MODAL ANALYSIS OF TRANSIENT VIBRATION PROBLEMS IN LINEARLY VISCOELASTIC SOLIDS,

Abstract

Transient vibration problems in linear viscoelasticity may be solved by means of the Sturm-Liouville theory provided the homogeneous boundary conditions for the free vibrations can be combined to give a characteristic equation with real roots. This characteristic equation will depend on the geometric and inertial characteristics of the system, and not on the viscoelastic properties of the solid. If all the conditions above are not satisfied, it is still generally possible to reduce the homogeneous boundary conditions to a complex frequency equation by assuming separable solutions with exp (st) as the time dependent factor. The associated modes of deflection will generally be nonorthogonal. Transient vibration problems of this type may be solved by contour integrals, which may be evaluated by residue theory or reduced to a Fourier integral by a change of variable. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1963
Accession Number
AD0612137

Entities

People

  • Alexander S. Elder

Organizations

  • Ballistic Research Laboratory

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Contour Integrals
  • Deflection
  • Doppler Effect
  • Equations
  • Frequency
  • Frequency Shift
  • Integrals
  • Mathematics
  • Modal Analysis
  • United States
  • United States Military Academy
  • Vibration
  • Viscoelasticity

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Structural Dynamics.