双参数地基系统中，在含自由边界或弹性边界处，其上板结构弯曲位移不为零，将导致基底压力向地基板外域传递和扩散，从而使板外域地基产生沉降。然而，现有的研究因边界条件的局限性忽略了板外域地基沉降，使得该类边界的计算结果产生较大的误差。针对双参数地基上矩形薄板的弯曲振动问题，基于改进Fourier级数法和Vlazov假定，提出了一种能在任意边界条件下考虑板外域地基沉降的振动分析方法。通过参数化分析，并与文献和有限元计算结果进行对比，验证了该方法具有较快的收敛速度和较高的计算精度；在此基础上，研究了不同自由边界数组合和弹性边界下地基沉降对振动特性的影响。

In a two-parameter foundation system, the bending deflection of the rectangle thin plate is not equal to zero at the free or elastic boundary, which will lead to the transfer and diffusion of the foundation pressure to other parts of the foundation beyond plate edges.Due to the limitation in the simplification of boundary conditions, in existing researches the settlement of the foundation outside the plate is usually ignored, which leads to a large error in the calculation results.Based on an improved Fourier series method and the Vlazov hypothesis, a vibration analysis method, bing able to consider the settlement of the foundation outside the plate under arbitrary boundary conditions, was proposed for studying the bending vibration of rectangular thin plates on the two-parameter foundation.Through parametric analysis and comparison with the results in literatures and by finite element analysis, it is verified that the method had a fast convergence speed and a high computational accuracy.On this basis, the effects of the combination of different number of free boundaries and the foundation settlement under elastic boundaries on vibration characteristics were studied.