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http://hdl.handle.net/10985/7362
On waveguide modeling of stiff piano string
DUCASSE, Eric
Bensa et al. [J. A Coust. Soc. Am. 114(2) 1095-1107 (2003), Section IV] recently proposed a waveguide model for the transverse displacement of a stiff piano string. The study described here is an attempt to cast a complementary light on this topic, based on a common wave approach instead of a modal approach. A pair of weakly attenuated traveling waves and a pair of fast-decaying waves both satisfy the one-dimensional wave equation developed by Bensa et al.. These solutions have to be carefully considered, however, for portions of string interacting with the hammer felt, the bridge, or the capo d'astro bar.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10985/73622005-01-01T00:00:00ZDUCASSE, EricBensa et al. [J. A Coust. Soc. Am. 114(2) 1095-1107 (2003), Section IV] recently proposed a waveguide model for the transverse displacement of a stiff piano string. The study described here is an attempt to cast a complementary light on this topic, based on a common wave approach instead of a modal approach. A pair of weakly attenuated traveling waves and a pair of fast-decaying waves both satisfy the one-dimensional wave equation developed by Bensa et al.. These solutions have to be carefully considered, however, for portions of string interacting with the hammer felt, the bridge, or the capo d'astro bar.Time-domain computation of the response of composite layered anisotropic plates to a localized source
http://hdl.handle.net/10985/8562
Time-domain computation of the response of composite layered anisotropic plates to a localized source
DUCASSE, Eric; DESCHAMPS, Marc
This paper describes how a modal approach in the time-domain can be suitable for calculating the elastodynamic field in a layered plate. This elastodynamic field is generated by impulsive sources located in a small region of a composite plate consisting of anisotropic layers stuck together. The aim is to calculate the transient response of the elastic plate around the location of the sources, generally emitting nn-cycle pulses. First, we apply a 2D Fourier transform to the wave equation with respect to the coordinates in the plate plane, and then, in the 2D spectrum domain, for any given wave-vector in the plate plane, solving a vibration problem with respect to time and position in the direction perpendicular to the plate. The solution is expressed as the sum of mode responses, each mode having a resonance frequency and a shape which depend on the wave-vector in the plate plane. These calculations are different from those obtained by the usual method in the harmonic domain, where the modes are searched for a fixed frequency, such as Lamb waves, i.e. guided waves that propagate along the plate. In our case, the solution is given as a summation of plate resonances, i.e. a decomposition on the real eigenfrequencies, associated to Lamb waves with the same fixed wave-vector. This difference is of importance since only Lamb modes with real frequencies and real-valued wavenumbers in the plate plane are involved here, contrary to the usual harmonic methods, where these modes can be evanescent. This is of great interest as it can simplify the calculation of the generated field near the source. Finally, we obtain a solution in the physical domain by performing an inverse 2D Fourier transform. After a detailed description of the method, results are shown for two typical plates. It is emphasized that the method is accurate for observation points located both above or below the source and reasonably far from it along the plate.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/85622014-01-01T00:00:00ZDUCASSE, EricDESCHAMPS, MarcThis paper describes how a modal approach in the time-domain can be suitable for calculating the elastodynamic field in a layered plate. This elastodynamic field is generated by impulsive sources located in a small region of a composite plate consisting of anisotropic layers stuck together. The aim is to calculate the transient response of the elastic plate around the location of the sources, generally emitting nn-cycle pulses. First, we apply a 2D Fourier transform to the wave equation with respect to the coordinates in the plate plane, and then, in the 2D spectrum domain, for any given wave-vector in the plate plane, solving a vibration problem with respect to time and position in the direction perpendicular to the plate. The solution is expressed as the sum of mode responses, each mode having a resonance frequency and a shape which depend on the wave-vector in the plate plane. These calculations are different from those obtained by the usual method in the harmonic domain, where the modes are searched for a fixed frequency, such as Lamb waves, i.e. guided waves that propagate along the plate. In our case, the solution is given as a summation of plate resonances, i.e. a decomposition on the real eigenfrequencies, associated to Lamb waves with the same fixed wave-vector. This difference is of importance since only Lamb modes with real frequencies and real-valued wavenumbers in the plate plane are involved here, contrary to the usual harmonic methods, where these modes can be evanescent. This is of great interest as it can simplify the calculation of the generated field near the source. Finally, we obtain a solution in the physical domain by performing an inverse 2D Fourier transform. After a detailed description of the method, results are shown for two typical plates. It is emphasized that the method is accurate for observation points located both above or below the source and reasonably far from it along the plate.A Physical Model of a Single-Reed Wind Instrument, Including Actions of the Player
