Damping: An Introduction to Viscoelastic Models

Abstract

This chapter provides an examination of viscoelastic damping normally characterized by hysteresis, a complex modulus or frequency dependent damping. Viscoelastic damping exhibited in polymeric and glassy materials as well as in some enamels. Such materials are often added to structures and devices to increase the amount of damping. Examples are rubber mounts and constrained layer damping treatments. Typically in modal analysis the simplest form of modeling damping is used. This form assumes that the damping is a linear, time invariant phenomena chosen to be viscous, or proportional to velocity, motivated by the ability to solve the equations of motion. With this as a first model, one is lead to conclude that viscoelastic behavior causes frequency dependent damping coefficients resulting in the concept of complex modulus. Thus it is not clear how to perform modal analysis of structures with viscoelastic components. Here an alternative formulation is discussed and presented for multiple degree of freedom systems that allows the treatment of hysteretic damping in dynamic finite element formulations, and hence provides a connection to modal analysis and testing.