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圆柱型正交各向异性圆板的自由振动分析

DOI: 10.3969/j.issn.1006-7043.201404082

Keywords: 正交各向异性, 圆板, 改进的Fourier-Bessel级数, 自由振动, 复杂边界条件

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Abstract:

在Kirchhoff薄板理论和复合材料理论的基础上,利用改进的Fourier-Bessel级数方法分析了圆柱型正交各向异性圆板的自由振动。通过将板的振动位移函数表示为标准的Fourier-Bessel级数和辅助多项式的组合,有效地提高了位移函数在边界处的连续性;同时边界条件采用均匀分布的线性位移弹簧和扭转约束弹簧来模拟。基于Rayleigh-Ritz方法建立了圆柱型正交各向异性圆板自由振动的矩阵方程,通过计算矩阵特征值问题,获得了圆板自由振动的频率和模态振型。最后进行了复杂边界条件下圆板结构的数值算例,计算结果表明,文中的计算结果与文献、有限元结果相一致。

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