Accession Number : ADP003695

Title :   Some Closed-Form Solutions in Random Vibration of Timoshenko Beams,

Corporate Author : TECHNION - ISRAEL INST OF TECH HAIFA DEPT OF AERONAUTICAL ENGINEERING

Personal Author(s) : Elishakoff,I. ; Livshits,D.

Report Date : 1984

Pagination or Media Count : 10

Abstract : Random vibration of simply supported uniform Timoshenko beams is considered under stationary space- and time-wise ideal white noise excitation. An approximate differential equation is used with both shear distortion and rotary inertial included, but with the term which takes the simultaneous action of these effects, omitted. A closed-form solution is derived for the displacement and velocity space-time correlation function of the Timoshenko beam with transverse damping, generalizing the corresponding result by Eringen for the classical Bernoulli-Euler beam. Closed-form solutins are also derived for beams with structural or Voigt damping mechanisms. The mean-square value of the stresses diverges for both the classical and 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 Timoshenko theory and the classical Bernoulli-Euler theory, when joint action of rotary inertia and shear deformation is neglected. This remarkable coincidence takes place for beams possessing transverse viscous damping, Voigt damping, combined rotary and transverse viscous damping. (Author)

Descriptors :   *Structural mechanics, *Random vibration, *Timoshenko beam, *Differential equations, Solutions(General), White noise, Excitation, Stationary, Displacement, Damping

Distribution Statement : APPROVED FOR PUBLIC RELEASE