随从力作用轴向运动叠层板的亚谐波共振

研究随从力作用轴向运动正交各向异性叠层板的亚谐波共振问题。基于给出的叠层板动能、势能、中面应变势能、轴向拉力引起的应变势能以及外力虚功,通过哈密顿原理导出叠层板的非线性振动方程。将非线性振动方程运用伽辽金积分法离散并进行无量纲化,推得关于时间变量的非线性振动微分方程组。应用多尺度法求解非线性方程组,分别得到前三阶模态稳态运动下1/3亚谐波共振幅频响应方程。最后通过算例分析,得到了振幅-调谐值特性变化曲线图、振幅-速度特性变化曲线图、振幅-激励幅值特性变化曲线图和激发共振双值解临界点曲线图。结果表明,共振幅值均是双值解,不同阶共振振幅有明显区别。     

复合材料层合板的非线性组合共振特性及分岔

考虑几何非线性项和阻尼的影响, 给出了四边简支的正交各向异性矩形层合板在两项横向简谐激励作用下的非线性振动微分方程, 利用伽辽金法导出了相应的达芬型非线性强迫振动方程。应用多尺度法对组合共振问题进行求解, 得到了系统在稳态运动下的幅频响应方程。基于李雅普诺夫稳定性理论, 得到了解的稳定性判定条件。通过数值算例, 分析了不同参数对系统组合共振及其分岔特性的影响。结果表明, 随着调谐参数、板厚度、阻尼系数以及激励力等参数的改变, 系统存在多幅值现象、滞后现象和跳跃现象, 出现不稳定解, 且在某些参数点处具有运动性态发生变化的分岔特性, 表现出较为复杂的动力学特性。      

线载荷作用下面内运动正交各向异性板的亚谐波共振

研究面内运动正交各向异性薄板在线载荷作用下的亚谐波共振问题。给出面内运动正交各向异性薄板的动能和势能表达式,并推得几何非线性下正交各向异性条形板的非线性振动方程。针对简支边界约束情况,考虑三阶模态并运用伽辽金积分法,推得关于时间变量的无量纲化达芬型非线性振动微分方程组。应用多尺度法对非线性系统的亚谐波共振问题进行求解,得到了稳态运动下关于不同阶模态的共振幅值响应方程。应用李雅普诺夫稳定性理论,对解的稳定性进行分析,得到了稳态解的稳定性判别式。通过数值算例,得到了振幅特性变化曲线图,分析了速度、线载荷、材料属性等参量对系统共振特性的影响,结果表明,系统呈现较为明显的非线性共振特征。     

四边固支功能梯度矩形板的主共振分析

针对四边固支约束的陶瓷-金属材料功能梯度矩形板,在给出非均匀材料的应力应变关系及非线性几何方程基础上,应用虚功原理导出了横向简谐激励力作用下功能梯度板的非线性振动偏微分方程。通过位移函数的设定,利用伽辽金积分法推得了相应的达芬型非线性振动方程。应用多尺度法对非线性系统的主共振问题进行解析求解,得到了稳态运动下的幅频响应方程。基于李雅普诺夫稳定性理论,得到了共振下解的稳定性判别条件。作为算例,给出了不同参数下功能梯度矩形板共振的幅频曲线图和动相平面相轨迹图,讨论了不同参数对系统非线性振动特性的影响     

横向磁场中旋变运动导电圆板的参强联合共振

研究变速旋转圆板的非线性磁弹性参强联合振动问题。给出旋转圆板在磁场中的磁弹性振动方程,应用伽辽金法离散变量,得到横向磁场中旋转圆板轴对称参强联合振动微分方程。运用多尺度法求解振动微分方程,分析久期项得到系统发生参强联合共振时的两种共振状态,并分别给出两种状态下系统的幅频响应方程。通过数值计算,给出圆板的协调参数、磁场、转速、激励力等参数变化对振动特性的影响,对比两种共振条件下的幅值-参数曲线,讨论不同参数变化对系统稳定性的影响。通过系统的全局分岔图,讨论分岔参数变化对系统动力学特性的影响。     

