Development and Experimental Verification of Damping Enhancement Methodologies for Space Structures

Nesbitt W. Hagood, Edward F. Crawley

Abstract

A frequency domain modelling technique is developed for mechanical systems. The technique is derived from Tellegen's Theorem for electrical networks and is applied to discrete mechanical systems. The elements are modelled in terms of their mechanical impedances. A global system model is assembled from the constitutive impedances. The global system model is used to determine the model exact pole locations and system energy dissipation and storage properties. An approximate method fro finding modal frequencies and loss factors using the system impedance matrix and assumed modeshapes is developed. This method reduces to Rayleigh's Quotient in the case of an undamped system.

Impedance models for several damping enhancement mechanisms are presented. Among these are models for viscoelastic materials, the classical proof mass damper, and a new damping enhancement concept called the shunted piezoelectric. The shunted piezoelectric damping mechanism is based on a piezoelectric material which has its electroded surfaces shunted by an arbitrary electrical circuit. Methods are developed for analyzing this special damper and optimizing its damping properties in the case of shunting by a resistor or by a resonant circuit. Parallels are drawn between the resistive shunted piezoelectric and viscoelastic materials and between the resonant shunted piezoelectric and the classical proof mass damper.

Experiments were conducted on a 5 meter, 10 bay box truss with a quasi free-free 3 dimensional suspension. A tunable, linear electromechanical driver was implemented for use as a proof mass damper. Electrical feedback of the proof mass position and velocity enabled accurate tuning of the dampers resonant frequency and internal damping. Piezoelectric truss members were designed and constructed for implementation of the shunted piezoelectric damping concepts. These members could replace the standard aluminium truss members. In the resonant shunted piezoelectric experiments the tuning of the piezoelectrics was accomplished by creation of an "active" variable inductor.

Experiments were conducted to test truss structure dynamics and the damping enhancement concepts. These tests were compared to the results obtained from the frequency domain system modelling technique. The proof mass damper implementation was found to increase system damping from 0.6% of critical to 6.4% of critical with a system mass increase of 2.7% The resonant shunted piezoelectric increased system damping with a similar mass penalty. These resonant dampers were found to have negligible effect on the system modes other than the mode to which they were tuned. The analytical model was found to be capable of predicting global system damping with these two concepts

SSL Report #18-88, September 1988

To obtain a copy of this report, contact slbrown@mit.edu.