We present a modal sound synthesis technique using a generalized proportional damping (GPD) model capable of capturing nonlinear frequency-dependent damping functions. We extend a prior method for automatic extraction of audio material parameters directly from recorded audio clips to determine material parameters for alternative damping models. We demonstrate the results with example-guided synthesized sounds, accompanied by a preliminary, perceptual study comparing the audio quality of the commonly used, linear Rayleigh damping model against a collection of alternative models.