磁场中旋转运动圆板磁弹性超谐-组合共振

针对磁场中的旋转运动导电圆板,基于弹性理论和电磁原理,给出旋转圆板的动能、应变能和电磁力表达式。应用Hamilton原理,推导出几何非线性下圆板的磁弹性横向振动方程。针对横向磁场中双频外载作用下圆板的轴对称振动问题进行分析,利用辽金积分法得到夹支约束下旋转板的无量纲化振动微分方程;应用多尺度法求解非线性方程,得到超谐-组合联合共振下系统的幅频响应方程,并对稳态解的稳定性进行分析,得出稳定解的判定条件。由算例给出了旋转运动圆板共振幅值随频率参数、磁场及力幅的变化规律曲线图,分析了转速、磁场等参量对共振稳态解的影响;通过分析所绘制动相平面图上奇点附近相轨迹的变化趋向,进一步阐明了稳态解的多值性和稳定性。     

功能梯度矩形板的强非线性共振分析

针对陶瓷-金属功能梯度矩形板,在给出非均匀材料应力-应变关系及非线性几何方程的基础上,应用虚功原理导出了横向简谐激励力作用下功能梯度板的非线性振动偏微分方程。对于四边简支约束功能梯度矩形板,通过位移函数的设定,利用伽辽金积分法推得了关于时间自变量的达芬型强非线性振动方程。针对强非线性系统的主共振问题,应用改进的多尺度法进行解析求解,得到了稳态运动下的幅频响应方程。通过数值算例,给出了功能梯度矩形板共振下的幅频曲线图和相图,讨论了激励幅值及频率等参数对系统非线性振动特性的影响,并对改进多尺度法和经典多尺度法的结果进行了比较。     

横向磁场中机械载荷作用梁式薄板的非线性主共振

研究了磁场环境中受机械载荷作用梁式薄板的非线性主共振问题。在给出薄板的非线性电磁弹性耦合运动基本方程及电磁力表达式的基础上，得到了横向稳恒磁场和机械载荷共同作用下梁式薄板的振动方程。应用伽辽金积分法，并进行无量纲化处理，进一步导出了相应的非线性振动微分方程。采用平均法对主共振问题进行了求解，得到了稳态运动下的幅频响应方程。通过算例给出了几种情况下的幅频响应曲线图和时间历程图，分析了板厚和磁场对系统振动的影响。     

外激励力作用下的轴向运动梁非线性振动的联合共振

研究轴向运动梁在外激励力作用下非线性振动的联合共振问题.利用哈密顿原理建立横向振动的轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用Galerkin方法离散运动方程.采用IHB法进行非线性振动求解,分析在内共振条件且外激励作用下的联合共振问题,对周期解进行稳定性的判定.典型算例获得了不同外激励力振幅时系统非线性振动的复杂频幅响应曲线.     

载流导线间轴向运动导电梁的参数-主共振

研究轴向运动导电梁在载流导线产生的周期变化磁场中的参数-主共振问题。给出载流导线间导电梁处的磁感应强度、梁的应变能、动能及所受电磁力表达式,推得轴向运动导电梁的磁弹性横向振动微分方程。应用伽辽金积分法,得到导电梁无量纲化的非线性参数-主共振微分方程。利用多尺度法求解方程,得到系统关于非线性参数-主共振联合方程的近似解析解。通过计算,得到了轴向运动导电梁共振幅值随调谐参数变化的幅频图,共振系统的动相平面轨迹图,以及在变化调谐参数下的时程图和相图。结果表明,相关参数的改变对系统的共振幅值及稳定性影响明显。     

复合材料层合扁锥壳的冲击屈曲

研究了计及横向剪切的对称铺设正交异性复合材料层合扁锥壳在三角脉冲载荷作用下的非线性动力屈曲问题；通过在复合材料层合扁锥壳非线性稳定性的基本方程中增加横向转动惯量项并引入三角脉冲冲击力，得到了层合扁锥壳的冲击控制方程，采用Galerkin方法得到以顶点挠度表达的冲击响应方程，并用Runge—Kutta方法进行数值求解，应用B—R准则确定冲击屈曲的临界荷载；讨论了壳体几何参数、物理参数和边界条件对复合材料层合扁锥壳冲击屈曲的影响。     

Nonlinear dynamics of composite laminated cantilever rectangular plate subject to third-order piston aerodynamics

This paper presents the analysis of the nonlinear dynamics for a composite laminated cantilever rectangular plate subjected to the supersonic gas flows and the in-plane excitations. The aerodynamic pressure is modeled by using the third-order piston theory. Based on Reddy’s third-order plate theory and the von Kármán-type equation for the geometric nonlinearity, the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate under combined aerodynamic pressure and in-plane excitation are derived by using Hamilton’s principle. The Galerkin’s approach is used to transform the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate to a two-degree-of-freedom nonlinear system under combined external and parametric excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation of the non-automatic nonlinear system. The case of 1:2 internal resonance and primary parametric resonance is taken into account. A numerical method is utilized to study the bifurcations and chaotic dynamics of the composite laminated cantilever rectangular plate. The frequency–response curves, bifurcation diagram, phase portrait and frequency spectra are obtained to analyze the nonlinear dynamic behavior of the composite laminated cantilever rectangular plate, which includes the periodic and chaotic motions.     

