Abstract
We propose a continuous model for rectangular plates that involves a mesh of slender interconnected beams. These beams are disposed orthogonally. The advantage of this model is that simple equations are involved and the behavior of the plate is accurately described. After a brief description of the model, we present an application written in the Python programing language that allows calculating the mode shapes for rectangular plates with various boundary conditions. The mode shapes achieved with the application for a specific plate are found to be similar with those obtained from simulation involving the SolidWorks software. In consequence, we conclude that the proposed model is reliable and the application developed on this base can be used to study the behavior of rectangular plates with different boundary conditions.
Highlights
The dynamic behavior of plates was investigated in the past decades by many researchers [1,2,3,4], due to their wide-range applications in various fields, such as: aerospace, marine engineering and naval architecture
Boscolo and Banerjee [8] studied the vibration behavior of plates involving the dynamic stiffness method. As it can be concluded from the above short review, even if the vibration of rectangular thin plates has received a significant amount of researches, there is still potential for innovative approaches
To be able to plot rapidly the mode shapes for any combination of mode numbers m and n, we developed the PyPLATE application, which is written in the Python programming language
Summary
The dynamic behavior of plates was investigated in the past decades by many researchers [1,2,3,4], due to their wide-range applications in various fields, such as: aerospace, marine engineering and naval architecture. Wang and Wereley [5] have proposed analytical solutions for the modal frequencies and displacement mode shapes in a rectangular plate with different boundary conditions, by involving the Kantorovich-Krylov method. Based on the asymptotic method, Adrianov et al [7] proposed an analytical solution for the free in-plane vibration of rectangular plates with complex boundary conditions. Boscolo and Banerjee [8] studied the vibration behavior of plates involving the dynamic stiffness method. As it can be concluded from the above short review, even if the vibration of rectangular thin plates has received a significant amount of researches, there is still potential for innovative approaches. The study presented propose a new and simple model for thin rectangular plates, developed for accurate calculus of the mode shapes
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