应用同伦分析方法（HAM）研究了四边固支对称蜂窝夹层板主共振情况下的非线性动力学特性。将铝基蜂窝芯层等效为一正交异性层，等效弹性参数由修正后的Gibson方程得出。基于经典叠层板理论（CPT）和几何大变形理论建立了四边固支蜂窝夹层板受横向激振力作用下的受迫振动微分方程，通过振型正交化将蜂窝夹层板受迫振动微分方程简化成双模态下的动力学控制方程，得到了主共振情况下的平均方程，研究了不同结构参数对动力学特性的影响。计算结果表明，蜂窝夹层板的幅频特性曲线类似单自由度Dulling方程响应曲线，随着结构参数的增大，硬特性明显加大并且振幅的峰值明显减小，所得结论可为蜂窝夹层板的设计和实际应用提供理论依据。
Nonlinear dynamics characteristics of symmetric rectangular honeycomb sandwich panels with completed clamped supported boundaries in primary resonance case were investigated using the homotopy analysis method (HAM). The honeycomb core of aluminum matrix was equivalent to a thick layer of orthotropic material whose equivalent elastic constants were calculated by the modified Gibson's formula. Based on the classical laminated plate theory(CPT) and geometric large deformation theory, the forced vibration differential equations under transverse exciting force were derived. By means of vibration mode orthogonalization, the differential equations were simplified into dynamic control equations with dual-mode, and the average equations of primary resonance was obtained. Then the influences of different structural parameters on dynamic characteristics were studied. Numerical results show that the amplitude - frequency curves of honeycomb sandwich panels correspond to the response curves of Duffing equation with single degree. With the increase of the structural parameters, the obvious enhancement of the hard characteristic, and the remarkable decrease of the peak value of amplitude were observed. The conclusion can be applied to designing honeycomb sandwich panels and provide a theoretical basis for practical applications.
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