Fatemeh Zarghami - Master of Science Student, School of Mechanical Engineering, Shiraz University, Shiraz, Iran,
Ramin Vatankhah - Associated professor, School of Mechanical Engineering, Shiraz University, Shiraz, Iran,
Kamyar Hashemnia - Assistant professor, School of Mechanical Engineering, Shiraz University, Shiraz, Iran,

This paper considers the passive vibration control of an Euler-Bernoulli beam under impact loading using combination of tuned mass dampers (TMD) and nonlinear energy sinks (NES). It is assumed that the impact load is the result of spherical object collision with certain mass and initial velocity on the beam. Impact load is approximated as a harmonic load and its parameters are estimated based on nonlinear Hertz theory. Governing equations are derived and solved using Galerkin method and fourth-order Runge-Kutta. Optimum absorbers’ parameters are achieved by minimizing the settling time and peak over shoot. To this end, a multi-objective optimization problem is solved employing decomposition method and particle swarm optimization algorithm (PSO) and butterfly optimization algorithm (BOA). Results depict that combination of TMD and NES can perfectly reduce the vibration of beam under impact loading with different initial velocities of the spherical object. The optimization gives us different solutions. Achieved solutions are reported and time responses of the beam vibration are plotted for each solution. It can be observed that all the obtained solutions result proper answers and are acceptable. Considering the run time of both utilized optimization algorithms and obtained magnitude of objective functions, we can admit that PSO is more efficient algorithm for this problem. The combination of TMD and NES for vibration control of beam under impact was not studied before. Also, optimization of multiple different absorbers using proposed method in this study was not performed.

passive control, nonlinear energy sink, tuned mass damper, optimization