High-Order Modal Vibration Control of Timoshenko Beams Based on Nonlinear Energy Sink Cells.

Purpose: In engineering design, attention is usually paid to avoiding the low-order modal resonance of elastomers, but it is difficult to avoid high-order modal resonance. Although the amplitude of high-order modal resonance is generally not large, due to the higher frequency, it will also lead to vibration fatigue of the structure. To accurately analyze the higher order modes of a one-dimensional elastomer, the vibration reduction efficiency of a nonlinear energy sink (NES) cell element at higher order excitation frequencies is explored. Methods: First, a Timoshenko beam dynamic model of transverse nonlinear vibration of elastic body is established. The natural frequencies and the modes of the first eight orders of the elastic beam are analyzed and compared with the numerical results of ANSYS software. The correctness of modal analysis of elastic beam is verified. To suppress the resonance of the higher order modes of the elastomer, the centralized and distributed control strategies of the NES cell are introduced. The dynamic model of forced vibration of Timoshenko beam coupled with NES cell is established. The harmonic balance method (HBM) and the pseudo arc-length method are combined to solve the partial differential–integral equation of Timoshenko beam coupled with multiple NES cell nonlinear differential equations. The amplitude–frequency response curve of the system is obtained. The approximate analytical results are numerically verified by the Runge–Kutta method (RKM). The resonant steady-state response of the nonlinear vibration of Timoshenko beam without NES cell control is compared. Results and Conclusion: For both different vibration reduction strategies, the NES cell element has good vibration reduction efficiency. As the number of NES cell elements increases, the vibration reduction efficiency also increases. However, the vibration reduction efficiency does not keep increasing, but tends to a stable value. For both vibration reduction strategies, the NES cell elements have highly similar vibration reduction efficiencies at higher order resonant frequencies. [ABSTRACT FROM AUTHOR]