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Nonlinear vibration analysis of a generally restrained double-beam structure coupled via an elastic connector of cubic nonlinearity

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Abstract

Double-beam structures are frequently encountered in various engineering applications. Their vibration behavior is attracting more and more research attention. The majority of the existing studies are mainly limited to double-beam structures coupled via linear connectors. Additionally, the rotational boundary restraints of double-beam structures are usually neglected, limiting the dynamic analysis of double-beam structures in engineering applications. To study the potential application of the elastic cubic nonlinearity on double-beam structures, the dynamic analysis model of a generally restrained double-beam structure coupled via a flexible connector of cubic nonlinearity is modeled in this study. The Galerkin truncated method (GTM) is employed to solve the nonlinear governing equations of the double-beam structure. Mode functions of beam structures without any nonlinearity and damping are selected as the trail and weight functions. The Galerkin condition is applied to discretize the nonlinear governing equations. Then, residual equations of the double-beam structure are established and arranged into a matrix form. The Runge–Kutta method is utilized to solve the corresponding matrix. The finite difference method (FDM) is applied to verify the correctness and reliability of the current model. Based on the model established, the influence of the coupling nonlinearity on the dynamic behavior of the double-beam structure is studied and discussed. The research found that the variation of nonlinear stiffness, coupling viscous damping, and coupling position can effectively transform vibration states of the double-beam structure. For the determined boundary conditions and structural parameters, a suitable combination of coupling nonlinear stiffness, coupling position, and coupling viscous damping has a beneficial effect on the vibration suppression of the double-beam structure.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11972125) and the Fok Ying Tung Education Foundation (Grant No. 161049).

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  1. College of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Yuhao Zhao & Jingtao Du

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  1. Yuhao Zhao
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Correspondence to Jingtao Du.

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Zhao, Y., Du, J. Nonlinear vibration analysis of a generally restrained double-beam structure coupled via an elastic connector of cubic nonlinearity. Nonlinear Dyn 109, 563–588 (2022). https://doi.org/10.1007/s11071-022-07410-w

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  • DOI: https://doi.org/10.1007/s11071-022-07410-w

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