Download Modal Spring Reverb Based on Discretisation of the Thin Helical Spring Model The distributed nature of coupling in helical springs presents specific challenges in obtaining efficient computational structures
for accurate spring reverb simulation. For direct simulation approaches, such as finite-difference methods, this is typically manifested in significant numerical dispersion within the hearing range.
Building on a recent study of a simpler spring model, this paper presents an alternative discretisation approach that employs
higher-order spatial approximations and applies centred stencils at
the boundaries to address the underlying linear-system eigenvalue
problem. Temporal discretisation is then applied to the resultant
uncoupled mode system, rendering an efficient and flexible modal
reverb structure. Through dispersion analysis it is shown that numerical dispersion errors can be kept extremely small across the
hearing range for a relatively low number of system nodes. Analysis of an impulse response simulated using model parameters calculated from a measured spring geometry confirms that the model
captures an enhanced set of spring characteristics.
Download Tunable Collisions: Hammer-String Simulation with Time-Variant Parameters In physical modelling synthesis, articulation and tuning are effected via time-variation in one or more parameters. Adopting hammered strings as a test case, this paper develops extended forms of such control, proposing a numerical formulation that affords online adjustment of each of its scaled-form parameters, including those featuring in the one-sided power law for modelling hammerstring collisions. Starting from a modally-expanded representation of the string, an explicit scheme is constructed based on quadratising the contact energy. Compared to the case of time-invariant contact parameters, updating the scheme’s state variables relies on the evaluation of two additional analytic partial derivatives of the auxiliary variable. A numerical energy balance is derived and the numerical contact force is shown to be strictly non-adhesive. Example results with time-variant tension and time-variant contact stiffness are detailed, and real-time viability is demonstrated.