@inproceedings{ViTa2015_72,
	author = {Bridges, Jamie and Van Walstijn, Maarten},
	title = {Investigation of tanpura string vibrations using a two-dimensional time-domain model incorporating coupling and bridge friction},
	booktitle = {Proceedings of the Third Vienna Talk on Music Acoustics},
	year = {2015},
	pages = {126--131},
	editor = {Mayer, Alexander and Chatziioannou, Vasileios and Goebl, Werner},
	abstract = {Tanpura string vibrations have been investigated previously using numerical models based on energy conserving schemes derived from a Hamiltonian description in one-dimensional form.  Such time-domain models have the property that – for the lossless case - the numerical Hamiltonian (representing total energy of the system) can be proven to be constant from one time step to the next, irrespective of any of the system parameters; in practice the Hamiltonian can be shown to be conserved within machine precision. Models of this kind can reproduce a jvari effect, which results from the bridge-string interaction.  However the one-dimensional formulation has recently been shown to fail to replicate the jvari’s strong dependence on the thread placement. As a first step towards simulations which accurately emulate this sensitivity to the thread placement, a two-dimensional model is proposed, incorporating coupling of a controllable level between the two string polarisations at the string termination opposite from the barrier. In addition, a friction force acting when the string slides across the bridge in the horizontal direction is introduced, thus effecting a further damping mechanism.  In this preliminary study, the string is terminated at the position of the thread. As in the one-dimensional model, an implicit scheme has to be used to solve the system, employing Newton’s method to calculate the updated positions and momentums of each string segment.  The two-dimensional model is proven to be energy conserving when the loss parameters are set to zero, irrespective of the coupling constant. Both frequency-dependent and independent losses are then added to the string, so that the model can be compared to analogous instruments. The influence of coupling and the bridge friction are investigated.},
	address = {Vienna, Austria},
	publisher = {Institute Of Music Acoustics (Wiener Klangstil)},
	
}