Premium
A new approach to analysis of free beam vibrations
Author(s) -
Saurin V.,
Kostin G.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700525
Subject(s) - cartesian coordinate system , mathematical analysis , vibration , mathematics , boundary value problem , beam (structure) , elasticity (physics) , linear elasticity , ordinary differential equation , differential equation , geometry , physics , finite element method , quantum mechanics , optics , thermodynamics
Based on the linear theory of elasticity and the method of integrodifferential relations a countable system of ordinary differential equations is derived to describe longitudinal and lateral free vibrations of rectilinear beams. In the approach under consideration the stress‐strain relation is specified by an integral equality instead of the local Hooke's law. After expansion of unknown stress and displacement functions in polynomial series with respect to transversal Cartesian coordinates and system decomposition due to domain symmetry the consistent boundary value problems are solved. The influence of geometrical and elastic characteristics of rectilinear beams on eigenfrequencies is investigated. The various kinds of longitudinal and lateral free motions are found out in the models under study. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)