Nonlinear Vibration for the Moderate Thickness Rectangular Cracked Plates Including the Coupled Effect of Elastic Foundation
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摘要: 基于Reissner板理论和Hamilton变分原理，建立了双参数地基上具有表面横向贯穿裂纹的中厚矩形板的非线性运动控制方程．在周边自由的条件下,提出了一组满足问题全部边界条件和裂纹处连续条件的试函数．且利用Galerkin法和谐波平衡法对方程进行求解，分析了考虑地基耦合效应的中厚矩形裂纹板的非线性振动特性．数值计算中， 讨论了不同裂纹位置、 裂纹深度、 板的结构参数和地基物理参数对弹性地基上具裂纹的四边自由中厚矩形板的非线性幅频响应的影响．Abstract: Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, aset of trial functions satisfying all boundary conditions and crack's continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitue frequency response curves of the plate were discussed.
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Key words:
- moderate thickness rectangular plate /
- elastic foundation /
- crack /
- nonlinear vibration
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