An improve Fourier series method was employed to establish the vibration model of a skew plate and to analyze the vibration characteristics of the plate under arbitrary elastic boundary conditions.The vibration displacements were expressed as the linear combination of a two-dimensional Fourier cosine series and suppelmentary series.The supplementary series were used to solve the discontinuity problems encountered for displacement partial differentials along the boundaries.So this method could be applied for arbitrary elastic boundary conditions.Based on Hamilton's principle, the matrix form for the governing vibration equations of the plate was derived,the natural frequencies and modal shapes of the plate were obtained through solving the eigen-problem of the matrix equation.Finally,the numerical simulations were performed,the natural vibration frequencies of the plate with different boundary conditions were solved.The results were compared with those in literatures and those of FEA,the correctness of the ;proposed method was verified.%平行四边形活塞声源模拟舰船声场线谱特征时，为了实现其具有较高的效率，应保证声源膜板结构的固有频率与线谱频率相等，因此，分析膜板结构的振动特性具有重要意义。采用改进 Fourier 级数的方法建立平行四边形膜板结构的振动模型，通过在膜板结构的四边上布置弹簧来模拟任意弹性边界条件，结构的振动位移函数表示为标准的二维 Fourier 余弦级数和辅助级数的线性组合。通过辅助级数的引入，解决了位移函数的导数在边界潜在的不连续的问题，从而使此法适用于任意的弹性边界条件。结合 Hamilton 原理，推导出平行四边形板结构振动方程的矩阵表达示，板结构的振动参数可通过求解矩阵值得到。最后进行了数值仿真，求解出结构在不同参数下的线谱频率，并与文献以及有限元结果进行对比，验证了该方法的精确性。
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