预变形对非线性结构响应特征的影响

EFFECTS OF THE INITIAL DEFORMATION ON THE DYNAMIC RESPONSE OF LOCAL NONLINEAR SYSTEMS

含有大变形非线性约束的结构中,往往存在不同程度的预变形,导致系统静平衡点的改变.预变形的存在使得系统的动力学控制方程同时含有平方和立方非线性.实验结果表明,较小的激励力就能激发出含预变形非线性结构的软弹簧频响特征.以实验中的参数作仿真分析,结果表明,随着预变形的逐渐增大,非线性结构频响特征呈现从硬弹簧特性向软弹簧特性的转变,并求出了转变过程的临界变形.而随着外载荷幅值的增大,则是从软弹簧特性向硬弹簧特性转变.在不同预变形和激励力幅值下,还出现了超谐波共振和次谐波共振的现象.

There often exists initial deformation of various extents in a large-deformed structure with nonlinear components, which means the change of the system＇ s static equilibrium point. Moreover, under the initial de- formation, in the dynamic differential equations will appear the cubic stiffness non-linearity term and the asym- metric squared term. The experimental results show that a ＂softening＂ effect can be observed under the excitation of a quite small force. A numerical simulation was executed with the physical parameters in the experiment, which shows that the nonlinear frequency response changes from ＂hardening＂ to ＂softening＂ along with the incre- ment of the initial deformation, and the critical deformation was computed; while ＂softening＂ to ＂hardening＂ with the increment of the amplitude of the exciting force. Under various initial deformations and amplitudes of the exciting force, superharmonic resonances and subharmonic resonances were observed.