A modified Fourier-Ritz method for free vibration of rectangular plates with elastic constrains
Tao Wu 1
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School of Mechatronics Engineering Harbin Institute of Technology, Harbin, China
Zhao Bo Chen   

School of Mechatronics Engineering, Harbin Institute of Technology, China
Submission date: 2021-05-24
Final revision date: 2021-10-10
Acceptance date: 2021-11-08
Online publication date: 2021-12-13
Publication date: 2022-01-20
Journal of Theoretical and Applied Mechanics 2022;60(1):77–89
In this paper, a modified Fourier-Ritz method is used to study free vibration of a rectangular plate with a set of simply supported opposite sides and another set of arbitrary elastic constraints. The influence of different elastic constraint stiffness values on the modal response of the rectangular plate is also analyzed. In order to avoid that the displacement function of the rectangular plate calculated by the traditional method and its derivative may be discontinuous or non-derivable at the boundary, the displacement function is expressed in the form of the sum of standard cosine series and a periodic polynomial function. Compared with the sine series expansion, the convergence of the result is enhanced. Several sets of numerical examples with different boundary conditions are given in the article, the data shows that the results calculated by this method have good accuracy and fast convergence. In addition, this paper also analyzes the boundary conditions and discusses the influence of different spring stiffness values on the setting of boundary conditions. The results can be applied to the setting of general boundary conditions and the study of vibration control of rectangular plates.
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