Natural mode analysis of an acoustic cavity with multiple elliptical boundaries by using the collocation multipole method

Lee, W.M.

doi:10.1016/j.jsv.2011.05.001

Cited by 24 publications

(9 citation statements)

References 19 publications

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“…e sound field obtained by the analytical model was similar to that obtained by the boundary element method model. Lee [33] proposed a semianalytical method for solving the cavity eigenvalue problem with multiple elliptic boundaries. ey gave the multipole expansion of sound pressure in the form of angular and radial Mathieu functions.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Acoustic Characteristics of Arbitrary Triangular Prism and Quadrangular Prism Acoustic Cavities

Shi

Zhang

2019

Shock and Vibration

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This paper proposes a method for the analysis of acoustic modals and steady-state responses of arbitrary triangular prism and quadrangular prism acoustic cavities based on the three-dimensional improved Fourier series. First, the geometric models of arbitrary triangular prism and quadrangular prism acoustic cavities are established. To facilitate the calculation, the bottom and top surfaces of the irregular cavity are converted into the unit square domain by a coordinate transformation. Internal sound pressure-admissible functions are constructed, and energy expressions are derived after coordinate transformation based on the three-dimensional improved Fourier series. The acoustic modals of arbitrary triangular prism and quadrangular prism acoustic cavities are obtained by the Rayleigh–Ritz technique. At the same time, a point sound source excitation is introduced into the cavity to further study the steady-state responses of prismatic acoustic cavities with different acoustic impedance boundary conditions. The reliability and universality of the method are verified by comparing with the finite element results. The method and results can provide some references and benchmarks for future research and application.

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Section: Introductionmentioning

confidence: 99%

Analysis of Acoustic Characteristics of Arbitrary Triangular Prism and Quadrangular Prism Acoustic Cavities

Shi

Zhang

2019

Shock and Vibration

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“…By means of a semi-analytical and semi-empirical method, an explicit expression of the stress concentration factor for a tension finite-width strip with a central elliptical hole was obtained in [6]. Furthermore, a semi-analytical approach based on the collocation multipole technique was developed by Lee [7,8] to solve the acoustic eigenproblem of elliptical cylindrical cavities with a multiple elliptical boundary. In addition, scattering problems by cavities of arbitrary shape in an infinite and isotropic plate for guide waves [9] and vibration problems [10] have been investigated in recent years.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of elastic waves by an arbitrary cavity in an inhomogeneous medium with density variation

Hei

Yang

Wang

et al. 2016

Mathematics and Mechanics of Solids

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Based on complex function theory, an analytical solution for the dynamic stress concentration due to an arbitrary cylindrical cavity in an infinite inhomogeneous medium is investigated. Two different conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. By assuming that the medium density continuously varies in the horizontal direction with an exponential law and the elastic modulus is constant, the complex-value displacements and stresses of the inhomogeneous medium are explicitly obtained. The distribution of the dynamic stress for the case of an elliptical cavity are obtained and discussed in detail via a numerical example. The results show that the wavenumber, inhomogeneous parameters, and different values of aspect ratio have a significant influence on the dynamic stress concentration factors around the elliptical cavity.

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“…Moreover, an in-depth understanding of the natural mode frequencies and mode shapes of pressure oscillations in modern combustion systems (such as gas turbines and rocket engines) is critically important for safety reasons, as thermo-acoustic excitation is commonly observed, which may lead to strong discretefrequency oscillations and combustion instabilities (Davis, 2008;Dowling and Stow, 2003;Keller, 1995). While methods for both numerical and analytical solutions have been developed to obtain natural frequencies and mode shapes of acoustic resonance in cavities with different shapes (Blevins, 1979;Dowling, 1995;Dowling and Stow, 2003;Hong and Kim, 1995;Kim and Soedel, 1989;Lee, 2011;Mirsky, 1965aMirsky, , 1965b, experimental studies were mostly limited to natural frequencies based on local pressure measurement (Hickling et al, 1983;Payri et al, 2005;Stanković and Böhme, 1999). Only a few studies have been conducted to visualize the mode shapes in cavities using microphone measurements (Gregory et al, 2006;Mamede and Varoto, 2003) and Schlieren measurements (Chinnery and Humphrey, 1996).…”

Section: Introductionmentioning

confidence: 99%

Visualization of the Mode Shapes of Pressure Oscillation in a Cylindrical Cavity

Wang

et al. 2015

Combustion Science and Technology

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This article describes a novel experimental method to visualize the mode shapes of pressure oscillation in a cylindrical cavity. Acoustic resonance in a cavity is a grand old problem that has been under investigation (using both analytical and numerical methods) for more than a century. In this article, a novel method based on high speed imaging of combustion chemiluminescence was presented to visualize the mode shapes of pressure oscillation in a cylindrical cavity. By generating high-temperature combustion gases and strong pressure waves simultaneously in a cylindrical cavity, the pressure oscillation can be inferred due to the chemiluminescence emissions of the combustion products. The mode shapes can then be visualized by reconstructing the images based on the amplitudes of the luminosity spectrum at the corresponding resonant frequencies. Up to 11 resonant mode shapes were clearly visualized, each matching very well with the analytical solutions.

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Natural mode analysis of an acoustic cavity with multiple elliptical boundaries by using the collocation multipole method

Cited by 24 publications

References 19 publications

Analysis of Acoustic Characteristics of Arbitrary Triangular Prism and Quadrangular Prism Acoustic Cavities

Analysis of Acoustic Characteristics of Arbitrary Triangular Prism and Quadrangular Prism Acoustic Cavities

Dynamic analysis of elastic waves by an arbitrary cavity in an inhomogeneous medium with density variation

Visualization of the Mode Shapes of Pressure Oscillation in a Cylindrical Cavity

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