http://hdl.handle.net/10985/7360
A Physical Model of a Single-Reed Wind Instrument, Including Actions of the Player
DUCASSE, Eric
For the Physical Modeling Synthesis of wind instruments, we choose to design a model adapted to time domain simulation which takes into account the main part of the physical phenomena, including instrument/player interactions. The virtual instrument is designed as a set of lumped elements, e.g. the mouth, the key or the bell, connected to each other by two-ports representing the tube. The sounds obtained show that the accuracy of the modeling of a specific mechanism is less important than the modeling, even simplified, of all the significant actions of the player on his instrument.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10985/73602003-01-01T00:00:00ZDUCASSE, EricFor the Physical Modeling Synthesis of wind instruments, we choose to design a model adapted to time domain simulation which takes into account the main part of the physical phenomena, including instrument/player interactions. The virtual instrument is designed as a set of lumped elements, e.g. the mouth, the key or the bell, connected to each other by two-ports representing the tube. The sounds obtained show that the accuracy of the modeling of a specific mechanism is less important than the modeling, even simplified, of all the significant actions of the player on his instrument.A nonstandard wave decomposition to ensure the convergence of Debye series for modeling wave propagation in an immersed anisotropic elastic plate
http://hdl.handle.net/10985/7388
A nonstandard wave decomposition to ensure the convergence of Debye series for modeling wave propagation in an immersed anisotropic elastic plate
DUCASSE, Eric; DESCHAMPS, Marc
When ultrasonic guided waves in an immersed plate are expressed as Debye series, they are considered as the result of successive reflections from the plate walls. Against all expectations, the Debye series can diverge for any geometry if inhomogeneous waves are involved in the problem. For an anisotropic elastic plate immersed in a fluid, this is the case if the incidence angle is greater than the first critical angle.Physically, this divergence can be explained by the energy coupling between two inhomogeneous waves of same kind of polarization, which are expressed by conjugate wavenumbers. Each of these latter inhomogeneous waves does not transfer energy but a linear combination of them can do it. Mathematically, this is due to the fact that inhomogeneous waves do not constitute a basis orthogonal in the sense of energy, contrarily to homogeneous waves. To avoid that difficulty, an orthogonalization of these inhomogeneous waves is required. Doing so, nonstandard upgoing and downgoing waves in the plate are introduced to ensure the convergence of the new Debye series written in the basis formed by these latter waves. The case of an aluminum plate immersed in water illustrates this study by giving numerical results and a detailed description of the latter nonstandard waves. The different reflection and refraction coefficients at each plate interface are analyzed in terms of Debye series convergence and of distribution of energy fluxes between the waves in the plate. From that investigation, an interesting physical phenomenon is described for one specific pair “angle of incidence/frequency”. For this condition, the quasi-energy brought by the incident harmonic plane wave crosses the plate without any conversion to reflected waves either at the first interface or at the second interface. In this zone, there is a perfect impedance matching between the fluid and the plate.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/73882012-01-01T00:00:00ZDUCASSE, EricDESCHAMPS, MarcWhen ultrasonic guided waves in an immersed plate are expressed as Debye series, they are considered as the result of successive reflections from the plate walls. Against all expectations, the Debye series can diverge for any geometry if inhomogeneous waves are involved in the problem. For an anisotropic elastic plate immersed in a fluid, this is the case if the incidence angle is greater than the first critical angle.Physically, this divergence can be explained by the energy coupling between two inhomogeneous waves of same kind of polarization, which are expressed by conjugate wavenumbers. Each of these latter inhomogeneous waves does not transfer energy but a linear combination of them can do it. Mathematically, this is due to the fact that inhomogeneous waves do not constitute a basis orthogonal in the sense of energy, contrarily to homogeneous waves. To avoid that difficulty, an orthogonalization of these inhomogeneous waves is required. Doing so, nonstandard upgoing and downgoing waves in the plate are introduced to ensure the convergence of the new Debye series written in the basis formed by these latter waves. The case of an aluminum plate immersed in water illustrates this study by giving numerical results and a detailed description of the latter nonstandard waves. The different reflection and refraction coefficients at each plate interface are analyzed in terms of Debye series convergence and of distribution of energy fluxes between the waves in the plate. From that investigation, an interesting physical phenomenon is described for one specific pair “angle of incidence/frequency”. For this condition, the quasi-energy brought by the incident harmonic plane wave crosses the plate without any conversion to reflected waves either at the first interface or at the second interface. In this zone, there is a perfect impedance matching between the fluid and the plate.An alternative to the traveling-wave approach for use in two-port descriptions of acoustics bores
