Analysis of the Damping of Beams With Discontinuous Viscoelastic Damping Layer Using Integral Finite Elements

The damping performance of discontinuous constrained viscoelastic damping layer using Integral Finite Elements (IFE) are investigated in this paper. The IFE involves the dynamic analysis of Elastic-Viscoelastic Composite (EVC) structures with frequency-dependant material properties. EVC structures, which incorporate constrained viscoelastic damping treatment, are modelled using IFE’s and conventional FE’s together to deal with the discontinuous treatment of the constraint damping layers. This approach dramatically reduces the number of degrees of freedom of the FE model compared with conventional FE models. By using specialised algorithms developed for EVC structural dynamics analysis, IFE makes the estimation of the dynamic properties of the EVC structures an easy task similar to the structural dynamics analysis using conventional finite element method. Using an IFE model and the special algorithms, the damping performance of various designs of viscoelastic damping treatments are investigated at extremely low computational costs compared with the use of current commercial FE software packages. A guideline is introduced based on the results of the damping performance analysis for the structural design of viscoelastic damping treatments.

A Stability Theorem for Mechanical Systems With Constraint Damping

The effect of energy dissipation on the stability of motion of a mechanical system is a topic that has received considerable attention over the past 100 years. Since the advent of artificial Earth satellites, investigations concerned with spacecraft stability have led to renewed interest in this subject. Whereas previous work has dealt almost exclusively with damping forces that may be classified as generalized velocity damping forces; i.e., damping forces that satisfy the inequality ∑i=1nQiq˙i≦0 where the Qi’s are nonconservative generalized forces and the q˙i’s are generalized velocities, it has been found recently that a more general description of damping is sometimes desirable. Damping forces not satisfying the previously mentioned inequality have been called “constraint damping forces.” In the present paper, a theorem useful in the study of systems with constraint damping is stated and proved. This theorem represents a generalization of the Kelvin-Tait-Chetaev theorem for systems with generalized velocity damping only.