New mathematical solution to free vibration of rectangular plates supported by an elastic foundation
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تهران، خیابان کریمخان زند، خیابان شهید عضدی، ساختمان وزارت علوم، طبقه دوم، انجمن مهندسی سازه ایران
چکیده
This paper presents a new mathematical approach to analyze the free vibration of corner-supported rectangular plates which is supported fully or partially by an elastic foundation. A two-dimensional Fourier sine series along with cubic polynomial functions are used for displacement function of the plate to satisfy the governing differential equation as well as boundary conditions. The auxiliary polynomial functions of order three are picked out to fulfill the boundary conditions of this plate and to cope with the third-order discontinuity of derivative of the displacement function which appears when a two-dimensional Fourier series is considered lonely.
Although this paper concentrates on corner supported plates, the proposed method can deal with all other combinations of clamped, simply supported and free boundary conditions by simply exerting their corresponding equations. Some numerical examples are included to show the accuracy and applicability of the presented method. This solution can also be extended to other problems such as plates with variable thickness and non-uniform foundation.
کلیدواژه ها
موضوعات

Title
New mathematical solution to free vibration of rectangular plates supported by an elastic foundation
Authors
Abstract
This paper presents a new mathematical approach to analyze the free vibration of corner-supported rectangular plates which is supported fully or partially by an elastic foundation. A two-dimensional Fourier sine series along with cubic polynomial functions are used for displacement function of the plate to satisfy the governing differential equation as well as boundary conditions. The auxiliary polynomial functions of order three are picked out to fulfill the boundary conditions of this plate and to cope with the third-order discontinuity of derivative of the displacement function which appears when a two-dimensional Fourier series is considered lonely.
Although this paper concentrates on corner supported plates, the proposed method can deal with all other combinations of clamped, simply supported and free boundary conditions by simply exerting their corresponding equations. Some numerical examples are included to show the accuracy and applicability of the presented method. This solution can also be extended to other problems such as plates with variable thickness and non-uniform foundation.
Keywords
Free vibration, elastic foundation, Fourier series, Auxiliary polynomial functions