Modelling the mechanical response of the reed-mouthpiece-lip system of a clarinet. Part II: A lumped model approximation

A non-linear lumped model of the reed-mouthpiece-lip system of a clarinet is formulated, in which the lumped parameters are derived from numerical experiments with a finite-difference simulation based on a distributed reed model. The effective stiffness per unit area is formulated as a function of the pressure signal driving the reed, in order to simulate the effects of the reed bending against the lay, and mass and damping terms are added as a first approximation to the dynamic behaviour of the reed. A discrete-time formulation is presented, and its response is compared to that of the distributed model. In addition, the lumped model is applied in the simulation of clarinet tones, enabling the analysis of the effects of using a pressure-dependent stiffness per unit area on sustained oscillations. The analysed effects and features are in qualitative agreement with players' experiences and experimental results obtained in prior studies.

A refined physical model of the clarinet using a variable air jet height

A time-domain formulation of a lumped model ap-
proximation of a clarinet reed excitation mechanism is presented.
The lumped model is based on an analytical representation of
the ow within the reed channel, incorporating a contraction
coefcient (vena contracta factor) that is dened as the ratio of
the effective ow over the Bernoulli ow. This coefcient has
been considered to be constant in previous studies focusing on
sound synthesis. In this paper it will be treated as a function
of the reed opening, varying between 0 and 1 as predicted by
boundary layer ow theory. Focussing on a specic mouthpiece
geometry, the effect of modelling a variable air jet height on the
synthesised sound is analysed.

Parameter Optimisation for Woodwind Single-Reed Models

Time-domain modelling of single-reed woodwind instruments usually involves a lumped model of the excitation mechanism. The parameters of this lumped model have to be estimated for use in numerical simulations. Several attempts have been made to estimate these parameters, including observations of the mechanics of isolated reeds, measurements under artificial or real playing conditions and estimations based on numerical simulations. In this study an optimisation routine is presented, that can estimate reed-model parameters, given the pressure and flow signals in the mouthpiece. The method is validated, tested on a series of numerically synthesised data. In order to incorporate the actions of the player in the parameter estimation process, the optimisation routine has to be applied to signals obtained under real playing conditions. The estimated parameters can then be used to resynthesise the pressure and flow signals in the mouthpiece. In the case of measured data, as opposed to numerically synthesised data, special care needs to be taken while modelling the bore of the instrument. In fact, a careful study of various experimental datasets revealed that for resynthesis to work, the bore termination impedance should be known very precisely from theory. An example is given, where the above requirement is satisfied, and the resynthesised signals closely match the original signals generated by the player.

Developing an integrated hydrograph separation and lumped modelling approach to quantifying hydrological pathways in Irish river catchments

An appreciation of the quantity of streamflow derived from the main hydrological pathways involved in transporting diffuse contaminants is critical when addressing a wide range of water resource management issues. In order to assess hydrological pathway contributions to streams, it is necessary to provide feasible upper and lower bounds for flows in each pathway. An important first step in this process is to provide reliable estimates of the slower responding groundwater pathways and subsequently the quicker overland and interflow pathways. This paper investigates the effectiveness of a multi-faceted approach applying different hydrograph separation techniques, supplemented by lumped hydrological modelling, for calculating the Baseflow Index (BFI), for the development of an integrated approach to hydrograph separation. A semi-distributed, lumped and deterministic rainfall runoff model known as NAM has been applied to ten catchments (ranging from 5 to 699 km2). While this modelling approach is useful as a validation method, NAM itself is also an important tool for investigation. These separation techniques provide a large variation in BFI, a difference of 0.741 predicted for BFI in a catchment with the less reliable fixed and sliding interval methods and local minima turning point methods included. This variation is reduced to 0.167 with these methods omitted. The Boughton and Eckhardt algorithms, while quite subjective in their use, provide quick and easily implemented approaches for obtaining physically realistic hydrograph separations. It is observed that while the different separation techniques give varying BFI values for each of the catchments, a recharge coefficient approach developed in Ireland, when applied in conjunction with the Master recession Curve Tabulation method, predict estimates in agreement with those obtained using the NAM model, and these estimates are also consistent with the study catchments’ geology. These two separation methods, in conjunction with the NAM model, were selected to form an integrated approach to assessing BFI in catchments.

Kinetostatic-model-based Stiffness Analysis of Exechon PKM

As a comparative newly-invented PKM with over-constraints in kinematic chains, the Exechon has attracted extensive attention from the research society. Different from the well-recognized kinematics analysis, the research on the stiffness characteristics of the Exechon still remains as a challenge due to the structural complexity. In order to achieve a thorough understanding of the stiffness characteristics of the Exechon PKM, this paper proposed an analytical kinetostatic model by using the substructure synthesis technique. The whole PKM system is decomposed into a moving platform subsystem, three limb subsystems and a fixed base subsystem, which are connected to each other sequentially through corresponding joints. Each limb body is modeled as a spatial beam with a uniform cross-section constrained by two sets of lumped springs. The equilibrium equation of each individual limb assemblage is derived through finite element formulation and combined with that of the moving platform derived with Newtonian method to construct the governing kinetostatic equations of the system after introducing the deformation compatibility conditions between the moving platform and the limbs. By extracting the 6 x 6 block matrix from the inversion of the governing compliance matrix, the stiffness of the moving platform is formulated. The computation for the stiffness of the Exechon PKM at a typical configuration as well as throughout the workspace is carried out in a quick manner with a piece-by-piece partition algorithm. The numerical simulations reveal a strong position-dependency of the PKM's stiffness in that it is symmetric relative to a work plane due to structural features. At the last stage, the effects of some design variables such as structural, dimensional and stiffness parameters on system rigidity are investigated with the purpose of providing useful information for the structural optimization and performance enhancement of the Exechon PKM. It is worthy mentioning that the proposed methodology of stiffness modeling in this paper can also be applied to other overconstrained PKMs and can evaluate the global rigidity over workplace efficiently with minor revisions.