Modal Analysis of Triangular Plate

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Modal Analysis of Isosceles Triangle-Shaped Membrane The objective of this investigation is to perform a modal analysis on an isosceles triangle-shaped membrane. This research aims to determine the vibrational modes and frequencies of such a membrane, considering it as an idealized model for various real-world structures. The triangular plate in question has a uniform thickness and is made of a homogeneous material with specified elastic properties. The dimensions of this plate are fixed, with its base length and height being well-defined. To simplify the analysis, the following assumptions will be made: 1. The membrane is perfectly flat and free from any curvature. 2. The boundary conditions are such that the edges are simply supported. 3. Vibration modes are uncoupled. Mathematical modeling of this problem involves solving the wave equation for a triangular membrane using separation of variables in polar coordinates. The resulting differential equations will be solved to obtain the displacement function, which represents the deflection of the membrane at any point within its area. The modal analysis will focus on determining the natural frequencies and corresponding mode shapes for each vibrational mode. This will involve solving the characteristic equation obtained from the wave equation and analyzing the resulting eigenvalues and eigenvectors.