Frequency Response and Jump Avoidance in a Nonlinear Passive Engine Mount

Abstract

This paper explores a model for a nonlinear one-degree of freedom passive vibration isolator system, known as a smart engine mount. Nonlinearities are employed to analyze and possibly improve the behavior of the optimal linear mount. Nonlinear damping and stiffness rates of the isolator have interacting effects on the dynamic behavior of the mount. The frequency response of the system is obtained using the averaging perturbation method, and a parametric analysis shows that the effect of nonlinear stiffness rate on frequency response is opposite to that of the nonlinear damping rate. Stability of the steady state periodic response has also been analyzed. Jump avoidance criteria are introduced, and the conditions for jump avoidance are studied. Closed form solutions for the absolute acceleration and relative displacement frequency responses are derived, since they are essential to use of the RMS optimization method.

Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

“…(10) needs to be solved iteratively [8,[25][26][27][28][29][30] or inversely [31] to obtain the responses sincek eq f is dependent on the responses X 2 , although it can be written in a form of 'linear' transfer function. After solving Eq.…”

“…Next, the critical equation [8] corresponding to a vertical slope can be established by ∂Ω/∂ |X 2 | = 0 to evaluate the jump condition of this isolator, where the jump zone and non-jump zone are divided by the solution curve of this critical equation, i.e.,…”

“…This concept was also extended to the study of multi-degree-of-freedom (MDOF) isolation problems by Peng [6] and Lang [7]. Another type of nonlinear damping of similar beneficial effects is also cubic, whose force is a function of both displacement and velocity [8,9] (referred as the second type of nonlinear damping in the following sections), i.e., f II d ∝ r 2ṙ ( f II d is the damping force, r andṙ denotes the displacement and velocity, respectively) or a more general form of velocity-displacement-dependent nonlinear damping force described in Ref. [10].…”

“…As been discussed above, in order to simultaneously meet the requirements of low resonance amplitude and good isolation performance at high-frequency range, these scholars [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] studied the lightly damped or even no damped linear isolators (already have good isolation efficiency at high frequencies) and added nonlinear damping elements to improve their poor resonance performances. While in this paper, we develop another novel way by presenting a sufficient damped isolator (naturally owns low resonance amplitude) and employ a nonlinear spring to reduce its vibration transmissibility at high frequencies without deteriorating its resonance performance.…”

Frequency domain analysis of a dimensionless cubic nonlinear damping system subject to harmonic input

“…The dynamics of the system can be described by (1c) which is the transmitted force from u(t) to the base. The dimensionless model (1a) can be found in many engineering systems, usually acting or known as a vibration isolator [3,12] as shown in Figure 1 with a nonlinear damping, or be found in circuit systems as shown in Figure 2 with a nonlinear resistor. Note that there is a cubic nonlinear damping terms in (1a).…”