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# Applying a Step Approach Method in Solving the Multi-Frequency Radiation From a Complex Obstacle

Jui-Hsiang Kao1

Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung, Taiwan, R.O.C.

Computer Modeling in Engineering & Sciences 2016, 112(1), 59-73. https://doi.org/10.3970/cmes.2016.112.059

## Abstract

In this paper, a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies. The computing scheme is based on the Boundary Integral Equation and derived in the time domain; thus, the time-harmonic Neumann boundary condition can be imposed. By the present method, the values of the initial conditions are set to zero, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated. After several loops, the correct radiated pressures can be obtained. A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first. This result is compared with the analytical solution, and both of them are in good agreement. Then, a complex-shaped radiator is taken as the studied case. The pulsating frequency of this case is multiple, and the waves propagate in half space. It is shown that the present method can treat multiple-frequency pulsation well, even when the radiator is a complex shape, and a robust convergence can be attained quickly.

## Keywords

APA Style
Kao, J. (2016). Applying a step approach method in solving the multi-frequency radiation from a complex obstacle. Computer Modeling in Engineering & Sciences, 112(1), 59-73. https://doi.org/10.3970/cmes.2016.112.059
Vancouver Style
Kao J. Applying a step approach method in solving the multi-frequency radiation from a complex obstacle. Comput Model Eng Sci. 2016;112(1):59-73 https://doi.org/10.3970/cmes.2016.112.059
IEEE Style
J. Kao, "Applying a Step Approach Method in Solving the Multi-Frequency Radiation From a Complex Obstacle," Comput. Model. Eng. Sci., vol. 112, no. 1, pp. 59-73. 2016. https://doi.org/10.3970/cmes.2016.112.059

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