Acoustical investigation of a thin plate having a part–through surface crack surrounded by an air enclosure is studied in this paper. The enclosure comprises five rigid walls and a flexible plate based on the Kirchhoff plate theory. It is also assumed that the crack is located at an arbitrary position and orientation with a specific length. Accordingly, partial differential equation related to the coupled cracked plate–cavity system is presented. In order for the partial differential equation (PDE) to be solved, firstly, the sound pressure inside the cavity is estimated by a suitable number of the plate modes. Then, the coupled PDE decomposes to some ordinary differential equations in the time-domain by employing the Galerkin method for three different boundary conditions. In addition, the linear natural frequencies are obtained in vacuo and coupled conditions for an uncracked plate and then, a similar procedure is performed for a cracked plate. Furthermore, comparing the results with available data in the literature shows the reliability and accuracy of the present work. Finally, the influences of the crack angle, crack length, crack position, and cavity depth on the natural frequencies are investigated.
BoseTMohantyA (2013) Vibration analysis of a rectangular thin isotropic plate with a part–through surface crack of arbitrary orientation and position. Journal of Sound and Vibration332(26): 7123–7141.
2.
BoseTMohantyAR (2015) Sound radiation response of a rectangular plate having a side crack of arbitrary length, orientation, and position. Journal of Vibration and Acoustics137(2): 021019.
3.
BoseTMohantyAR (2016) Detection and monitoring of side crack in a rectangular plate using mobility. Journal of Vibration and Control22(2): 585–594.
4.
ChenYJinGFengZ, et al.(2017) Modeling and vibro-acoustic analysis of elastically restrained panel backed by irregular sound space. Journal of Sound and Vibration409: 201–216.
5.
DibaFEsmailzadehEYounesianD (2014) Nonlinear vibration analysis of isotropic plate with inclined part–through surface crack. Nonlinear Dynamics78(4): 2377–2397.
6.
GormanDGTrendafilovaIMulhollandAJ, et al.(2008) Vibration analysis of a circular plate in interaction with an acoustic cavity leading to extraction of structural modal parameters. Thin-Walled Structures46(7–9): 878–886.
7.
IsmailRCartmellM (2012) An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation. Journal of Sound and Vibration331(12): 2929–2948.
8.
Israr A (2008) Vibration Analysis of Cracked Aluminium Plates. PhD Thesis. University of Glasgow, UK. Available at: https://core.ac.uk/download/pdf/9653631.pdf (accessed June 2008).
9.
IsrarACartmellMPKrawczukM, et al.(2006) On approximate analytical solutions for vibrations in cracked plates. Applied Mechanics and Materials5–6: 315–322.
10.
Israr ACartmellMPManoachE, et al.(2009) Analytical modeling and vibration analysis of partially cracked rectangular plates with different boundary conditions and loading. Journal of Applied Mechanics76(1): 011005.
11.
JosephPErdoganF (1991) Surface crack in a plate under antisymmetric loading conditions. International Journal of Solids and Structures27(6): 725–750.
12.
JoshiPJainNRamtekkarG (2014) Analytical modeling and vibration analysis of internally cracked rectangular plates. Journal of Sound and Vibration333(22): 5851–5864.
13.
KhademSERezaeeM (2000) Introduction of modified comparison functions for vibration analysis of a rectangular cracked plate. Journal of Sound and Vibration236(2): 245–258.
14.
LeeY (2002) Structural–acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate. Applied Acoustics63(11): 1157–1175.
15.
LiYChengL (2004) Modifications of acoustic modes and coupling due to a leaning wall in a rectangular cavity. Journal of the Acoustical Society of America116(6): 3312–3318.
16.
LiYChengL (2007) Vibro-acoustic analysis of a rectangular-like cavity with a tilted wall. Applied Acoustics68(7): 739–751.
17.
NakanishiSSakagamiKDaidoM, et al.(1999) Effect of an air-back cavity on the sound field reflected by a vibrating plate. Applied Acoustics56(4): 241–256.
18.
PirnatMČeponGBoltežarM (2014) Structural–acoustic model of a rectangular plate–cavity system with an attached distributed mass and internal sound source: theory and experiment. Journal of Sound and Vibration333(7): 2003–2018.
19.
PretloveA (1965) Free vibrations of a rectangular panel backed by a closed rectangular cavity by a closed rectangular cavity. Journal of Sound and Vibration2(3): 197–209.
20.
QaisiMI (1988) Free vibrations of a rectangular plate–cavity system. Applied Acoustics24(1): 49–61.
21.
RiceJRLevyN (1972) The part–through surface crack in an elastic plate. Journal of Applied Mechanics39(1): 185–194.
22.
SadriMYounesianD (2013) Nonlinear harmonic vibration analysis of a plate–cavity system. Nonlinear Dynamics74(4): 1267–1279.
23.
SadriMYounesianD (2014) Nonlinear free vibration analysis of a plate–cavity system. Thin-Walled Structures74: 191–200.
24.
SadriMYounesianD (2015) Vibro-acoustic analysis of a coach platform under random excitation. Thin-Walled Structures95: 287–296.
25.
SadriMYounesianD (2016) Vibroacoustic analysis of a sandwich panel coupled with an enclosure cavity. Composite Structures146: 159–175.
26.
SarıgülASKaragözlüE (2018) Vibro-acoustic coupling in composite plate–cavity systems. Journal of Vibration and Control24(11): 2274–2283.
27.
ShenMNagamuraKNakagawaN, et al.(2013) Noise reduction through elastically restrained sandwich polycarbonate window pane into rectangular cavity. Journal of Vibration and Control19(3): 415–428.
28.
ShiSSuZJinG, et al.(2018) Vibro-acoustic modeling and analysis of a coupled acoustic system comprising a partially opened cavity coupled with a flexible plate. Mechanical Systems and Signal Processing98: 324–343.
29.
SoleckiR (1985) Bending vibration of a rectangular plate with arbitrarily located rectilinear crack. Engineering Fracture Mechanics22(4): 687–695.
30.
SoniSJainNJoshiP (2018) Vibration analysis of partially cracked plate submerged in fluid. Journal of Sound and Vibration412: 28–57.
31.
StahlBKeerL (1972) Vibration and stability of cracked rectangular plates. International Journal of Solids and Structures8(1): 69–91.
32.
TanakaNTakaraYIwamotoH (2012) Eigenpairs of a coupled rectangular cavity and its fundamental properties. Journal of the Acoustical Society of America131(3): 1910–1921.
33.
WenYSJinZ (1987) On the equivalent relation of the line spring model: A suggested modification. Engineering Fracture Mechanics26(1): 75–82.
34.
XinFLuT (2009) Analytical and experimental investigation on transmission loss of clamped double panels: implication of boundary effects. Journal of the Acoustical Society of America125(3): 1506–1517.
35.
XinFLuT (2011) Analytical modeling of sound transmission through clamped triple-panel partition separated by enclosed air cavities. European Journal of Mechanics–A/Solids30(6): 770–782.
36.
XinFLuTChenC (2008) Vibroacoustic behavior of clamp mounted double-panel partition with enclosure air cavity. Journal of the Acoustical Society of America124(6): 3604–3612.
37.
ZhangHShiDZhaS, et al.(2018) Vibro-acoustic analysis of the thin laminated rectangular plate–cavity coupling system. Composite Structures189: 570–585.
