非线性弹性地基上矩形薄板受双频参数激励作用的非线性振动

应用弹性理论和Galerkin方法建立小挠度矩形薄板在非线性弹性地基上受两对均布纵向简谐激励作用的双模态非线性动力学方程。应用多尺度法求得系统满足双频主参数共振条件的一次近似解和对应的定常解,并进行了数值计算。分析了阻尼系数、地基系数、几何参数等对系统双频主参数共振的影响。     

轴向周期激励下圆柱形壳动力学高余维分岔、普适开折问题

本文讨论两端受到谐波激励的粘弹性圆柱形壳的非线性动力学行为，利用奇异性理论，研究[1]中分岔方程的普适开折问题，严格证明了它是一个高余维分岔问题。余维数为5（含有一个模分岔参数），给出了它的所有可能的普适开折形式。在分岔参数满足某些条件时得到该分岔问题的转迁集及分岔图，本文结果包含了[1]中相应结果，展示了一些新的动力学行为。     

Nonlinear dynamic modeling and periodic vibration of a cantilever beam subjected to axial movement of basement

Dynamic modeling of a cantilever beam under an axial movement of its basement is presented. The dynamic equation of motion for the cantilever beam is established by using Kane's equation first and then simplified through the Rayleigh-Ritz method. Compared with the older modeling method, which linearizes the generalized inertia forces and the generalized active forces, the present modeling takes the coupled cubic nonlinearities of geometrical and inertial types into consideration. The method of multiple scales is used to directly solve the nonlinear differential equations and to derive the nonlinear modulation equation for the principal parametric resonance. The results show that the nonlinear inertia terms produce a softening effect and play a significant role in the planar response of the second mode and the higher ones. On the other hand, the nonlinear geometric terms produce a hardening effect and dominate the planar response of the first mode. The validity of the present modeling is clarified through the comparisons of its coefficients with those experimentally verified in previous studies. Project supported by the Fundamental Fund of National Defense of China (No. 10172005).     

ELASTIC-PLASTIC DYNAMIC RESPONSE OF A CANTILEVER BEAM SUBJECTED TO OBLIQUE IMPACT AT ITS TIP

By employing large deformation governing equations expressed in the form of finite difference, the dynamic responses of an elastic, perfectly plastic cantilever subjected to an oblique impact at its tip was numerically studied. Through analyzing the instantaneous distribution of the yield function （φ = ｜M/Mo｜ ＋ （N/No）^2）, bending moment and axial force during the early stage of the response, the elastic-plastic deformation mechanism and the influence of axial component of an oblique impact on the dynamic response of a cantilever beam were discussed. The present analysis shows that the deformation mechanism of an elastic-plastic cantilever subjected to an oblique impact consists of four phases, i.e. ‘the expanding compressed plastic region＇ mode; the ‘generalized traveling plastic hinge＇ and ‘shrinking plastic region＇ mixed mode; the ‘stationary plastic hinge＇ mode and ‘elastic vibration＇ mode. Compared with the two-phase deformation mode obtained by using the rigid, perfectly plastic approach, the mode of shrinking plastic region that occurred instantly after the oblique impact and the mode of stationary hinge were both confirmed. The primary features of the deformation mechanism are captured by both analysis methods. It has also been found that the beam＇s deformation is mainly controlled by the axial component of the oblique impact in the early phase of the dynamic response, the deformation mechanism is obviously different from the case of a transverse impact. With further development of the response, the axial component attenuates rapidly and gives negligible contribution to the yielding of the beam cross-section. At the same time, the bending moments along the cantilever develop gradually and dominate the beam＇s deformation. The numerical results indicate that the mass, impact speed and oblique angle are the important factors that influence the elastic-plastic dynamic response of a cantilever beam.     

空间悬臂梁的动力学分析与迭代求解

本文从柔性体的真-伪混合坐标形式的拉格朗日方程出发,导出了空间双柔性连杆机械臂系统的真-伪混合坐标形式的动力学方程.由于采用伪坐标和矩阵运算,避免了繁冗的对方位参数的求导过程,使方程结构紧凑,便于建立递推形式,并且在选择不同参数描述整体刚性运动情况下,方程形式保持不变,因而具有一般性.     

