基于时频域交替法的迟滞非线性振动系统的稳态响应分析

连接界面的黏滑、摩擦行为不仅是引起结构刚度和阻尼非线性的主要原因,而且是结构无源阻尼的主要来源.Iwan模型能够较好地复现连接界面的黏滑、摩擦行为.本文采用时频域交替法(Alternating Frequency/Time Domain Method,AFT)研究含Iwan非线性模型的单自由度振子系统的稳态响应.时频域交替法具有频域法求解线性系统响应的高效性和时域法判断非线性力的便捷性特点,采用离散傅里叶变换和傅里叶逆变换,在频域和时域内分别求解系统响应和对应的非线性恢复力,再反复迭代计算系统的稳态响应.将时频域交替法计算结果和中心差分法计算的结果进行对比,并研究激励幅值对系统非线性特征的影响.结果表明,时频域交替法计算的结果与中心差分计算的结果具有较好的一致性,且求解效率较高,计算耗时减少50%;随着激励幅值的增加,系统的能量耗散增加,刚度降低,固有频率降低.

Alternating time/frequency domain method for calculating the steady-state response of hysteresis nonlinear vibration systems

Stick slip and friction of the joint interface pay a significant role not only on structure nonlinear stiffness and damping but also on structure passive damping. Iwan model provides a preferable recurrence of the stick slip and friction characteristics of the joint interface. The alternating frequency/time domain method (AFT) is used to study the steady state response of single degree of freedom oscillator system containing Iwan nonlinear model in this paper. This method takes both advantages of the effectiveness of calculating response for linear system by frequency domain method and the ease of evaluating nonlinear force by time domain method. The discrete Fourier transform alternating from the time domain to the frequency domain is applied through iterating to obtain the steady state response of the system. The result of AFT is compared with that from the central difference method, and the influence of excitation amplitude on nonlinear characteristic is also examined in this paper. The results show that the steady state response by AFT method agrees well with that of the central difference method. Moreover, the AFT method performs better computational efficiency, as the time consuming is reduced by 50 percent. In a whole, it is found that the application of higher excitation amplitude results in the increase of the system energy dissipation and the reduces stiffness and natural frequency.