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Free and forced vibration analyses of the two parallel beams connected to each other by the uniformly distributed vertical springs have been conducted in this contribution. The coupled motion equations were derived by using the free interface substructural method, and both of the free vibration characteristics and the forced vibration responses of the complex double-beam system were obtained. The mode localization and frequency loci veering phenomena would take place in such weakly coupled double beam system when there is a disorder in the system. By comparing with the available data in the literature, our numerical results were verified, and the well agreements were observed. These investigations showed that the proposed method is general and can be extended easily for vibration analysis of coupled double plate system or other complex systems.

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This paper presents an accurate and efficient hybrid solution method, based on Newmark-β algorithm, for solving nonlinear oscillators containing fractional derivatives (FDs) of arbitrary order. Basically, this method employs a quadrature method and the Newmark-β algorithm to handle FDs and integer derivatives, respectively. To reduce the computational burden, the proposed approach provides a strategy to avoid nonlinear algebraic equations arising routinely in the Newmark-β algorithm. Numerical results show that the presented method has second-order accuracy. Importantly, it can be applied to both linear and nonlinear oscillators with FDs of arbitrary order, without losing any precision and efficiency.

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