FINITE-ELEMENT, LARGE-DEFLECTION RANDOM RESPONSE OF THERMALLY BUCKLED BEAMS

The effects of temperature and acoustic loading are included in a theoretical finite element, large-deflection formulation for the random response of thin, isotropic beams. Thermal loads are applied as steady-state temperature distributions, and acoustic loads are taken to be ergodic and Gaussian with zero mean and uniform magnitude and phase along the length of the beam. Material properties are considered to be independent of temperature. Also, in-plane and rotary inertia terms are assumed to be negligible, and all in-plane edge conditions are taken to be immovable. For the random response analysis, both auto- and cross-correlation terms are included. The nature of the loads leads to the solution of two separate problems. First, the problem of thermal postbuckling is solved to determine the deflections and stresses due to the thermal load only. These deflections and stresses are then used as initial deflections and stresses for the random vibration analysis. Root-mean-square maximum deflections and strains are obtained and compared with previous classical equivalent linearization results.