Bandwidth of Linear Classically Damped Systems with Application to 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.

Figures (18)

• Figure 1: Demonstration of half-power bandwidth used in damping estimation of a monochromatic response.
• Figure 2: Linear, time-invariant SDOF system.
• Figure 3: Comparison of RMS and ARMS Bandwidth results using different simulation times: a) 80-second simulation results and b) 150-second simulation results.
• Figure 4: Comparison of simulation results using extreme values ($A_{min}=5$ and $A_{max}=50$) of the time-varying stiffness coefficient: a) velocity time series and b) RMS and ARMS Bandwidth.
• Figure 5: Simulation results demonstrating the effect of data processing parameters: a) sample velocity time history and b) RMS Bandwidth effects; the linearized system modal damping coefficient is shown as the black dot-dashed line.