Piecewise Linear Isolator Research Articles

Two-step transfer function calculation method and asymmetrical piecewise-linear vibration isolator under gravity

Piecewise-linear isolators are widely used in spacecraft for satisfying ever more stringent vibration requirements of high precision payloads. This paper focuses on ground tests of such isolators, with special consideration of gravitational asymmetry and mount flexibility. With asymmetrical equivalent isolator parameters derived with the extended equivalent linearization method, a two-step transfer function calculation method is proposed for enhancing the computation efficiency in dealing with studies where huge amount of computations are required, such as design parameter studies. The asymmetrical effect due to the gravity is presented by the movement of dynamic equilibrium positions as well as the softening and hardening characteristics of frequency responses. The effects and differences of the rigid mount and flexible mount, which respectively correspond to the shake table test and the whole spacecraft structure ground test, are studied with various design parameters. Numerical results show that the preload is an important factor in determining such effects and differences.

Design of a piecewise linear vibration isolator for jump avoidance

Piecewise linear isolators are smart passive vibration isolators that provide effective isolation for high frequency/low amplitude excitation. This can be done by introducing a soft primary suspension and a relatively damped secondary suspension. Such a piecewise isolator prevents the system from a high relative displacement in low frequency/high amplitude excitation. By employed an averaging method it is possible to obtain an implicit function for frequency response of a symmetric bilinear vibration isolator system under steady-state harmonic excitation. This function is examined for jump avoidance. A condition is derived which when met ensures that the undesirable phenomenon of ‘jump’ does not occur and the system response is functional. The jump avoidance and sensitivity of the condition are examined and investigated as the dynamic parameters vary. The results of this investigation can be directly employed in design of effective piecewise linear vibration isolators. A linear vibration system is defined as one in which the quantities of mass (or inertia), stiffness, and damping are linear in behaviour and do not vary with time [1]. Although mathematical models employing a linear ordinary differential equation with constant coefficients portray a simple and manageable system for analytical study, in most cases they are an incomplete representation simplified for the sake of analysis. Most real physical vibration systems are more accurately depicted by non-linear governing equations, in which the non-linearity may stem from structural constraints causing a change in stiffness and damping characteristics, or from inherent non-linear behaviour of internal springs and dampers. This paper focuses on a general form of such a non-linear system. This study of piecewise-linear systems will allow hazardous system behaviour over operating frequency ranges to be gauged and controlled in order to avoid premature fatigue damage, and prolong the life of the system.

Frequency Response of a Piecewise Linear Vibration Isolator

Piecewise linear vibration isolators are designed to optimally balance the competing goals of motion control and isolation. The piecewise linear system represents a hard nonlinearity, which cannot be assumed small, and hence standard perturbation methods are unable to provide a complete analytical solution. To date there is no frequency response equation reported for piecewise linear isolator systems to include both dual damping and stiffness behavior. In this investigation an averaging method was adopted to explore the frequency response of a symmetric piecewise linear isolator at resonance. The result obtained by an averaging method is in agreement with numerical simulation and experimental measurements. Preliminary sensitivity analysis is conducted to find the effect of system parameters. It appears that the damping ratio plays a more dominant role than stiffness in piecewise linear vibration isolators.