黏弹性复合材料梁动力学实验建模的研究

以ABS树脂为基材, 填充1%~10%的金红石纳米二氧化钛制成纳米复合材料样本系列,搭建了参数激励非线性振动实验系统. 采用实验建模的方法, 基于非线性增量谐波平衡识别理论,建立了黏弹性复合材料屈曲梁的动力学控制方程. 通过数值模拟与实验结果的比较, 验证了理论模型和实验系统在定性定量分析上的一致性, 并且对一类不同配比成分的纳米复合材料也有很好的适用性.      

参强联合作用非线性结构动力学实验建模

搭建以L 型梁为实验研究对象的参强联合作用多自由度非线性振动实验系统, 将增量谐波平衡非线性识别理论运用到实验建模方法中, 建立了L 型梁的动力学控制方程. 通过对不同激励频率和不同响应情况下的数值模拟与实验数据的比较, 验证了基于增量谐波平衡识别的实验建模方法对多自由度参强联合作用非线性动力学结构的有效性, 以及动力学控制方程的普适性.     

压电自感知悬臂梁振动的主动控制研究

利用压电片的正逆压电效应,提出了一种基于分时结构的自感知作动器,将压电片作为传感器和作动器的功能在时间上进行分离,以实现用同一压电片在作动与传感之间的功能切换,并探讨了其用于主动控制的可行性.对一悬臂梁的振动主动控制研究表明该自感知作动器在实际上是可行的.     

含切口悬臂梁的大变形塑性冲击动力响应

本文分析了含切口的悬臂梁受飞射物撞击的刚塑性动力响应的完全解,推导了考虑几何大变形效应的“双铰模式”的动力学方程,给出了计算方法和计算结果,最后讨论了耗散能的分配和切口对梁最终变形的影响。     

累积线性法在细长柔性悬臂梁结构分析中的应用

为了研究几何大位移悬臂梁的结构响应,在充分利用线性有限元原理与流程的基础上,本文提出"累积线性法" 来对这一问题进行结构建模与求解策略的探讨,数值计算过程表明：该方法在常规有限元软件平台上十分容易实现,并与常规的"一次线性法" 和"非线性求解" 进行了数值对比. 针对本文问题,不仅从理论上指出"累积线性法" 的合理与可行和"一次线性法" 存在的结果不可信等问题;同时,数值仿真也表明前两种方法得到的结果也是不同的, 前者更接近非线性求解的结果. 最后,给出4 点结论.     

AN EFFICIENT DYNAMIC MODELING METHOD OF AN AXIALLY MOVING CANTILEVER BEAM AND FREQUENCY RESPONSE ANALYSIS

轴向移动梁动力学问题具有广泛的工程应用背景,如：机械手、机床主轴、武器身管等.计算轴向移动梁动力学响应是评估结构动力学性能以及最终指导结构设计的一个重要手段.采用Rayleigh-Ritz法、拉格朗日方程推导了轴向移动悬臂梁时变动力学方程.选取幂级数函数构造试函数对轴向移动系统动力问题进行求解.幂级数函数良好的积分与微分性能,使得推导容易以矩阵的形式快速进行,便于符号运算软件直接生成MATLAB程序.由于MATLAB基本数据单位为矩阵,符号软件生成的程序只需经过简单修改便可进行动力学计算.大大缩短了轴向移动梁从建模到动力学分析的时间,过程十分高效.通过四组算例,将本文方法计算得到的动力学响应与文献数据进行对比,对该方法准确性进行了验证,并给出了幂级数函数拟合阶数的选取原则.以此为基础,研究了轴向移动梁的频率响应特性.分为考虑重力与忽略重力两种情况,讨论了轴向振动幅度对其频率响应特性的影响.     

ELASTIC EFFECT IN DYNAMIC RESPONSE OF PLASTIC CANTILEVER BEAMS TO IMPACT

A lumped masses-springs model is proposed to analyze the dynamicresponse of an elastic-plastic cantilever beam resulting from impact. The numericalresults are in good agreement with those by finite-element approaches. The simplifiedmodel can catch the most essential features of elastic-plastic response of beams; inparticular, it demonstrates the effect of elastic deformation on the distribution ofbending moment and energy dissipation, and provides valuable quatitative results.