Abstract
In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The study of plate behavior is a very sensitive subject because it is part of the structural elements. The study of the dynamic behavior of free vibration structures is done by modal analysis in order to calculate natural frequencies and modal deformations. In this paper, we present the modal analysis of a thin rectangular plate simply supported. The analytical solution of the differential equation is obtained by applying the method of separating the variables. We are talking about the exact solution of the problem to the limit values. However, numerical methods such as the finite element method allow us to approximate these functions with greater accuracy. It is one of the most powerful computational methods for predicting dynamic response in a complex structure subject to arbitrary boundary conditions. The results obtained by MEF through Ansys 15.0 are then compared with those obtained by the analytical method.
Highlights
Structures and buildings are generally subject to increasingly complex excitations
The study of the dynamic behavior of free vibration structures is done by modal analysis in order to calculate natural frequencies and modal deformations
We present the modal analysis of a thin rectangular plate supported
Summary
Structures and buildings are generally subject to increasingly complex excitations. It appears essential to characterize them and to control their vibratory behavior in order to preserve them against fatigue and rupture [1]. The finite element method is certainly the most favorable because it is one of the most powerful calculation methods for predicting the dynamic response in a complex structure with arbitrary boundary conditions [9] In this modest work, we are involved in this vast and important field, whose objective is to determine the eigenfrequencies as well as the modes of the vibrations of homogeneous thin isotropic plates in free dynamics by different methods (analytic, finite element method). We are involved in this vast and important field, whose objective is to determine the eigenfrequencies as well as the modes of the vibrations of homogeneous thin isotropic plates in free dynamics by different methods (analytic, finite element method) To treat these vibratory problems, the general idea is to express the deflection of the plate w by a linear combination of the eigen modes.
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