Time-domain damping models in structural acoustics using digital filtering. (February 2016) - Parret-Fréaud, Augustin; Cotté, Benjamin; Chaigne, Antoine
Abstract: This paper describes a new approach in order to formulate well-posed time-domain damping models able to represent various frequency domain profiles of damping properties. The novelty of this approach is to represent the behavior law of a given material directly in a discrete-time framework as a digital filter, which is synthesized for each material from a discrete set of frequency-domain data such as complex modulus through an optimization process. A key point is the addition of specific constraints to this process in order to guarantee stability, causality and verification of thermodynamics second law when transposing the resulting discrete-time behavior law into the time domain. Thus, this method offers a framework which is particularly suitable for time-domain simulations in structural dynamics and acoustics for a wide range of materials (polymers, wood, foam, etc.), allowing to control and even reduce the distortion effects induced by time-discretization schemes on the frequency response of continuous-time behavior laws. Abstract : Highlights: We propose an original approach to provide well-posed time-domain damping modeling. We build a discrete-time constitutive law which is interpreted as a digital filter. The filter is synthetized from complex modulus data through an optimization problem. We add constraints to ensure stability, causality and dissipation of the model. Resulting discrete model is implemented in an energy-preserving numerical scheme.