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External and Internal Resonances in a Mass-Spring-Damper System with 3-dof

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Nonlinear Dynamics of Structures, Systems and Devices

Abstract

The chapter deals with the analytical investigation of the physical pendulum mounted on the spring-damper suspension. The pendulum exhibits three degrees of freedom in plane motion. Three types of external loading and viscous damping are considered. The method of multiple scales is used to solve the initial value problem defined through Lagrange formalism. The proposed analytical method allows for the prediction of resonance conditions. The amplitude-frequency response curves have been determined for the external resonance, and their stability has been assessed using the Routh–Hurwitz criterion. The modulation equations of the amplitudes and phases are the basis for studying the impact of the chosen parameters on the internal resonance 1:2.

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Correspondence to Roman Starosta .

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Awrejcewicz, J., Starosta, R., Sypniewska-Kamińska, G. (2020). External and Internal Resonances in a Mass-Spring-Damper System with 3-dof. In: Lacarbonara, W., Balachandran, B., Ma, J., Tenreiro Machado, J., Stepan, G. (eds) Nonlinear Dynamics of Structures, Systems and Devices. Springer, Cham. https://doi.org/10.1007/978-3-030-34713-0_17

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