Analytical method of the modal damping ratio of the beam with distributed dissipative oscillators and application in broadband vibration mitigation

Abstract Distributed dissipative oscillators are considered effective measures to broaden the vibration mitigation bandwidth of structures. However, the existing calculation methods are mainly based on parameter analysis, which is not convenient for engineering applications. Modal damping ratio can be used to evaluate the frequency band and degree of vibration attenuation quickly. Therefore, the explicit analytical formulas of modal damping ratio for the beam distributed with single-frequency and dual-frequency oscillators are derived and verified by comparing with FEM results. And the influence of mode order, boundary conditions, the mass ratio, and frequency ratio of the oscillators on modal damping ratio is also discussed. As an application of the presented equations, the optimized frequencies of single-frequency or dual-frequency oscillators satisfying the Minimax optimization (maximize the minimum damping in a target frequency band) are obtained. The frequency response of the beam with optimized oscillators is compared with modal damping ratio curves to discuss the influence of mass ratio and loss factor on vibration suppression and the adaptability of modal damping to design. The results show that the presented formulas have satisfied accuracy and can be used for broadband mitigation design.