An efficient method for simulating the dynamic behavior of periodic structures with piecewise linearity
An efficient method for simulating the dynamic behavior of periodic structures with piecewise linearity
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一种分段线性模拟周期性结构动态行为的有效方法
DOI：
10.1007/s11071-018-4475-8
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发表时间：
2018-10
影响因子：
5.6
通讯作者：
Wanxie Zhong
中科院分区：
文献类型：
--
作者：
Dongdong He;Qiang Gao;Wanxie Zhong
提出了一种基于参数变分原理(PVP)的数值模拟周期结构动力行为的有效方法。提出了基于PVP的间隙激励弹簧的计算公式，该公式能够准确地确定间隙激励弹簧的状态。基于系统的周期性和精细积分法，提出了一种求解系统动力响应的有效的数值时间积分方法。该方法只需计算系统的一个单胞的矩阵指数，大大提高了计算效率。给出了三自由度分段线性系统在简谐激励下的动力响应，验证了该方法的有效性。分段线性动力系统可以表现出非常复杂的振动行为，如稳定周期运动、多周期运动、准周期运动和混沌运动，这些行为可以用分叉理论成功地预测出来。此外，该方法还可以有效地计算周期分段线性系统在简谐激励下的动力响应。
An efficient method based on the parametric variational principle (PVP) is proposed for simulating the dynamic behavior of periodic structures with large number of piecewise linearity. The formulation for the gap-activated springs is proposed based on PVP, which can accurately determine the states of the gap-activated springs. Based on the periodicity of the system and the precise integration method, an efficient numerical time-integration method is developed to obtain the dynamic responses of the system. For this method, the matrix exponential of only one unit cell of the system is computed, which greatly improves the computational efficiency. Dynamic responses of a 3 degrees of freedom (DOF) piecewise linear system under harmonic excitations are given to demonstrate the validation of the proposed method. The piecewise linear dynamic system can exhibit very complex vibrational behavior, such as stable periodic motion, multi-periodic motion, quasi-periodic motion and chaotic motion, which can be successfully predicted by using bifurcation theory. Moreover, it is demonstrated that the proposed method can be used to efficiently determine dynamic responses of a periodic piecewise linear system with large number of DOFs and large number of gap-activated springs under harmonic excitations.
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影响因子：
5.6
作者：
T. Kalmár-Nagy;R. Csikja;T. Elgohary
通讯作者：
T. Kalmár-Nagy;R. Csikja;T. Elgohary
影响因子：
1.4
作者：
Dongyan Chen;Yonglong Yu;Long Xu;Xiaohui Liu
通讯作者：
Dongyan Chen;Yonglong Yu;Long Xu;Xiaohui Liu
影响因子：
1.9
作者：
C. Hommes;H. E. Nusse;A. Simonovits
通讯作者：
C. Hommes;H. E. Nusse;A. Simonovits
影响因子：
4.7
作者：
Haiyan Hu
通讯作者：
Haiyan Hu
DOI：
10.23919/acc.1988.4790000
发表时间：
1988-06
期刊：
1988 American Control Conference
影响因子：
--
作者：
B. Heck;A. Haddad
通讯作者：
B. Heck;A. Haddad