A combined nonlinear and hysteresis model of shock absorber for quarter car simulation on the basis of experimental data

Modeling dynamic characteristics of an automotive shock absorber is a challenging task due to its complex behavior. In the present paper, the nonparametric and hybrid approach is proposed to represent the nonlinear and hysteresis characteristics of the shock absorber. An experiment is carried out on a car damper utilizing INSTRON to obtain force-velocity characteristics of the shock absorber. The experimental data is used to devise two different models, namely, piecewise linear model and hysteresis model, to capture the damping properties of the absorber and for consequent use in simulations. The complexity involved due to certain physical phenomenon such as oil compressibility, gas entrapment etc. gives rise to hysteresis behavior and the present paper tries to model such behavior with the help of Neural Networks. Finally, a combined (hybrid) shock absorber model (including the characteristics of both piecewise linear and hysteresis behavior) is developed in Simulink and integrated into a quarter car simulation to verify its feasibility. The results generated by the combined (hybrid) model are compared with linear as well as piecewise linear model and the comparison shows that the proposed model substantially a better option to study the vehicle characteristics more accurately and precisely

Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

The nonlinear vibration of a travelling beam subjected to principal parametric resonance in presence of internal resonance is investigated. The beam velocity is assumed to be comprised of a constant mean value along with a harmonically varying component. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times that of first mode; a three-to-one internal resonance is possible. The method of multiple scales (MMS) is directly applied to the governing nonlinear equations and the associated boundary conditions. The nonlinear steady state response along with the stability and bifurcation of the beam is investigated. The system exhibits pitchfork, Hopf, and saddle node bifurcations under different control parameters. The dynamic solutions in the periodic, quasiperiodic, and chaotic forms are captured with the help of time history, phase portraits, and Poincare maps showing the influence of internal resonance

Free out-of-plane vibrations of a rotating beam with non-linear elastomeric constraints

Free out-of-plane vibration of a rotating beam with a non-linear, elastomeric constraint has been investigated. The elastomer is modelled as a parallel combination of spring and damper elements. The stiffness and damping parameters are evaluated by using the previous experimental data. The linear analysis is performed by two techniques, one based on a power series expansion and the other based on the Rayleigh-Ritz principle. The results are found to be in excellent agreement. In the non-linear analysis, a numerical-perturbation technique is applied to determine the frequency-amplitude relationship. A parametric study revealing the influence of the non-linear constraint is presented

Influence of nonlinear elastomer on isolated lag dynamics and rotor/Fuselage Aeromechanical Stability

This paper presents a study on the effect of nonlinearities of an elastomeric bearing on isolated lag dynamics and coupled rotor/fuselage ground resonance stability of an idealized bearingless rotor blade. The rotor blade is modeled as an elastic beam with a nonlinear elastomer and a rigid torque tube. First, amplitudedependent natural frequency of the blade in lag mode is analyzed using numerical perturbation technique. Then the problem of amplitudedependent stability of the coupled rotor/fuselage system under ground resonance condition is investigated. The stability of the system is analyzed by two approaches, namely, 1) by eigenanalysis of the linearized equations and 2) by response of the nonlinear system to an initial disturbance by time integration. The results of the eigenanalysis indicate that the effect of amplitude seems to be more dominant on the progressive lag mode damping than on regressive lag mode damping. It is also observed that so far as the stability in ground resonance is concerned there exist optimum locations for the attachment of both the elastomer and torque tube. Results of the time-domain analysis of the nonlinear equations indicate clearly that the stability of the system is dependent on the magnitude of initial disturbance