Some closed-form solutions in random vibration of Bresse-Timoshenko beams

Author Type

Outside Researcher

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Probabilistic Engineering Mechanics

Publication Status

Version of Record

Abstract

Random vibration of simply supported uniform Bresse-Timoshenko beams is considered under 'rain-on-the-roof' (stationary space- and time -wise ideal white noise) excitation. An approximate differential equation is used with both shear distortion and rotary inertia included, but with the term which covers the simultaneous action of these effects omitted. A closed-form solution is derived for the displacement and velocity space-time correlation function of the Bresse-Timoshenko beam with transverse damping, generalizing the corresponding result by Eringen for the classical Bernoulli-Euler beam. Closed-form solutions are also derived for beams with structural or Voigt damping mechanisms. The mean-square value of the stress diverges for both the classical Bernoulli-Euler and Bresse-Timoshenko beams with transverse damping, but converges for the beam possessing structural damping. The main finding of this study is identity of the space-time correlation functions of displacement according to the refined Bresse-Timoshenko and classical Bernoulli-Euler theories, when the joint action of rotary inertia and shear deformation is neglected for the beam under the 'rain-on-the-roof' excitation. This remarkable coincidence takes place for beams possessing (a) transverse viscous damping, (b) Voigt damping, and (c) combined rotary and transverse viscous damping. © 1989.

First Page

49

Last Page

54

DOI

10.1016/0266-8920(89)90007-6

Publication Date

1-1-1989

This document is currently not available here.

Share

COinS