• The Journal of the Acoustical Society of Korea
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• v.7 no.4
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• pp.22-30
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• 1988

In this paper, the sound radiation from a clamped circular plate in an infinite baffle is calculated by using the FFT technique. The radiated sound fields are obtained by two-dimensional fast Fourier transform method is the spatial domain instead of a direct numerical evaluation of Rayleigh integral for economy of the computation time. The computation time is consumed at least by 1/200 times of the direct numerical evaluation on the Rayleigh integral in acoustic fields. The FFT method can be applicable to any shaped geometry as well as circular plate. The FFT solution could be very powerful in predicting the near and far fields of complex structures.

• Journal of Biomedical Engineering Research
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• v.11 no.1
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• pp.89-96
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• 1990

The numerical evaluation of Rayleigh's integral for the sound source reconstruction can be speeded up by the use of angular frequency propagation method and the FFT. However, are several source of errors involved during the reconstruction. Besides the aliasing error due to undersampling in space, the wrap around error. which is caused by undersampling the kernel functionin frequency domain, and windowing effect are present. We found that there is no replicated source problem and the windowing effect is due to the windowing the kernel function In frequency domain, and, xero padding is always required to improve the quality of reconstruction.

• Journal of Biomedical Engineering Research
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• v.10 no.3
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• pp.323-330
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• 1989

Large bias errors which occur during a numerical evaluation of the Rayleigh's integral is not due to the replicated source problem but due to the coincidence of singularities of the Green's function and the sampling points in Fourier domain. We found that there is no replicated source problem in evaluating the Rayleigh's integral numerically by the reason of the periodic assumption of the input sequence in Dn or by the periodic sampling of the Green's function in the Fourier domain. The wrap around error is not due to an overlap of the individual adjacent sources but berallse of the undersampling of the Green's function in the frequency domain. The replicated and overlApped one is inverse Fourier transformed Green's function rather than the source function.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.417-425
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• 2018

The main aim of this paper is to investigate the bending of Euler-Bernouilli nano-beams made of bi-directional functionally graded materials (BDFGMs) using Eringen's non-local elasticity theory in the integral form with compare the differential form. To the best of the researchers' knowledge, in the literature, there is no study carried out into integral form of Eringen's non-local elasticity theory for bending analysis of BDFGM Euler-Bernoulli nano-beams with arbitrary functions. Material properties of nano-beam are assumed to change along the thickness and length directions according to arbitrary function. The approximate analytical solutions to the bending analysis of the BDFG nano-beam are derived by using the Rayleigh-Ritz method. The differential form of Eringen's non-local elasticity theory reveals with increasing size effect parameter, the flexibility of the nano-beam decreases, that this is unreasonable. This problem has been resolved in the integral form of the Eringen's model. For all boundary conditions, it is clearly seen that the integral form of Eringen's model predicts the softening effect of the non-local parameter as expected. Finally, the effects of changes of some important parameters such as material length scale, BDFG index on the values of deflection of nano-beam are studied.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.9
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• pp.695-705
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• 2014

In this paper, two types of techniques for the prediction of radiated sound pressure due to vibration of a structure are investigated. The prediction performance using wave-number sensing technique is compared to that of conventional prediction method, such as Rayleigh's integral method, for the prediction of far-field radiated sound pressure. For a coupled plate, wave-number components are predicted by the vibration response of plate and the prediction performance of far-field sound is verified. In addition, the applicability of distributed sensors that are not allowable to Rayleigh's integral method is considered and these can replace point sensors. Experimental implementation verified the prediction accuracy of far-field sound radiation by the wave-number sensing technique. Prediction results from the technique are as good as those of Rayleigh's integral method and with distributed sensors, more reduced computation time is expected. To predict the radiated sound by the efficient configuration of structural sensors, composed(synthesized) mode considering sound power contribution is determined and from this size and location of sensors are chosen. Four types of sensor configuration are suggested, simulated and compared.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.229-244
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• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• The Journal of the Acoustical Society of Korea
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• v.27 no.8
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• pp.411-417
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• 2008

An alternative formulation of the Helmholtz integral equation derived to express the pressure field explicitly in terms of the velocity vector of a radiating surface is used to solve acoustic radiation and fluid/structure interaction problems. This formulation, derived for arbitrary sources, is similar in form to the Rayleigh's formula for planar sources. Because the surface pressure field is expressed explicitly as a surface integral of the surface velocity, which can be implemented numerically using standard Gaussian quadratures, there is no need to use BEM to solve a set of simultaneous equations for the surface pressure at the discretized nodes. Furthermore the non-uniqueness problem inherent in methods based on Helmholtz integral equation is avoided. Validation of this formulation is demonstrated for some simple geometries.

• Journal of the Korean Society for Nondestructive Testing
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• v.20 no.2
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• pp.91-101
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• 2000

Modeling of radiation beam from ultrasonic transducers has been investigated extensively, since it is one of the most important, fundamental issues that have great influence on the accuracy of an ultrasonic measurement model. Here, three popular radiation models, namely the Rayleigh-Sommerfeld integral model, the boundary diffraction wave model and the edge element model, are discussed briefly, and the radiation beam fields from ultrasonic transducers with planar, circular and rectangular cross-sections are calculated using these three models. Then, the accuracy and the time-efficiency of these methods are compared based on the calculation results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.5
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• pp.430-436
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• 2011

The purpose of this study is to analyze the vibration and sound generation characteristics of the sandwich panel. Two thick panels were assumed to be separated by a compliant viscoelastic core. The transverse vibration induced by an external impact was analyzed using the Rayleigh-Ritz method. For applying arbitrary boundary condition of the panels, the edges were assumed to be supported by the translational and rotational springs. The beam functions were used as the trial functions. The effect of the boundary condition and viscoelastic core on the resulting vibration characteristics was investigated. The radiated sound power was analyzed using the proposed numerical model and the Rayleigh integral. The dynamic properties of the core and the mass-stiffness-mass resonance frequency had significant influence on the impact sound.

• Journal of Advanced Marine Engineering and Technology
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• v.33 no.1
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• pp.19-27
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• 2009

Globally, customer appreciation and demand for quieter products has driven noise control engineers to develop efficient and quieter products in a relatively short time. In the vehicles and ship industry, noise has become an important attribute because of the competitive market and increasing customer awareness. Noise reduction is often achieved through structural modifications by typical approaches. In the present paper, author describes a fundamental study on optimum design of curvature. Bezier curve. and rib attachment to reduce noise from simple panel using a genetic algorithm(GA). The acoustic optimization procedure employed p-FEM for structural analysis, the Rayleigh integral method for acoustic analysis and the GA for searching optimum design. In the optimization procedure. the objective function to be minimized is the average sound power radiated from an objective structure over a given frequency range $0{\sim}300$ Hz.