http://hdl.handle.net/10985/7361
An alternative to the traveling-wave approach for use in two-port descriptions of acoustics bores
DUCASSE, Eric
For more than a decade, the digital waveguide model for musical instruments has been improved through the simulation of cylindrical and conical bores. But several difficulties remain, such as instabilities due to growing exponentials which appear when two conical bores are connected with decreasing taper. In this paper, an alternative overcoming these difficulties is proposed and can be extended to shapes other than cylinders, cones, and hyperbolic horns. A two-port model with more general state variables than usual traveling waves works efficiently for any shape without discontinuities in cross-section. The equations for connecting separate elements at discontinuities make this two-port model appropriate for use in time domain simulation of the physical behavior of the wind instrument and its interactions with the player. The potential of this new approach is illustrated by several detailed examples.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10985/73612002-01-01T00:00:00ZDUCASSE, EricFor more than a decade, the digital waveguide model for musical instruments has been improved through the simulation of cylindrical and conical bores. But several difficulties remain, such as instabilities due to growing exponentials which appear when two conical bores are connected with decreasing taper. In this paper, an alternative overcoming these difficulties is proposed and can be extended to shapes other than cylinders, cones, and hyperbolic horns. A two-port model with more general state variables than usual traveling waves works efficiently for any shape without discontinuities in cross-section. The equations for connecting separate elements at discontinuities make this two-port model appropriate for use in time domain simulation of the physical behavior of the wind instrument and its interactions with the player. The potential of this new approach is illustrated by several detailed examples.The Hankel transform of first- and second-order tensor fields: definition and use for modeling circularly symmetric leaky waveguides.
http://hdl.handle.net/10985/7374
The Hankel transform of first- and second-order tensor fields: definition and use for modeling circularly symmetric leaky waveguides.
DUCASSE, Eric; YAACOUBI, Slah
A tensor Hankel transform'' (THT) is defined for vector fields, such as displacement, and second-order tensor fields, such as stress or strain. The THT establishes a bijection between the real space and the wave-vector domain, and, remarkably, cannot be reduced to a scalar transform applied separately to each component. One of the advantages of this approach is that some standard elasticity problems can be concisely rewritten by applying this tensor integral transform coupled with an azimuthal Fourier series expansion. A simple and compact formulation of the boundary conditions is also achieved. Thanks to the THT, we obtain for each azimuthal wavenumber and each azimuthal direction exactly the same wave equation as for a standard 2D model of elastic wave propagation. Thus, waves similar to the standard plane P, SV and SH waves are naturally found. Lastly, the THT is used to calculate the ultrasonic field in an isotropic cylindrical leaky waveguide, the walls of which radiating into a surrounding elastic medium, by using a standard scattering approach.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/73742010-01-01T00:00:00ZDUCASSE, EricYAACOUBI, SlahA tensor Hankel transform'' (THT) is defined for vector fields, such as displacement, and second-order tensor fields, such as stress or strain. The THT establishes a bijection between the real space and the wave-vector domain, and, remarkably, cannot be reduced to a scalar transform applied separately to each component. One of the advantages of this approach is that some standard elasticity problems can be concisely rewritten by applying this tensor integral transform coupled with an azimuthal Fourier series expansion. A simple and compact formulation of the boundary conditions is also achieved. Thanks to the THT, we obtain for each azimuthal wavenumber and each azimuthal direction exactly the same wave equation as for a standard 2D model of elastic wave propagation. Thus, waves similar to the standard plane P, SV and SH waves are naturally found. Lastly, the THT is used to calculate the ultrasonic field in an isotropic cylindrical leaky waveguide, the walls of which radiating into a surrounding elastic medium, by using a standard scattering approach.Transient 3D elastodynamic field in an embedded multilayered anisotropic plate
http://hdl.handle.net/10985/10734
Transient 3D elastodynamic field in an embedded multilayered anisotropic plate
MORA, Pierric; DUCASSE, Eric; DESCHAMPS, Marc
