Abstract
This paper presents a nonlinear parametrically excited cantilever beam with electromagnets. A parametrically excited two-degree-of-freedom (2-DOF) system with linear time-varying stiffness, nonlinear cubic stiffness, nonlinear cubic parametric stiffness and nonlinear damping is considered. In previous studies the stability and bifurcation of the nonlinear parametrically excited 2-DOF were investigated through analytical, semi-analytical and numerical methods. Unlike previous studies, in this contribution the system’s response amplitude and phase at parametric resonance and parametric combination resonance are demonstrated experimentally and some novel results are discussed. Experimental and analytical amplitude-frequency plots are presented to show the stable solutions. Solutions for the system response are presented for specific values of parametric excitation frequency and the energy transfer between modes of vibrations is observed. The results presented in this paper prove that the bifurcation point and hence the bandwidth of the parametric resonance can be predicted correctly with the proposed analytical method. The proposed nonlinear parametrically excited 2-DOF can be used to design Micro ElectroMechanical Systems (MEMS) actuators and sensors. Validating the experimental results with the theory can improve the efficiency of these electrical systems.
Highlights
The majority of research on parametric excitation (PE) addresses systems with undesirable excitations
Solutions for the system response are presented for specific values of parametric excitation frequency and the energy transfer between modes of vibrations is observed
The results presented in this paper prove that the bifurcation point and the bandwidth of the parametric resonance can be predicted correctly with the proposed analytical method
Summary
The majority of research on parametric excitation (PE) addresses systems with undesirable excitations. This paper presents a nonlinear parametrically excited cantilever beam with electromagnets. In previous studies the stability and bifurcation of the nonlinear parametrically excited 2-DOF were investigated through analytical, semi-analytical and numerical methods. Experimental and analytical amplitude-frequency plots are presented to show the stable solutions.
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