VIBRATIONS IN HETEROGENEOUS ELASTIC PLATES,

Abstract

A two-dimensional heterogeneous dynamic plate theory was deduced from the three-dimensional dynamic equations of elasticity. The heterogeneity of the material was considered to be only along the thickness coordinate of the plate. Approximations of shear deformations and of rotary inertia were included. A tenth order differential equation was derived. Five boundary conditions and proper initial conditions were obtained to insure an unique solution. It was recognized that the fact of coupling between stretching and bending in the heterogeneous plate led to this higher order (tenth) differential equation. The heterogeneous plate theory was specialized to cases of symmetrically laminated aeolotropic, orthotropic and isotropic plates respectively. A heterogeneous plate theory neglecting shear deformations was also deduced from the three-dimensional dynamic equation of elasticity. It was shown that the method of solving the forced vibration of a homogeneous plate of finite length could be extended to a heterogeneous plate. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1962
Accession Number
AD0281755

Entities

People

  • Charles H. Norris
  • Peng-chih Yang

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Couplings
  • Differential Equations
  • Elastic Properties
  • Equations
  • Geometry
  • Heterogeneity
  • Materials
  • Mathematics
  • Physical Properties
  • Sizes (Dimensions)
  • Three Dimensional
  • Two Dimensional
  • Vibration

Readers

  • Seismology
  • Structural Dynamics.