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Research Papers

Sound Radiation Response of a Rectangular Plate Having a Side Crack of Arbitrary Length, Orientation, and Position

[+] Author and Article Information
Tanmoy Bose

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: tanmoy.jgec04@gmail.com

Amiya R. Mohanty

Professor
Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: amohanty@mech.iitkgp.ernet.in

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 28, 2014; final manuscript received December 17, 2014; published online February 12, 2015. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 137(2), 021019 (Apr 01, 2015) (10 pages) Paper No: VIB-14-1150; doi: 10.1115/1.4029449 History: Received April 28, 2014; Revised December 17, 2014; Online February 12, 2015

Here, sound radiation characteristics of a rectangular plate having a side crack of different crack lengths, orientations, and positions are studied considering clamped boundary conditions. First, a free and forced vibration response analysis of a cracked plate is done using the Ritz method. Orthogonal polynomials are used for faster convergence and some corner functions are used to generate the effect of a crack. Radiated sound power and radiation efficiency of the cracked plate are computed by the quadruple integration. A convergence test of radiation efficiency is carried out to fix the number of polynomials and corner functions in the analysis. It is found that the radiation efficiency and radiated sound power computed by the Ritz method are close to the same obtained from the boundary element method (BEM). The natural frequencies computed using the Ritz method are also found to be close to that obtained from the finite element method (FEM). The radiation efficiency curves of different modes are shown for a change in crack length, orientation and position. Finally, the variations of normalized sound power are shown to be due to a change in the crack parameters.

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Figures

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Fig. 1

A rectangular plate with a side crack

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Fig. 2

Rectangular cracked plate surrounded by an infinite baffle and subjected to a concentrated force

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Fig. 3

Comparison of (a) radiation efficiency and (b) sound power of a cracked plate computed by the BEM and the Ritz method (using N = 5)

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Fig. 4

Radiation efficiency variation with crack length for four modes of a cracked plate: (a) first mode, (b) second mode, (c) fourth mode, and (d) fifth mode

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Fig. 5

Radiation efficiency variation with crack angle for four modes of a cracked plate: (a) first mode, (b) second mode, (c) fourth mode, and (d) fifth mode

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Fig. 6

Radiation efficiency variation with crack position for four modes of a cracked plate: (a) first mode, (b) second mode, (c) fourth mode, and (d) fifth mode

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Fig. 7

(a) Normalized sound power of a cracked plate and (b) its variation with different crack length ratios in the fourth mode

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Fig. 8

(a) Normalized sound power of a cracked plate and (b) its variation with different crack angles in the fourth mode

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Fig. 9

(a) Normalized sound power of a cracked plate and (b) its variation with different crack positions in the fourth mode

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