is verified by comparing the present results with published literatures. The effects of structural and material parameters on the vibration characteristics of lattice sandwich plate are analyzed. The present method will be useful for vibration analysis and design of lattice sandwich plates.     

Effects of local damage on vibration characteristics of composite pyramidal truss core sandwich structure

The effects of local damage on the natural frequencies and the corresponding vibration modes of composite pyramidal truss core sandwich structures are studied in the present paper. Hot press molding method is used to fabricate intact and damaged pyramidal truss core sandwich structures, and modal testing is carried out to obtain their natural frequencies. A FEM model is also constructed to investigate their vibration characteristics numerically. It is found that the calculated natural frequencies are in relatively good agreement with the measured results. By using the experimentally validated FEM model, a series of numerical analyses are conducted to further explore the effects of damage extent, damage location, damage form on the vibration characteristics of composite pyramidal truss core sandwich structures as well as the influence of boundary conditions. The conclusion derived from this study is expected to be useful for analyzing practical problems related to structural health monitoring of composite lattice sandwich structures.