连接局部迟滞非线性的时频域动力学降阶方法  

Dynamic reduction analysis for local hysteresis nonlinearity of joint interfaces in time and frequency domains

作　　者：王东 张周锁[1] WANG Dong;ZHANG Zhou-suo(School of Mechanical Engineering,Xi'an Jiaotong University,Xi'an 710049,China;Institute of Systems Engineering,China Academy of Engineering Physics,Mianyang 621999,China)

机构地区：[1]西安交通大学机械工程学院,陕西西安710049 [2]中国工程物理研究院总体工程研究所,四川绵阳621999

出　　处：《振动工程学报》2021年第3期559-566,共8页Journal of Vibration Engineering

摘　　要：针对连接结构时域和频域的非线性振动问题,提出一种基于局部非线性转化的动力学降阶方法。采用Newmark法和多谐波平衡法分别将时域和频域的非线性动力学方程转化为非线性代数方程组,将整体结构的非线性动力学响应降阶到仅与连接非线性相关的自由度上进行求解,通过减小迭代过程中Jacobian矩阵的维数来提高计算效率。采用Iwan模型描述连接界面的局部迟滞非线性,利用三自由度质量弹簧振子和连接梁结构研究非线性动力学分析方法的计算精度和效率。结果表明,本文建立的降阶方法预测的非线性动力学响应与现有的未降价方法吻合较好,提出的非线性动力学降阶方法能够有效地减少迭代过程的计算耗费,提高计算效率,时域方法约提高30%,频域方法提高近70倍。The local nonlinearity dynamic transformation reduction is developed to obtain the nonlinear dynamic responses of jointed structures in the time and frequency domains.The Newmark’s integration and multi-harmonic balance methods are used to convert the nonlinear dynamic differential equilibrium into nonlinear algebraic ones in the time and frequency domains,respectively.The dynamic responses only related to the degree-of-freedoms(DOFs)of nonlinear joints are defined as the iteration vector to decrease the dimensions of nonlinear algebraic equations.The dimensions of Jacobian matrix are consequently reduced to improve the computational efficiency.The Iwan model is used to describe the local hysteresis nonlinearity of joint interfaces,and two examples of 3 DOFs mass-spring-stiffness oscillator and lap-type jointed beam system are simulated to contrast the prediction precision and computational efficiency.The comparison result of nonlinear dynamic responses shows a good agreement with the existed methods.The proposed nonlinear dynamic reduction method reduces the computation cost of iteration process and indicates a higher computational efficiency with about 30%speedup in the time domain and 70 times speedup in the frequency domain.

关 键 词：迟滞非线性 连接界面 动力学降阶 多谐波平衡法 NEWMARK法 

分 类 号：O322[理学—一般力学与力学基础]