This research focuses on the development of new analytical and semi-analytical models for a class of elastomeric and hydraulic bushings. Historically, such vibration isolators have been studied in the context of the linear system theory using simplified viscoelastic elements with focus on uniaxial behavior at lower frequencies. Relatively few researchers have utilized advanced viscoelastic models or nonlinear, excitation-amplitude sensitive models. To overcome these voids, the primary goals of this work are to develop isolator models using a fractional calculus viscoelastic formulation and to accurately predict amplitude dependent dynamic stiffness of fluid-filled devices.
First, the fractional calculus is utilized to describe the damping properties of elastomeric bushings in both time and frequency domains. For the frequency domain, a new spectral element approach is proposed to determine the multi-axis dynamic stiffness terms of elastomeric isolators with fractional damping over a broad range of frequencies using the continuous system theory (in terms of homogeneous rods or Timoshenko beams). The transfer matrix type dynamic stiffness expressions are developed from analytical harmonic solutions given translational or rotational displacement excitations. Predictions match well with available measurements up to 600 Hz. Second, a lumped parameter system model with fractional damping is developed to explore the dynamic stiffness behavior over the lower frequency range. The inverse Laplace transform of the dynamic stiffness spectrum is taken via the Residue Theorem to produce impulse response functions. Since the fractional calculus based solution is given in terms of problematic integrals, a new time-frequency domain estimation technique is proposed which approximates time-domain responses for a class of transient excitation functions. The approximation error is found to be reasonably small, and tractable closed-form transient response functions are generated.
Third, refined quasi-linear and nonlinear hydraulic bushing models are proposed with focus on the sinusoidal excitation amplitude sensitivity in the dynamic stiffness magnitude and loss angle spectra (up to 50 Hz). Nonlinear chamber compliance and track resistance elements are incorporated in order to improve amplitude sensitive predictions. New solution approximations for the governing equations are constructed using the multi-term harmonic balance term method. Finally, fractional calculus and friction type damping elements are added to the chamber compliance. Improved quasi-linear models are proposed at four amplitudes, demonstrating amplitude sensitivity in model parameters. Refined nonlinear models are validated using measurements at multiple amplitudes. The sensitivity of the fractional and frictional damping parameters to shaping the dynamic stiffness spectra is qualitatively evaluated.
This dissertation makes three distinct contributions to the scientific literature. First, fractional calculus based viscoelasticity better captures the damping properties of elastomeric and hydraulic isolators. Next, a novel estimation procedure allows for the calculation of transient responses of fractionally damped systems to steady-state and transient excitations, revealing dynamic properties that are usually masked in the frequency-domain. Finally, new nonlinear fluid system models clarify the underlying physics that governs the amplitude sensitive dynamic behavior of hydraulic bushings.