The logical clarinet: numerical optimization of the geometry of woodwind instruments

The tone hole geometry of a clarinet is optimized numerically. The instrument is modeled as a network of one dimensional transmission line elements. For each (non-fork) fingering, we first calculate the resonance frequencies of the input impedance peaks, and compare them with the frequencies of a mathematically even chromatic scale (equal temperament). A least square algorithm is then used to minimize the differences and to derive the geometry of the instrument. Various situations are studied, with and without dedicated register hole and/or enlargement of the bore. With a dedicated register hole, the differences can remain less than 10 musical cents throughout the whole usual range of a clarinet. The positions, diameters and lengths of the chimneys vary regularly over the whole length of the instrument, in contrast with usual clarinets. Nevertheless, we recover one usual feature of instruments, namely that gradually larger tone holes occur when the distance to the reed increases. A fully chromatic prototype instrument has been built to check these calculations, and tested experimentally with an artificial blowing machine, providing good agreement with the numerical predictions

Nonlinear modes of clarinet-like musical instruments

The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the normal modes of the air column, a system of second order ordinary differential equations is obtained. The equations are coupled through the nonlinear relation describing the volume flow of air through the reed channel in response to the pressure difference across the reed. The system is treated using an amplitude-phase formulation for nonlinear modes, where the frequency and damping functions, as well as the invariant manifolds in the phase space, are unknowns to be determined. The formulation gives, without explicit integration of the underlying ordinary differential equation, access to the transient, the limit cycle, its period and stability. The process is illustrated for a model reduced to three normal modes of the air column

Numerical Techniques for Acoustic Modelling and Design of Brass Wind Instruments

Acoustic horns are used in musical instruments and loudspeakers in order to provide an impedance match between an acoustic source and the surrounding air. The aim of this study is to develop numerical tools for the analysis and optimisation of such horns, with respect to their input impedance spectra. Important effects such as visco-thermal damping and modal conversion are shown to be localised to different parts of a typical brass instrument. This makes it possible to construct hybrid methods that apply different numerical techniques in different parts of the instrument. Narrow and slowly flaring parts are modelled using a one-dimensional transmission line analogy, and the rapidly flaring bell is modelled using a two-dimensional finite-difference method. The connection between the different regions is done by the aid of impedance boundary conditions. The use of such boundary conditions is investigated with respect to the required number of degrees of freedom. Numerical shape optimisation is employed in order to design horns with desired impedance characteristics throughout a design frequency band. A loudspeaker horn is optimised with respect to its sound power output, and a brass instrument is optimised with respect to its intonation. The horns are modelled using the finite-element method and a transmission line analogy. In order to achieve rapid convergence of the optimisation, gradient based minimisation algorithms are used. A prerequisite for success is the ability to accurately and inexpensively compute the gradient of the objective function. The gradient for the finite-element method is computed by an adjoint equation technique, whereas for the transmission line analogy, it is derived by formal differentiation of the model. In order to find smooth solutions, a smoothing technique is used, where optimisation is done with respect to the right hand side of a Poisson type equation

Continuous transportation as a material distribution topology optimization problem

The problem of moving a commodity with a given initial mass distribution to a pre-specified target mass distribution so that the total work is minimized can be traced back at least to Monge’s work from 1781. Here, we consider a version of this problem aiming to minimize a combination of road construction and transportation cost by determining, at each point, the local direction of transportation. This paper covers the modeling of the problem, highlights how it can be formulated as a material distribution topology optimization problem, and shows some results

A common Nordic-Baltic costing framework for road, rail and sea transport of roundwood

Transport cost calculations are fundamental for most types of transport research. Applications can range from estimating the cost benefits of developing transport technologies (e.g. increased truck GVWs) to comparing profitability between alternative infrastructure investments (e.g. rail or sea terminals). Most stakeholders rely on a favourite spreadsheet, however these vary considerably with respect to functionality, resolution and transparency. During 2019 and 2020 the NB Nord Road and Transport group has worked towards a common Nordic-Baltic costing framework for road, rail and sea transport. The goal has been to propose a general model per transport method which is user-friendly, while retaining the necessary resolution and functionality to model actual costs for specific transport orders or contracts. The handbook provides: a) complete explanation of its formulas, b) calculation examples and c) a corresponding Excel spreadsheet...publishedVersio

Geostängslade BK4-transporter vid bropassager och på tjälade vägar

Geofenced heavy trucks to protect bridges at crossings allowing higher weight on frozen roads Winter is our friend. When the road body is deep frozen it can handle more weight than during the rest of the year. However, the bridges are not affected by the cold weather, and they are therefore still vulnerable to increased loads. How can we allow increased loads on frozen roads while ensuring protection of the bridges? In this report, we share our insights from a project with the idea of using geofencing to protect the bridges. The geofencing technology ensures that the truck drives at a lower speed over the bridge and the bridge can withstand loads up to 74 tons since decreased speed reduces dynamic loads. If the road keeper can get guarantees that all heavy trucks drive at a low speed over the bridge, heavier traffic can be accommodated. This technology would of course also be beneficial to use across bridges in Europe regardless of the climate. ' The project “Frozen roads and 74 tons”, paid by the Swedish Transport Administration, consisted of three parts. One part was a pilot study during winter 22/23 demonstrating trucks from AB Volvo and Scania loaded with 74 tons using geofencing when the trucks passed over weak bridges. A speed limit, i.e. 50 km/h, was imposed in a zone around each bridge, whose coordinates were stored in the digital map accessible through the trucks’ Fleet Management System. Two different geofencing technologies were tested: on the one hand Scania’s system with “active” geofencing, where the truck was programmed to maintain the allowed speed over the bridge and calculated and implemented this itself (the driver could, however, override this by pushing the gas pedal to the floor); on the other hand AB Volvo’s system with “passive” geofencing, where the driver received a warning message when approaching the zone and would then slow down if necessary. The drivers were interviewed before and after the pilot about their experience. The results from the pilot showed that if the technology is verified, the truck will do the right thing and is on the right road network when the technology is activated. The drivers also liked geofencing. Geofences thus work in practice. The second part of the project was about quantifying the societal benefits of using geofencing. More efficient planning, control and follow-up can lower costs, reduce environmental impact, and increase traffic safety. Calculations in the project show that about 12 percent of timber transports in Norrland use frozen roads. They can benefit from the technology and if the technology is introduced, the industry would make savings of the equivalent of SEK 15 million / year and reduced energy use equivalent to 280 cubic meter diesel. At national level, this corresponds to an energy efficiency potential of 0.12 percent. The third part of the project was about policy and regulation. Can we use the current legislation, or do we need new legislation to scale the use of geofencing across bridges? How can we ensure compliance? How can we share data? How can we handle EU trade barriers? In the report, we have suggestions for policy and legislation to implement the geofencing technology to protect sensitive bridges. Our analysis shows that it is possible with today's regulations for an authority to introduce regulations on geofences. Such rules should preferably be based on functional requirements and a system of self-monitoring