Dynamics of a mechanical system with nonlinear elastic suspension and spectral analysis of the results

Abstract

The article considers the dynamics of a nonlinear mechanical system under the action of a kinematic perturbation on it. The object's vibration isolation system is described by a rigid cubic power characteristic and is based on compensation of external perturbations — the introduction of an additional elastic element with negative stiffness into the suspension. Numerical modeling of the system is performed, the results of which are analyzed by the method of spectral analysis, based on the representation of the correlation function on a small time interval by a square polynomial. As a result of the analysis, it is found that in the pre-resonant and resonant regions, the general solution should consist of three components: a subharmonic of the order of 1/3, the fundamental harmonic, and the third harmonic. It is noted that only the subharmonic of the order of 1/3 and the fundamental harmonic are important in the resonant zone. It is also noted that even simple nonlinear mechanical systems in the study of dynamics should use approximate analytical and numerical methods in combination with spectral analysis, since traditional methods of nonlinear mechanics are not adapted to solving problems taking into account a relatively large number of harmonic components that appear due to nonlinearity.

Keywords

• mechanical system
• rigid cubic force characteristic
• duffing equation
• approximate analytical methods
• mathematical modeling
• spectral density (power)
• subharmonics
• frequency response