Vibration Reduction of a Timoshenko Beam with Multiple Parallel Nonlinear Energy Sinks

A nonlinear energy sink is a promising device to reduce structural vibrations. In this work, the vibration reduction performances of multiple parallel nonlinear energy sinks attached to a short beam are investigated based on the Timoshenko beam theory. The dynamic equations of a vibration reduction system subjected to a harmonic excitation are established. The frequency responses are analyzed based on Galerkin discretization and the harmonic balance method, and the accuracy is verified by the Runge–Kutta method. An optimization method based on the genetic algorithm is proposed for the number, location, and cubic stiffness of the nonlinear energy sinks. The study reveals that, with the same total mass, multiple parallel nonlinear energy sinks can achieve a larger vibration reduction ratio than a single nonlinear energy sink. The parameter influences of the nonlinear energy sinks are revealed, and unstable responses with large cubic stiffness are presented. The optimal locations of the multiple parallel nonlinear energy sinks are related to low-order modal shapes. A larger reduction ratio on the resonant amplitude can be achieved compared to a uniform distribution of the nonlinear energy sinks. The optimal locations and cubic stiffness are related to the number of nonlinear energy sinks. In the studied case, the optimal number of nonlinear energy sinks was two.