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ARTICLE
A modified Fourier-Ritz method for free vibration of rectangular plates with elastic constrains
1
School of Mechatronics Engineering Harbin Institute of Technology, Harbin, 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
Corresponding author
Journal of Theoretical and Applied Mechanics 2022;60(1):77-89
KEYWORDS
TOPICS
ABSTRACT
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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