Search results for "Helmholtz"
showing 10 items of 75 documents
Melting temperature prediction by thermoelastic instability: An ab initio modelling, for periclase (MgO)
2021
Abstract Melting temperature (TM) is a crucial physical property of solids and plays an important role for the characterization of materials, allowing us to understand their behavior at non-ambient conditions. The present investigation aims i) to provide a physically sound basis to the estimation of TM through a “critical temperature” (TC), which signals the onset of thermodynamic instability due to a change of the isothermal bulk modulus from positive to negative at a given PC-VC-TC point, such that (∂P/∂V)VC,TC = -(∂2F/∂V2) VC,TC = 0; ii) to discuss the case of periclase (MgO), for which accurate melting temperature observations as a function of pressure are available. Using first princip…
Interferences in Locally Resonant Sonic Metamaterials Formed from Helmholtz Resonators
2019
[EN] The emergence of materials artificially designed to control the transmission of waves, generally called metamaterials, has been a hot topic in the field of acoustics for several years. The design of these metamaterials is usually carried out by overlapping different wave control mechanisms. An example of this trend is the so-called Locally Resonant Sonic Materials, being one of them the Phononic Crystals with a local resonant structure. These metamaterials are formed by sets of isolated resonators in such a way that the control of the waves is carried out by resonances and by the existence of Bragg bandgaps, which appear due to the ordered distribution of the resonators. Their use is b…
Enhancing the sound absorption of small-scale 3D printed acoustic metamaterials based on Helmholtz resonators
2018
Acoustic metamaterials have recently become of interest for their ability to attenuate sound by breaking the mass-density law. In this paper, acoustic metamaterials based on Helmholtz resonators and capable of attenuating sound up to 30 dB are fabricated for sound absorption applications in the small scale. The proposed metamaterials are subwavelength at a factor of $\lambda /12$ with respect to the lateral dimension of the units. The directional response due to the position of the acoustic source on the sound attenuation provided by the metamaterial is investigated by controlling the location of a loudspeaker with a robot arm. To enhance and broaden the absorption bands, structural modific…
Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function
2009
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A s…
Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics
2010
Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz pro…
An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation
2007
A preconditioner defined by an algebraic multigrid cycle for a damped Helmholtz operator is proposed for the Helmholtz equation. This approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRES method are studied with linear, quadratic, and cubic finite element discretizations. Numerical experiments are performed with two-dimensional problems describing acoustic scattering in a cross-section of a car cabin and in a layered medium. Asymptotically the number of iterations grows linearly with respect to the frequency while for lower freq…
A damping preconditioner for time-harmonic wave equations in fluid and elastic material
2009
A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains. peerReviewed
A class of shear deformable isotropic elastic plates with parametrically variable warping shapes
2017
A homogeneous shear deformable isotropic elastic plate model is addressed in which the normal transverse fibers are allowed to rotate and to warp in a physically consistent manner specified by a fixed value of a real non-negative warping parameter ω. On letting ω vary continuously (at fixed load and boundary conditions), a continuous family of shear deformable plates Pω is generated, which spans from the Kirchhoff plate at the lower limit ω=0, to the Mindlin plate at the upper limit ω=∞; for ω=2, Pω identifies with the third-order Reddy plate. The boundary-value problem for the generic plate Pω is addressed in the case of quasi-static loads, for which a principle of minimum total potential …
The Theories of Helmholtz in the Work of Varèse
2011
In 1905 Varese discovered the French edition of Die Lehre von den Tonempfindungen als physiologische Grundlage fur die Theorie der Musik [On the Sensations of Tone as a Physiological Basis for the Theory of Music] of Hermann von Helmholtz (1863), the explicit intention of which was to bring together the common frontiers of science and music. This discovery was a revelation for the 22-year-old composer that went on to condition his whole philosophy of sound. The experiences of the German scientist, achieved with the aid of sirens, resonators or tuning forks, caught the imagination of the young composer. This article investigates the importance of the theories of Helmholtz for the Varesian ae…
Modelling of thermo-chemical properties over the sub-solidus MgO–FeO binary, as a function of iron spin configuration, composition and temperature
2014
Thermo-chemical properties and T–X phase relations diagram of the (Mg,Fe)O solid solution are modelled using mixing Helmholtz energy, ΔF(T,x)mixing, calculated by quantum mechanical and semi-empirical techniques. The sub-solidus MgO–FeO binary has been explored as a function of composition, with iron either in high-spin (HS) or low-spin (LS) configuration. Only the HS model provides physically sound results at room pressure, yielding a correct trend of cell edge versus composition, whereas LS’s issues are at variance with observations. Mixing Helmholtz energy has been parametrized by the following relationship: ΔF(T,x)mixing = x × y × [U0(T) + U1(T) × (x – y) + U2(T) × (x − y)2]−T × S(x,y)c…