Showing papers by "Leif Kari published in 2003"

Nonlinear Isolator Dynamics at Finite Deformations: An Effective Hyperelastic, Fractional Derivative, Generalized Friction Model

Abstract: In presenting a nonlinear dynamic model of a rubber vibration isolator, the quasistatic and dynamic motion influences on the force response are investigated within the time and frequency domain. It is found that the dynamic stiffness at the frequency of a harmonic displacement excitation, superimposed upon the long term isolator response, is strongly dependent on static precompression, dynamic amplitude and frequency. The problems of simultaneously modelling the elastic, viscoelastic and friction forces are removed by additively splitting them, modelling the elastic force response by a nonlinear, shape factor based approach, displaying results that agree with those of a neo-Hookean hyperelastic isolator at a long term precompression. The viscoelastic force is modeled by a fractional derivative element, while the friction force governs from a generalized friction element displaying a smoothed Coulomb force. A harmonic displacement excitation is shown to result in a force response containing the excitation frequency and its every other higher-order harmonic, while using a linearized elastic force response model, whereas all higher-order harmonics are present for the fully nonlinear case. It is furthermore found that the dynamic stiffness magnitude increases with static precompression and frequency, while decreasing with dynamic excitation amplitude-eventually increasing at the highest amplitudes due to nonlinear elastic effects-with its loss angle displaying a maximum at an intermediate amplitude. Finally, the dynamic stiffness at a static precompression, using a linearized elastic force response model, is shown to agree with the fully nonlinear model except at the highest dynamic amplitudes.

On the dynamic stiffness of preloaded vibration isolators in the audible frequency range: Modeling and experiments

Abstract: The nonlinear, preload-dependent dynamic stiffness of a cylindrical vibration isolator is examined via measurements and modeling within an audible frequency range covering 50 to 1000 Hz at various preloads. The stiffness is found to depend strongly on frequency-resulting in peaks and troughs, and on preload-particularly above 500 Hz. The problems of simultaneously modeling the rubber prestrain dependence and its audible short-term response are removed by adopting a nearly incompressible material model, being elastic in dilatation while displaying viscoelasticity in deviation. The latter exhibits a time strain separable relaxation tensor with a single function embodying its time dependence. This function is based on a continuous fractional order derivative model, the main advantage being the minimum number of parameters required to successfully model the rubber properties over a broad structure-borne sound frequency domain, while embodying a continuous distribution of relaxation time. The weak formulations corresponding to the stiffness problem are solved by an updated Lagrangian nonlinear finite-element procedure. The model and measurement results agree strikingly well with static and dynamic measurements throughout the whole frequency domain for the examined preloads.

Audible-frequency stiffness of a primary suspension isolator on a high-speed tilting bogie

Abstract: The preload-dependent dynamic stiffness of a primary suspension isolator on a high-speed tilting bogie is examined via measurements and modelling within an audible frequency range. The stiffness is found to depend strongly on both frequency and preload. The former displays some resonance phenomena, such as stiffness peaks and troughs, while the latter exhibits a steep low-frequency stiffness increase in addition to an anti-resonance peak shifting to a higher frequency with increased preload. The problems of simultaneously modelling the preload and frequency dependence are removed by adopting a frequency-dependent waveguide approach, assuming incompressible rubber with an Abel operator kernel as its shear relaxation function. The preload dependence is modelled by a non-linear shape factor based approach, using a globally equivalent preload configuration. All the translational stiffnesses are modelled, including the vertical, longitudinal and lateral directions, and the vertical stiffness results ar...

A nonlinear dynamic stiffness model of a vibration isolator at finite deformations

Abstract: A nonlinear dynamic model of a vibration isolator is presented where influences of precompression and dynamic amplitude are investigated within the frequency domain. It is found that the dynamic stiffness at the frequency of a harmonic displacement excitation is strongly dependent on those parameters. The problems of simultaneously modeling the elastic, viscous and friction forces are removed by additively splitting them, where the elastic force is modeled by a nonlinear, shape factor based approach, the viscous force by a fractional derivative model while the friction force is modeled by a generalized friction element. The dynamic stiffness magnitude is shown to increase with static precompression and frequency while decreasing with dynamic excitation amplitude, with its loss angle displaying a maximum at an intermediate amplitude. The dynamic stiffness at a static precompression, using a linearized elastic force response model, is shown to agree with the fully nonlinear model except at the highest dynamic amplitudes. The latter model is displaying an increased stiffness magnitude at the highest amplitudes due to nonlinear elastic effects. Furthermore, a harmonic displacement excitation is shown to result in a force response containing the excitation frequency and all higher-order harmonics, whereas every other higher-order harmonics vanish for the elastically linearized case.