Bandwidth of Linear Classically Damped Systems with Application to Experimental Model Aircraft

TL;DR

This paper introduces an analytical RMS bandwidth measure for linear damped systems, enabling accurate assessment of energy dissipation capacity, with applications demonstrated on experimental model aircraft and other structures.

Contribution

It derives an explicit ARMS Bandwidth formula for multi-degree-of-freedom systems and develops a data-driven method for modal energy distribution assessment.

Findings

ARMS Bandwidth accurately measures dissipative capacity.

The method applies to single and multi-degree systems.

Validated on experimental model aircraft.

Abstract

Bandwidth is a widely known concept and tool used in structural dynamics to measure an oscillator's capacity to dissipate energy over time, for example when used in half-power damping estimation of structural modes. Root Mean Square (RMS) Bandwidth is a generalization of bandwidth that overcomes some of the limitations encountered with conventional bandwidth, including the prerequisite of linearity, single-mode response, and light damping. However, its mathematical form does not reveal much about the physics behind it. In this paper, we extend RMS Bandwidth to multiple degree-of-freedom, linear, time-invariant, classically damped systems by deriving an Analytical Root Mean Square (ARMS) Bandwidth in terms of a system's modal parameters and initial modal energy distribution. We demonstrate that ARMS Bandwidth reliably and accurately computes a single measure for a practical structure's dissipative capacity. Also, a purely data-driven methodology for assessing the modal energy distribution is developed. We apply ARMS Bandwidth to single and multiple degree-of-freedom systems and an experimental model aircraft to demonstrate its broad applicability. Future work will address the effects of non-classical damping distribution, time-varying parameters, and nonlinearities.