Analysis and perception of a viscoelastic, frequency-dependent Finite-Difference Time Domain damping model of a drum

This study investigates the influence of viscoelastic damping parameters in a Viscoelastic Finite Difference Time Domain (FDTD) model on the sound of a drum head. Due to the strong nonlinearity between the complex, frequency-dependent Young’s modulus as a model input parameter and resulting damping frequencies and damping strength, this relation can no longer be analyzed analytically. One reference and eight altered membranes are constructed. Integrating the sound into minor third bands, nonlinear mode couplings due to viscoelasticity are found, relating to the real part of the Young’s modulus as well as to the Laplace-Transform parameter of the FDTD model. Furthermore, the perception of the sounds was investigated. The results are compared to the physical observation, showing variations in brightness and pitch. Hereby, the perception can be described as proportional to the physical analysis, as long as the variation of the Laplace parameter in one or more damped frequencies does not lead to a huge difference in the sounds decay time, which seems to distract the attention from other acoustical characteristics.