FREE VIBRATION OF THICK ORTHOTROPIC PLATES USING TRIGONOMETRIC SHEAR DEFORMATION THEORY

Authors

  • YUWARAJ MAROTRAO GHUGAL DEPARTMENT OF APPLIED MECHANICS GOVT. ENGINEERING COLLEGE,
  • ATTESHAMUDDIN SHAMSHUDDIN SAYYAD GOVT. ENGINEERING COLLEGE AURANGABAD - 431005, MAHARASHTRA STATE

Keywords:

SHEAR DEFORMATION, THICK ORTHOTROPIC PLATE, TRANSVERSE NORMAL STRAIN, FREE VIBRATION, FREQUENCIES.

Abstract

 IN THIS PAPER A TRIGONOMETRIC SHEAR DEFORMATION THEORY IS PRESENTED FOR THE FREE VIBRATION OF THICK ORTHOTROPIC SQUARE AND RECTANGULAR PLATES. IN THIS DISPLACEMENT BASED THEORY THE IN-PLANE DISPLACEMENT FIELD USES SINUSOIDAL FUNCTION IN TERMS OF THICKNESS COORDINATE TO INCLUDE THE SHEAR DEFORMATION EFFECT. THE COSINE FUNCTION IN TERMS OF THICKNESS COORDINATE IS USED IN TRANSVERSE DISPLACEMENT TO INCLUDE THE EFFECT OF TRANSVERSE NORMAL STRAIN. THE MOST IMPORTANT FEATURE OF THE THEORY IS THAT THE TRANSVERSE SHEAR STRESS CAN BE OBTAINED DIRECTLY FROM THE CONSTITUTIVE RELATIONS SATISFYING THE SHEAR STRESS FREE SURFACE CONDITIONS ON THE TOP AND BOTTOM SURFACES OF THE PLATE. HENCE THE THEORY OBVIATES THE NEED OF SHEAR CORRECTION FACTOR.  GOVERNING EQUATIONS AND BOUNDARY CONDITIONS OF THE THEORY ARE OBTAINED USING THE PRINCIPLE OF VIRTUAL WORK. RESULTS OBTAINED FOR FREQUENCY OF BENDING MODE, SHEAR MODE AND THICKNESS STRETCH MODE OF FREE VIBRATION OF SIMPLY SUPPORTED ORTHOTROPIC SQUARE AND RECTANGULAR PLATES ARE COMPARED WITH THOSE OF OTHER REFINED THEORIES AND EXACT SOLUTION FROM THEORY OF ELASTICITY WHEREVER APPLICABLE.

Author Biographies

YUWARAJ MAROTRAO GHUGAL, DEPARTMENT OF APPLIED MECHANICS GOVT. ENGINEERING COLLEGE,

DEPARTMENT OF APPLIED MECHANICS

PROFESSOR

ATTESHAMUDDIN SHAMSHUDDIN SAYYAD, GOVT. ENGINEERING COLLEGE AURANGABAD - 431005, MAHARASHTRA STATE

RESEARCH SCHOLAR
DEPARTMENT OF APPLIED MECHANICS

Published

2011-09-05

Issue

Section

Articles