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Research Papers

Analytical Modeling and Vibration Analysis of Partially Cracked Rectangular Plates With Different Boundary Conditions and Loading

[+] Author and Article Information
Asif Israr

Department of Mechanical Engineering, University of Glasgow, James Watt South Building, Glasgow, G12 8QQ, Scotland, UKasifisrar@yahoo.com

Matthew P. Cartmell

Department of Mechanical Engineering, University of Glasgow, James Watt South Building, Glasgow, G12 8QQ, Scotland, UKmatthewc@mech.gla.ac.uk

Emil Manoach

Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bontchev Strasse, Block 4, 1113 Sofia, Bulgariae.manoach@imbm.bas.bg

Irina Trendafilova

Department of Mechanical Engineering, University of Strathclyde, 75 Montrose Strasse, Glasgow, G1 1XJ, Scotland, UKirina.trendafilva@strath.ac.uk

Wiesław Ostachowicz

Institute of Fluid Flow Machinery, Polish Academy of Sciences, ul. Gen Fiszera 14, 80-952, Gdańsk, Poland; Gdynia Maritime University, Faculty of Navigation, Al. Jana Pawla II, 81-345 Gdynia, Polandwieslaw@imp.gda.pl

Marek Krawczuk

Institute of Fluid Flow Machinery, Polish Academy of Sciences, ul. Gen Fiszera 14, 80-952, Gdańsk,Poland; Department of Electric and Control Engineering, Technical University of Gdańsk, Narutowicza 11/12, 80-952 Gdańsk, Polandmk@imp.gda.pl

Arkadiusz Żak

Institute of Fluid Flow Machinery, Polish Academy of Sciences, ul. Gen Fiszera 14, 80-952, Gdańsk, Polandarek@imp.gda.pl

J. Appl. Mech. 76(1), 011005 (Oct 31, 2008) (9 pages) doi:10.1115/1.2998755 History: Received November 02, 2007; Revised August 27, 2008; Published October 31, 2008

This study proposes an analytical model for vibrations in a cracked rectangular plate as one of the results from a program of research on vibration based damage detection in aircraft panel structures. This particular work considers an isotropic plate, typically made of aluminum, and containing a crack in the form of a continuous line with its center located at the center of the plate and parallel to one edge of the plate. The plate is subjected to a point load on its surface for three different possible boundary conditions, and one examined in detail. Galerkin’s method is applied to reformulate the governing equation of the cracked plate into time dependent modal coordinates. Nonlinearity is introduced by appropriate formulations introduced by applying Berger’s method. An approximate solution technique—the method of multiple scales—is applied to solve the nonlinear equation of the cracked plate. The results are presented in terms of natural frequency versus crack length and plate thickness, and the nonlinear amplitude response of the plate is calculated for one set of boundary conditions and three different load locations, over a practical range of external excitation frequencies.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Line spring model representing the bending and tensile stresses for a part-through crack of length 2a after Ref. 7

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Figure 2

Isotropic plate loaded by concentrated force and small crack of length 2a at the center and parallel to the x-axis

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Figure 3

The amplitude of the response as a function of the detuning parameter (rad/s) and the point load at different locations (m) of the plate element

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Figure 4

Plate first mode natural frequency as a function of half-crack length

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Figure 5

Plate first mode natural frequency as a function of the thickness of the plate for the half-crack length 0.05 m

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Figure 6

Comparison between linear and nonlinear models of the cracked rectangular plate

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