Analysis of systems with nonlinear auxiliary mass dampers by means of a special selection of linear generating functions

Nonlinear vibration isolation systems have a wider range of effective damping than linear ones. However, their analysis with an arbitrary load is quite laborious. In the article the method of special selection of linear generating systems for analyzing nonlinear systems proposed by professor Chernov Yu T is used. The linear generating system is chosen in such a way that the difference between the solutions of the linear and nonlinear systems in the first approximation for the first harmonic is minimal. Such an approach makes it possible to reduce the complexity of constructing the amplitude-frequency characteristics of nonlinear systems. In this paper, the amplitude-frequency characteristics were constructed to evaluate the efficiency of nonlinear auxiliary mass dampers at different frequencies of the external load. Tuned mass damper (TMD) was chosen as the type of auxiliary mass damper. The article looks at numerical examples of two systems with nonlinear TMD as a three degrees of freedom system. In the first numerical example, a stand with an equipment installed on it was analyzed. The TMD is installed on the stand. In the second numerical example the equipment is installed on a pedestal. The equipment is equipped with a nonlinear TMD. In both examples, there is cubic reaction-displacement relationship in the link that attaches the TMD. The amplitude-frequency characteristics for both systems are constructed for different variants: with a nonlinear, linear TMD and without a damper. The linear TMD was tuned to the first natural frequency of oscillations of the system without a damper. A comparative analysis of the options is given. The efficiency of using nonlinear TMD is determined from the numerical examples. There is a three times reduction in displacements in the nonlinear system as compared to the linear system. (paper)