基于Bessel和Meijer-G函数的楔形和锥形悬臂梁振动分析

基于欧拉-伯努利梁理论,利用Lagrange法建立了楔形和锥形截面梁在外激作用下的非线性微分方程.提出了一种基于Bessel函数和Meijer-G函数线性组合的无需迭代及近似截断的振型函数,且该振型函数不依赖于楔形和锥形变截面梁的弯曲振动的运动方程是否为标准的Bessel形式,该方法能快速求解线性基频和模态函数.随后将...     

受热复合材料层合板的非线性热振动——Part Ⅱ : 实验研究

对不同铺层方式和铺设角度的复合材料层合板的热振动进行实验研究, 实验结果给出了一些有益的结论, 并有力证明了作者提出的非线性高阶层合理论和非线性热振动分析有限元算法(Part Ι) [1]的正确性。     

两自由度轧机非线性扭振系统的振动特性及失稳研究

建立了含有非线性刚度和非线性摩擦阻尼的两自由度轧机非线性扭振动力学方程,研究了该非线性方程在电机加载力矩作用下的振动特性。首先通过坐标变换消除恒定加载力矩影响,得到轧机在稳态点附近的等效非线性扭振方程。其次采用平均法得到轧机受外部周期激励时的主共振幅频方程,并应用奇异性理论得到系统的转迁集以及系统出现各种分岔行为的条件。最后以某轧机实际参数为例,研究了不同非线性因素对轧机传动系统的幅频特性影响以及轧机出现失稳振动的条件,这为研究和抑制轧机传动系统的扭振提供了理论基础     

Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model

Nonlinear free vibration behavior of laminated composite curved panel under hygrothermal environment is investigated in this article. The mathematical model of the laminated panel is developed using Green–Lagrange-type geometrical nonlinearity in the framework of higher-order mid-plane kinematics. The corrugated composite properties are evaluated through the micromechanical model and all the nonlinear higher-order terms are included in the present model for the sake of generality. The equation of vibrated panel is obtained using Hamilton's principle and discretized with the help of the finite element steps. The solutions are computed numerically using the direct iterative method. The effect of parameters on the nonlinear vibration responses is examined thoroughly by solving the wide variety of numerical examples.     

Nonlinear vibration and postbuckling of unsymmetrically laminated imperfect shallow cylindrical panels with mixed boundary conditions resting on elastic foundation

This study is analytically concerned with the titled problem. The rotational stiffness variation is assumed to be identical along opposite edges. The panel is subjected to inplane edge forces but not tangential boundary forces. A unified approximate solution is formulated on the basis of the dynamic Marguerre-type equations. The edge condition for the rotational stiffness variation is satisfied by expansion of the edge bending moments and the varying rotational edgerestraint coefficients into generalized Fourier series. These moments are also replaced by an equivalent lateral pressure near these edges. The Galerkin procedure furnishes an equation for the time function which is solved by the method of perturbation. In the postbuckling case the equation reduces to a relation between the postbuckling load and the maximum deflection. Numerical results for nonlinear vibration and postbuckling behavior of orthotropic and unsymmetrically laminated angle-ply cylindrical panels are presented graphically for different parameters and compared with available data.     

Nonlinear free vibration of a shear deformable laminated composite annular elliptical plate

The nonlinear free vibration of a laminated composite annular elliptical plate with elliptically orthotropic plies is investigated. The effects of out-of-plane shear deformations, rotatory inertia and geometrical nonlinearity are taken into account. The problem is solved numerically using a new polynomially enriched sector elliptic p-element. The nonlinear equations of free motion are obtained using the harmonic balance method and solved iteratively by the linearized updated mode method. Results for the fundamental linear and nonlinear frequencies are obtained. Comparison is made with published results for a polar orthotropic annular plate and shows very good agreement. The minor semi-axis ratio, thickness ratio, moduli ratio, number of plies, layup sequence, and boundary conditions are shown to influence the hardening behavior.