Random vibration of a nonlinearly deformed beam by a new stochastic linearization technique
A new stochastic linearization technique is employed to investigate the large amplitude random vibrations of a simply supported or a clamped beam on elastic foundation under a stochastic loading which is space-wise either (a) white noise or (b) uniformly distributed load and time-wise white noise. The new method is based on the requirement that the mean square deviation of the strain energy of the nonlinearly deformed beam, and the strain energy of the equivalent beam in a linear state, should be minimal. As a result, the model mean square displacements are expressed as solutions of a set of nonlinear algebraic equations. Results obtained by the conventional equivalent linearization method and by the new technique are compared with the numerical results obtained from integration of the exact probability density function or with the result of the Monte Carlo simulations.
scientific article; zbMATH DE number 988965