Guaranteed-passive simulation of an electro-mechanical piano: a port-Hamiltonian approach
This paper deals with the time-domain simulation of a simplified electro-mechanical piano. The physical model is composed of a hammer (nonlinear component), a cantilever beam (damped linear resonator) and a pickup (nonlinear transducer). In order to ensure stable simulations, a method is proposed, which preserves passivity, namely, the conservative and dissipative properties of the physical system. This issue is addressed in 3 steps. First, each physical component is described by a passive input-output system, which is recast in the port-Hamiltonian framework. In particular, a passive finite dimensional model of the Euler-Bernoulli beam is derived, based on a standard modal decomposition. Second, these components are connected, providing a nonlinear finite dimensional port-Hamiltonian system. Third, a numerical method is proposed, which preserves the power balance and passivity. Numerical results are presented and analyzed.