Resonance, stability and period-doubling bifurcation of a quarter-car model excited by the road surface profile

Optimal Control of Nonlinear Resonances for Vehicle Suspension Using Linear and Nonlinear Control

“…The peak amplitude of the primary resonance response, obtained from Eq. ( 14), is given by (15) For the purpose of comparison, the equation of motion for the nonlinear primary oscillator without control is (16) The corresponding peak amplitude for the nonlinear primary oscillator without control can be written as (17) The performance of the vibration controllers on the reduction of nonlinear vibrations cannot be studied using a similar procedure based on the ratio of response amplitude for the linear system because it is difficult to find the analytical solutions for a nonlinear system. Therefore, an attenuation ratio is utilized to evaluate the performance of the vibration control by taking the proportion of vibration peak of primary resonance of the suspension system with and without control.…”

“…Hysteretic oscillation of nonlinear suspension system under various form of external excitations is a fundamental mechanics problem widely studied by many researchers. Theoretical models of chaotic response of quarter-car models due to nonlinear stochastic and deterministic excitation have been developed and experimentally observed due to the excitation of the road profile [12][13][14][15]. Naik et al studied the primary, superharmonic and subharmonic resonances of a harmonically excited nonlinear quarter-car model with linear time delayed active control by the method of multiple scales.…”

Analysis on Chaotic Vibrations of the Magneto-Rheological Suspension System

“…[8] employed the polynomial model to describe the spring stiffness of the suspension system, by considering the nonlinear characteristic of the suspension spring. Theory of Melnikov was used to build the system global bifurcation set, and then found the nonlinear dynamic characteristic of the system; Siewe [9] adopts the polynomial model of suspension damping force, under the single-frequency sinusoidal road excitation of single degree of freedom (Dof), vehicle suspension of chaos movement, analyzes the harmonic under the pavement of the harmonic resonance; Litak [10] based on the model of Yang, the application of Melnikov theory to discuss the global homoclinic orbit bifurcation, the produce chaos road excitation amplitude threshold determination. There is also few study of the nonlinear dynamic analysis on the MR suspension system.…”