Dynamic response of a nonlinear parametrically excited system subject to harmonic base excitation

13th International Conference on Motion and Vibration Control; 12th International Conference on Recent Advances in Structural Dynamics

Zaghari, Bahareh^1 ; Rustighi, Emiliano^1 ; Tehrani, Maryam Ghandchi^1

University of Southampton, Highfield Campus, Southampton, United Kingdom^1

关键词: Cubic stiffness non-linearity;    Electromagnetic systems;    Equation of motion;    Mechanical and electrical;    Non-linear response;    Parametric amplification;    Parametric excitations;    Parametrically excited systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/744/1/012125/pdf
DOI  :  10.1088/1742-6596/744/1/012125

来源: IOP

【 摘 要 】

A Nonlinear Parametrically Excited (NPE) system subjected to a harmonic base excitation is presented. Parametric amplification, which is the process of amplifying the system's response with a parametric excitation, has been observed in mechanical and electrical systems. This paper includes an introduction to the equation of motion of interest, a brief analysis of the equations nonlinear response, and numerical results. The present work describes the effect of cubic stiffness nonlinearity, cubic parametric nonlinearity, and the relative phase between the base excitation and parametric excitation under parametric amplification. The nonlinearities investigated in this paper are generated by an electromagnetic system. These nonlinearities were found both experimentally and analytically in previous work [1]; however, their effect on a base excited NPE is demonstrated in the scope of this paper. This work has application in parametric amplification for systems, which are affected by strong stiffness nonlinearities and excited by harmonic motion. A careful selection of system parameters, such as relative phase and cubic parametric nonlinearity can result in significant parametric amplification, and prevent the jump from upper stable solutions to the lower stable solutions.