Critical damping in nonviscously damped linear systems

TL;DR

This paper introduces a general method for determining critical damping surfaces in nonviscously damped linear systems, transforming algebraic conditions into differential equations and validating with numerical methods.

Contribution

It presents a novel approach to find critical damping surfaces in systems with hereditary damping, expanding analysis capabilities beyond viscous damping models.

Findings

Method successfully derives critical damping surfaces

Validated with numerical methods for various systems

Applicable to single and multiple degree of freedom systems

Abstract

In structural dynamics, energy dissipative mechanisms with non-viscous damping are characterized by their dependence on the time-history of the response velocity, mathematically represented by convolution integrals involving hereditary functions. Combination of damping parameters in the dissipative model can lead the system to be overdamped in some (or all) modes. In the domain of the damping parameters, the thresholds between induced oscillatory and non--oscillatory motion are called critical damping surfaces (or manifolds, since we can have a lot of parameters). In this paper a general method to obtain critical damping surfaces for nonviscously damped systems is proposed. The approach is based on transforming the algebraic equations which defined implicitly the critical curves into a system of differential equations. The derivations are validated with three numerical methods covering single and multiple degree of freedom systems.