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In this paper responses of beams subjected to random loading are analyzed by the dual approach of the equivalent linearization method. The external random loading is assumed to be a space-wise and time-wise white noise in which the exact solutions of the modal equations can be found. A system of nonlinear algebraic equations for linearization coefficients of the modal linearized system is obtained in a closed form and is solved by the fixed-point iteration method. Results obtained from the proposed dual criterion are compared with the exact solution and those obtained from other approaches including energy method, and conventional linearization method. It is observed that the solution obtained by the dual criterion is in good agreement with the exact solution, especially, in the case of strong nonlinearity of beam.

vietnam journal of mechanics/mechanics

Vibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearizationVibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearization