Here, forced vibration of a rectangular plate with a side crack of arbitrary length, orientation and position is studied by the Ritz method. Simply supported and clamped boundary conditions are used in the analysis. Numerical results obtained from the Ritz method are validated by finite element method software (ABAQUS). Good matching was found for first five modes. Mobility curves are presented for variation in force location, crack length, crack orientation and crack position in a square plate. Normalized mobility is found to increase with an increase in crack length ratios and decrease with an increase in crack angle. Again, it is observed that a change in crack position from side towards middle increases the normalized mobility. The results can be used for mobility-based crack detection.
AggarwalaBDArielPD (1981) Vibration and Bending of a Cracked Plate. Engineering Transactions29: 295–310.
2.
BamniosGTrochidisA (1995) Mechanical impedance of a cracked cantilever beam. Journal of Acoustical Society of America97: 3625–3635.
3.
BhatRB (1984) Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh-Ritz method. Journal of Sound and Vibration102(4): 493–499.
4.
BoseTMohantyAR (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.
5.
HiranoYOkazakiK (1980) Vibration of cracked rectangular plates. Bulletin JSME23: 732–740.
6.
HuangCSLeissaAWMcGeeOG (1993) Exact analytical solutions for the vibrations of sectorial plates with simply-supported radial edges. Journal of Applied Mechanics60: 478–483.
7.
HuangCSLeissaAW (2009) Vibration analysis of rectangular plates with side cracks via the Ritz method. Journal of Sound and Vibration323: 974–988.
8.
IsrarACartmellMPManoachE (2009) Analytical modelling and vibration analysis of partially cracked rectangular plates with different boundary conditions and loading. Journal of Applied Mechanics76: 1–9.
9.
IsmailRCartmellMP (2012) An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation. Journal of Sound and Vibration331: 2929–2948.
10.
KhademSERezaeeM (2000) Introduction of modified comparison functions for vibration analysis of a rectangular cracked plate. Journal of Sound and Vibration236(2): 245–258.
11.
KimMKKimEJAnYK (2011) Reference-free impedance-based crack detection in plates. Journal of Sound and Vibration330(24): 5949–5962.
12.
LeissaAWMcGeeOGHuangCS (1993) Vibrations of circular plates having V- notches or sharp radial cracks. Journal of Sound and Vibration161(2): 227–239.
13.
LiewKMHungKCLimMK (1994) A solution method for analysis of cracked plates under vibration. Engineering Fracture Mechanics48(3): 393–404.
14.
Lynn PP and Kumbasar N (1967) Free vibrations of thin rectangular plates having narrow cracks with simply supported edges. In Proceedings of Developments in Mechanics Conference, Colorado State University, Fort Collins, CO, Aug. 21–23, vol. 4, pp. 911–928.
15.
NekuK (1982) Free vibrations of a simple supported rectangular plate with a straight through-notch. Bulletin JSME25: 16–23.
16.
NezuKKodoguchiH (1980) A new damage detecting method by mechanical impedance measurements. Bulletin JSME23: 2125–2131.
17.
PrabhakarSSekharASMohantyAR (2001) Detection and monitoring of cracks using mechanical impedance of rotor-bearing system. Journal of Acoustical Society of America110(5): 2351–2359.
18.
PrabhakarSMohantyARSekharAS (2002) Crackdetection by measurement of mechanical impedance of a rotor-bearing system. Journal of Acoustical Society of America112(6): 2825–2830.
19.
SoleckiR (1983) Bending vibration of a simply supported rectangular plate with a crack parallel to one edge. Engineering Fracture Mechanics18: 1111–1118.
20.
StahlBKeerLM (1972) Vibration and stability of cracked rectangular plates. International Journal of Solids and Structures8: 69–91.
21.
Williams ML (1951) Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending. In Proceedings of First US National Congress of Applied Mechanics, Illinois Institute of Technology, Chicago, June 11–16, pp. 325–329.
