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

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. | Vietnam Journal of Mechanics, VAST, Vol. 38, No. 1 (2016), pp. 49 – 62 DOI:10.15625/0866-7136/38/1/6629 VIBRATION ANALYSIS OF BEAMS SUBJECTED TO RANDOM EXCITATION BY THE DUAL CRITERION OF EQUIVALENT LINEARIZATION Nguyen Nhu Hieu1,∗ , Nguyen Dong Anh1 , Ninh Quang Hai2 of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam 2 Hanoi Architectural University, Vietnam 1 Institute ∗ E-mail: nhuhieu1412@gmail.com Received July 29, 2015 Abstract. 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. Keywords: Random vibration, equivalent linearization, dual criterion, modal response, nonlinear beam. 1. INTRODUCTION Over decades, the equivalent linearization (EQL) is one of the most extensively used methods in investigating mechanical systems. The earliest researches on the EQL method were carried out by Booton [1], Kazakov [2] and Caughey [3,4]. The fundamental idea of the method lies on replacing the original nonlinear system under a random external excitation by a linearized system under the same excitation in which linearization coefficients are found from a specified optimal criterion, for example, the mean-square error criterion [4], spectral criterion [5]. This method has developed and