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Finite Element Method
Published in Young W. Kwon, Multiphysics and Multiscale Modeling, 2015
where c is the speed of sound, and c2=B/ρo. The boundary conditions to the acoustic wave equation are either prescribed velocity or pressure. The velocity is computed from the velocity potential as defined in Equation 2.232. On the other hand, the pressure boundary condition is expressed from Equation 2.233, such as () p=ρo∂ϕ∂t
Practical Numerical Acoustics
Published in David A. Bies, Colin H. Hansen, Engineering Noise Control, 2017
The acoustic wave equation (Equation (1.15)) is used to describe the acoustic response of the fluid. Because viscous dissipation of the fluid is neglected, the equation is referred to as the lossless wave equation. Suitable acoustic finite elements can be derived by discretising the lossless wave equation using the Galerkin method. For a derivation of the acoustic finite element the reader is referred to Craggs (1971).
Assessment of cavitation noise in a centrifugal pump using acoustic finite element method and spherical cavity radiation theory
Published in Engineering Applications of Computational Fluid Mechanics, 2023
Qiaorui Si, Asad Ali, Minquan Liao, Jianping Yuan, Yuanyuan Gu, Shouqi Yuan, Gerard Bois
The acoustic analogy method is based on the Lighthill acoustic analogy, in which the fluid is first regarded as incompressible to complete the hydrodynamic analysis. The CFD technique is usually used to solve the unsteady flow information of the ‘hydraulic near field’. Then, considering the fluid’s compressibility, the fluid dynamics calculation is transformed into the fluid source calculations. Finally, the acoustic field is solved by solving the acoustic wave equation. Compared with the direct method of the acoustic field, the analysis of the acoustic analogy method is relatively small. The theoretical basis of the indirect method is the Lighthill acoustic analog equation, which is derived from the N-S square path: where is the Lighthill stress tensor; is the fluid density; represents the Kronecker function; indicates fluid pressure; indicates the undisturbed pressure of the fluid; represents the time; indicates the sound speed; is the space coordinate; and are the coordinate axis locations.
Manufacturing of membrane acoustical metamaterials for low frequency noise reduction and control: A review
Published in Mechanics of Advanced Materials and Structures, 2023
Chao Wang, Lin Cai, Mingchen Gao, Lei Jin, Lucheng Sun, Xiaoyun Tang, Guangyu Shi, Xin Zheng, Chunyu Guo
The following equation is the acoustic wave equation in the passive homogeneous medium: where is sound pressure, is mass density, and is bulk modulus. The reason why acoustic metamaterials, as mentioned in the introduction, are able to absorb low-frequency sound is due to their specific structures that give them negative mass density or negative bulk density. In contrast, conventional materials typically have positive mass density and bulk density. Negative mass density refers to the acceleration generated inside the structure in the opposite direction of the external force when there is an external force, that is Negative bulk modulus means that when the structure is squeezed externally, the interior of the structure is not squeezed but expanded, that is Therefore, acoustic metamaterials can be classified into four types: conventional materials, negative mass density materials, negative bulk modulus materials, and “double negative” [49–52] materials, which refer to materials with both negative mass density and negative bulk modulus.
Regularization of the boundary control method for numerical solutions of the inverse problem for an acoustic wave equation
Published in Inverse Problems in Science and Engineering, 2021
Let . Let σ be a bounded domain in the plane , such that . The initial boundary value problem for an acoustic wave equation where p is the acoustic pressure, c and ρ are the sound speed and mass density, ν is the outward normal to the -plane, and T>0 is the final time, is considered as a mathematical model of propagation and scattering of acoustic waves in fluids. In this regard, the following inverse problem for Equation (1) is of our immediate interest in this paper. For a fixed control f denote a solution to the problem (1)–(2).