The aim of this paper is to study the ultrasonic response to a transient source that radiates ultrasonic waves in a 3D embedded multilayered anisotropic and dissipative plate. The source can be inside the plate or outside, in a fluid loading the plate for example. In the context of Non-Destructive Testing applied to composite materials, our goal is to create a robust algorithm to calculate ultrasonic field, irrespective of the source and receiver positions. The principle of the method described in this paper is well-established. This method is based on time analysis using the Laplace transform. In the present work, it has been customized for computing ultrasonic source interactions with multilayered dissipative anisotropic plates. The fields are transformed in the 2D Fourier wave-vector domain for the space variables related to the plate surface, and they are expressed in the partial-wave basis. Surprisingly, this method has been very little used in the ultrasonic community, while it is a useful tool which complements the much used technique based on generalized Lamb wave decomposition. By avoiding mode analysis -- which can be problematic in some cases -- exact numerical calculations (i.e., approximations by truncating infinite series that may be poorly convergent are not needed) can be made in a relatively short time for immersed plates and viscoelastic layers. Even for 3D cases, numerical costs are relatively low. Special attention is given to separate up- and down-going waves, which is a simple matter when using the Laplace transform. Numerical results show the effectiveness of this method. Three examples are presented here to investigate the quality of the model and the robustness of the algorithm: first, a comparison of experiment and simulation for a monolayer carbon-epoxy plate, where the diffracted field is due to a source located on the first free surface of the sample, for both dissipative and non-dissipative cases; second, the basic configuration of an aluminum plate immersed in water has been chosen to study wave propagation in ZGV (Zero Group Velocity) conditions; finally, a 2D plate consisting of 8 stacked carbon-epoxy layers immersed in water is treated, with a source located inside the plate, distributed in depth and extending over four layers.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/107342016-01-01T00:00:00ZMORA, PierricDUCASSE, EricDESCHAMPS, MarcThe aim of this paper is to study the ultrasonic response to a transient source that radiates ultrasonic waves in a 3D embedded multilayered anisotropic and dissipative plate. The source can be inside the plate or outside, in a fluid loading the plate for example. In the context of Non-Destructive Testing applied to composite materials, our goal is to create a robust algorithm to calculate ultrasonic field, irrespective of the source and receiver positions. The principle of the method described in this paper is well-established. This method is based on time analysis using the Laplace transform. In the present work, it has been customized for computing ultrasonic source interactions with multilayered dissipative anisotropic plates. The fields are transformed in the 2D Fourier wave-vector domain for the space variables related to the plate surface, and they are expressed in the partial-wave basis. Surprisingly, this method has been very little used in the ultrasonic community, while it is a useful tool which complements the much used technique based on generalized Lamb wave decomposition. By avoiding mode analysis -- which can be problematic in some cases -- exact numerical calculations (i.e., approximations by truncating infinite series that may be poorly convergent are not needed) can be made in a relatively short time for immersed plates and viscoelastic layers. Even for 3D cases, numerical costs are relatively low. Special attention is given to separate up- and down-going waves, which is a simple matter when using the Laplace transform. Numerical results show the effectiveness of this method. Three examples are presented here to investigate the quality of the model and the robustness of the algorithm: first, a comparison of experiment and simulation for a monolayer carbon-epoxy plate, where the diffracted field is due to a source located on the first free surface of the sample, for both dissipative and non-dissipative cases; second, the basic configuration of an aluminum plate immersed in water has been chosen to study wave propagation in ZGV (Zero Group Velocity) conditions; finally, a 2D plate consisting of 8 stacked carbon-epoxy layers immersed in water is treated, with a source located inside the plate, distributed in depth and extending over four layers.Modeling principles for time-domain simulations of wind instruments in playing situations.
http://hdl.handle.net/10985/7379
Modeling principles for time-domain simulations of wind instruments in playing situations.
DUCASSE, Eric
The development of an evolutive free software which simulates the physical behavior of wind instruments in playing situations can be based on the following modular postulates. In an object-oriented context, the virtual instrument is designed as a set of “anticipative” and lumped elements. After connection rules are laid down, new elements are progressively added and each element is separately improved. One example illustrating this approach for single reed instruments includes modeling of air columns by usual waveguide or two-port, considerations about the reed, and a key-pad model. The current state-of-the-art research in acoustics has a great potential for future extensions.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10985/73792002-01-01T00:00:00ZDUCASSE, EricThe development of an evolutive free software which simulates the physical behavior of wind instruments in playing situations can be based on the following modular postulates. In an object-oriented context, the virtual instrument is designed as a set of “anticipative” and lumped elements. After connection rules are laid down, new elements are progressively added and each element is separately improved. One example illustrating this approach for single reed instruments includes modeling of air columns by usual waveguide or two-port, considerations about the reed, and a key-pad model. The current state-of-the-art research in acoustics has a great potential for future extensions.