# City Research Online

## A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution

Papkov, S. O. & Banerjee, J. R. (2023). A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution. Mathematics, 11(3), article number 649. doi: 10.3390/math11030649

## Abstract

In this paper, a new method based on an accurate analytical series solution for free vibration of triangular isotropic and orthotropic plates is presented. The proposed solution is expressed in terms of undetermined arbitrary coefficients, which are exactly satisfied by the governing differential equation in free vibration. The approach used is based on an innovative extension of the superposition method through the application of a modified system of trigonometric functions. The boundary conditions for bending displacements and bending rotations on the sides of the triangular plate led to an infinite system of linear algebraic equations in terms of the undetermined coefficients. Following this development, the paper then presents an algorithm to solve the boundary value problem for isotropic and orthotropic triangular plates for any kinematic boundary conditions. Of course, the boundary conditions with zero displacements and zero rotations on all sides correspond to the case when the plate is fully clamped all around. The convergence of the proposed method is examined by numerical simulation applying stringent accuracy requirements to fulfill the prescribed boundary conditions. Some of the computed numerical results are compared with published results and finally, the paper draws significant conclusions.

Publication Type: Article © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). isotropic and orthotropic triangular plates; free vibration; natural modes; superposition method; infinite system of linear equations Q Science > QA MathematicsT Technology > TA Engineering (General). Civil engineering (General) School of Science & Technology > Engineering
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