...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Mechanical systems and signal processing >A novel modal superposition method with response dependent nonlinear modes for periodic vibration analysis of large MDOF nonlinear systems
【24h】

A novel modal superposition method with response dependent nonlinear modes for periodic vibration analysis of large MDOF nonlinear systems

机译：响应依赖非线性模式的新型模态叠加方法用于大型MDOF非线性系统的周期振动分析

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Design of complex mechanical structures requires to predict nonlinearities that affect the dynamic behavior considerably. However, finding the forced response of nonlinear structures is computationally expensive, especially for large ordered realistic finite element models. In this paper, a novel approach is proposed to reduce computational time significantly utilizing Response Dependent Nonlinear Mode (RDNM) concept in determining the steady state periodic response of nonlinear structures. The method is applicable to all type of nonlinearities. It is based on the use of RDNM which is defined as a varying modal vector with changing vibration amplitude. At steady-state, due to periodic motion, it is possible to define equivalent stiffness due to nonlinear elements as a function of response level which enables one to create new linear systems at each response level by modifying original stiffness matrix of the underlying linear system. In this method, a new linear system is defined at each response level corresponding to each excitation frequency step, and modal information of these equivalent linear systems is used to construct RDNMs which forms a very efficient basis for the nonlinear response space. The response of the nonlinear system is then written in terms of these RDNMs instead of the modes of the underlying linear system. This reduces the number of modes that should be retained in modal superposition method for accurate representation of solution of the nonlinear system, which decreases the number of nonlinear equations, hence the computational effort, significantly. Dual Modal Space method is employed to decrease the computational effort in the calculation of RDNMs for realistic finite element models, i.e. for large MDOF systems. In the solution, nonlinear differential equations of motion are converted into a set of nonlinear algebraic equations by using Describing Function Method, and the numerical solution is obtained by using Newton's method with arc-length continuation. The method is demonstrated on two different systems. Accuracy and computational time comparisons are performed by applying different case studies which include several different nonlinear elements such as gap, cubic spring and dry friction. Results show that the proposed method is very effective in determining periodic response of nonlinear structures accurately reducing the computational time considerably compared to classical modal superposition method that uses the modes of the underlying linear system. It is also observed that the variation of natural frequency with energy level in a nonlinear system can be approximately obtained by using RDNM concept.
机译：复杂机械结构的设计需要预测会严重影响动态行为的非线性。但是，找到非线性结构的强制响应在计算上是昂贵的，特别是对于大型有序逼真的有限元模型。在本文中，提出了一种新的方法来减少计算时间，该方法利用响应依赖非线性模式（RDNM）概念来确定非线性结构的稳态周期响应。该方法适用于所有类型的非线性。它基于RDNM的使用，RDNM被定义为具有变化的振动幅度的变化的模态矢量。在稳态下，由于周期性运动，可以将非线性元素引起的等效刚度定义为响应级别的函数，这使得人们可以通过修改基础线性系统的原始刚度矩阵在每个响应级别创建新的线性系统。在这种方法中，在与每个激励频率阶跃相对应的每个响应级别上定义了一个新的线性系统，并且使用这些等效线性系统的模态信息来构造RDNM，这为非线性响应空间奠定了非常有效的基础。然后根据这些RDNM而不是基础线性系统的模式来写非线性系统的响应。这减少了模态叠加方法中为精确表示非线性系统的解而应保留的模数，从而减少了非线性方程的数量，从而显着降低了计算量。对于实际的有限元模型，即大型MDOF系统，采用双模态空间方法来减少RDNM的计算工作量。在解决方案中，使用描述函数法将运动的非线性微分方程转换为一组非线性代数方程，并通过使用具有弧长连续性的牛顿法获得数值解。在两个不同的系统上演示了该方法。通过应用不同的案例研究来进行精度和计算时间的比较，其中包括几种不同的非线性元素，例如间隙，立方弹簧和干摩擦。结果表明，与使用基础线性系统模式的经典模态叠加方法相比，该方法在确定非线性结构的周期响应方面非常有效，可显着减少计算时间。还可以观察到，通过使用RDNM概念，非线性系统中固有频率随能级的变化可以近似地获得。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号