Exploiting Weak Softening in Linear Spring for Improved Near Resonant Vibration Isolation in Pivoted Levered Mechanisms

This study investigates the implication of weak softening in a linear spring on the isolation performances of pivoted levered vibration isolators. Asides conventional linear/nonlinear isolator which attains isolation near the equilibrium points, the levered isolator presented attained a near resonant isolation by taking advantage of weak softening in a linear spring. Although, softening effect in a linear spring is generally identified to induce nonlinear behavior in a mechanical system, this work successfully highlighted that softening nonlinearity are a consequence of beam flexibility and spring preloads/buckling or side way motions. Generally the softening nonlinearity are generally negligible when the spring softening parameter αk≤0.00001. Analytical validations showed that when the level of the maximum resonance response is below the critical displacement of 54.902 mm, the spring/system is operated in the limit below the critical stress value. Therefore, softening nonlinearity in the system are independent of stress they are associated with either individual or combined effect of beams flexibility or sideways movement of the spring. Also, the work showed that by increasing softening parameter, the near resonant isolation capacity is compromised. Therefore, to ensure linear approximations, the responses in the spring must be constrained in the desired DOF to avoid stochastic responses/buckling or sideways motion/making the beam rigid to eliminate flexibilities. Lastly, this work highlights that by taking advantage of the preload stress in the spring, a negative preload maximized the weak softening effect to enhance the isolation, while positive preload minimized the weak softening effect to compromise the isolation performances of the system.