Vibration analysis of the classical elastic structures is not only essential for the study of vibration reduction by predicting the dynamic behavior, but also important to ensure a reliable, safe, and lasting structural performance through the proper design procedure. In this paper, the influence of boundary conditions on the free and forced three-dimensional vibration analysis of thick rectangular plates has been performed using the improved Fourier series method. For the elastically restrained thick rectangular plate, the three-dimensional improved Fourier series displacement forms are used to model the vibration field. The energy formula is employed to describe the three-dimensional dynamics of the plate. All the unknown Fourier series coefficients are then solved by the Rayleigh-Ritz method. In order to validate the proposed model, several numerical examples are provided and compared against the results from the literature and Finite Element Analysis (FEA). In addition, the effects of the boundary restraining spring stiffness and the thickness ratios of thick rectangular plates are analyzed under elastically restrained boundary conditions to develop an in-depth understanding of the three-dimensional vibration characteristics of thick rectangular plates.

经典弹性结构的振动分析不仅对于通过预测动态行为来研究减振至关重要，而且对于通过正确的设计程序确保可靠、安全和持久的结构性能也很重要。本文利用改进的傅里叶级数法进行了边界条件对厚矩形板自由振动和受迫三维振动的影响分析。对于弹性约束厚矩形板，采用三维改进傅里叶级数位移形式对振动场进行建模。能量公式用于描述板的三维动力学。然后通过瑞利-里兹方法求解所有未知的傅立叶级数系数​​。为了验证所提出的模型，提供了几个数值示例，并将其与文献和有限元分析 (FEA) 的结果进行比较。此外，还分析了弹性约束边界条件下边界约束弹簧刚度和厚矩形板厚度比的影响，以深入了解厚矩形板的三维振动特性。