功能梯度简支矩形板的非线性动力响应

研究了功能梯度简支矩形板在横向简谐激励作用下的非线性动力响应问题。采用幂律分布规律描述功能梯度材料的等效材料参数，基于Galerkin法建立了系统广义坐标的常微分控制方程。利用平均法得到了系统的幅频响应特性，分析了功能梯度矩形薄板的非线性主共振特性。数值算例验证了平均化方法的正确性，揭示了功能梯度平板主共振响应中的多值性和跳跃现象；同时分析发现初始条件会改变功能梯度平板主共振的响应幅值。最后讨论了功能梯度材料的梯度指数对系统幅值响应的影响。

NONLINEAR DYNAMIC RESPONSE OF SIMPLY-SUPPORTED FUNCTIONALLY GRADED RECTANGULAR PLATES

The nonlinear dynamic response of simply-supported functionally graded rectangular plates subjected to a transverse harmonic excitation is studied. Equivalent material properties of functionally graded material are described as power-law distribution functions. The ordinary differential governing equation for generalized coordinate of system is deduced based on the Galerkin method. Using averaging method, the amplitude-frequency response of system is obtained, and the nonlinear principal resonance of functionally graded rectangular thin plates is analyzed. Numerical example validates the averaging method; the multivaluedness and jump phenomenon in principal resonance response of functionally graded plates are revealed. Meanwhile, it is found that the initial conditions may change the response amplitude of principal resonance of functionally graded plates. Finally, the effect of power-law exponent of functionally graded material on the response amplitude of system is discussed.