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.
Skip Nav Destination
e-mail: asifisrar@yahoo.com
e-mail: matthewc@mech.gla.ac.uk
e-mail: e.manoach@imbm.bas.bg
e-mail: irina.trendafilva@strath.ac.uk
e-mail: wieslaw@imp.gda.pl
e-mail: mk@imp.gda.pl
e-mail: arek@imp.gda.pl
Article navigation
January 2009
Research Papers
Analytical Modeling and Vibration Analysis of Partially Cracked Rectangular Plates With Different Boundary Conditions and Loading
Asif Israr,
Asif Israr
Department of Mechanical Engineering,
e-mail: asifisrar@yahoo.com
University of Glasgow
, James Watt South Building, Glasgow, G12 8QQ, Scotland, UK
Search for other works by this author on:
Matthew P. Cartmell,
Matthew P. Cartmell
Department of Mechanical Engineering,
e-mail: matthewc@mech.gla.ac.uk
University of Glasgow
, James Watt South Building, Glasgow, G12 8QQ, Scotland, UK
Search for other works by this author on:
Emil Manoach,
Emil Manoach
Institute of Mechanics,
e-mail: e.manoach@imbm.bas.bg
Bulgarian Academy of Sciences
, Acad. G. Bontchev Strasse, Block 4, 1113 Sofia, Bulgaria
Search for other works by this author on:
Irina Trendafilova,
Irina Trendafilova
Department of Mechanical Engineering,
e-mail: irina.trendafilva@strath.ac.uk
University of Strathclyde
, 75 Montrose Strasse, Glasgow, G1 1XJ, Scotland, UK
Search for other works by this author on:
Wiesław Ostachowicz,
Wiesław Ostachowicz
Institute of Fluid Flow Machinery,
e-mail: wieslaw@imp.gda.pl
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, Poland
Search for other works by this author on:
Marek Krawczuk,
Marek Krawczuk
Institute of Fluid Flow Machinery,
e-mail: mk@imp.gda.pl
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, Poland
Search for other works by this author on:
Arkadiusz Żak
Arkadiusz Żak
Institute of Fluid Flow Machinery,
e-mail: arek@imp.gda.pl
Polish Academy of Sciences
, ul. Gen Fiszera 14, 80-952, Gdańsk, Poland
Search for other works by this author on:
Asif Israr
Department of Mechanical Engineering,
University of Glasgow
, James Watt South Building, Glasgow, G12 8QQ, Scotland, UKe-mail: asifisrar@yahoo.com
Matthew P. Cartmell
Department of Mechanical Engineering,
University of Glasgow
, James Watt South Building, Glasgow, G12 8QQ, Scotland, UKe-mail: matthewc@mech.gla.ac.uk
Emil Manoach
Institute of Mechanics,
Bulgarian Academy of Sciences
, Acad. G. Bontchev Strasse, Block 4, 1113 Sofia, Bulgariae-mail: e.manoach@imbm.bas.bg
Irina Trendafilova
Department of Mechanical Engineering,
University of Strathclyde
, 75 Montrose Strasse, Glasgow, G1 1XJ, Scotland, UKe-mail: irina.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, Polande-mail: wieslaw@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, Polande-mail: mk@imp.gda.pl
Arkadiusz Żak
Institute of Fluid Flow Machinery,
Polish Academy of Sciences
, ul. Gen Fiszera 14, 80-952, Gdańsk, Polande-mail: arek@imp.gda.pl
J. Appl. Mech. Jan 2009, 76(1): 011005 (9 pages)
Published Online: October 31, 2008
Article history
Received:
November 2, 2007
Revised:
August 27, 2008
Published:
October 31, 2008
Citation
Israr, A., Cartmell, M. P., Manoach, E., Trendafilova, I., Ostachowicz, W., Krawczuk, M., and Żak, A. (October 31, 2008). "Analytical Modeling and Vibration Analysis of Partially Cracked Rectangular Plates With Different Boundary Conditions and Loading." ASME. J. Appl. Mech. January 2009; 76(1): 011005. https://doi.org/10.1115/1.2998755
Download citation file:
Get Email Alerts
Nonlinear Isogeometric Analyses of Instabilities in Thin Elastic Shells Exhibiting Combined Bending and Stretching
J. Appl. Mech (January 2025)
Related Articles
On the Magnetic Field Effect in Electroconductive Plates Under Nonconservative Loading
J. Appl. Mech (January,2009)
Free In-Plane Vibration Analysis of Rectangular Plates With Elastically Point-Supported Edges
J. Vib. Acoust (June,2010)
An Approximated Harmonic Balance Method for Nonlinear Vibration of
Viscoelastic Structures
J. Eng. Mater. Technol (July,2006)
Vibration of Pre-stressed Laminated Sandwich Plates With Interlaminar
Imperfections
J. Vib. Acoust (December,2006)
Related Proceedings Papers
Related Chapters
Three Dimensional Vibration Analysis of Functionally Graded Super-Elliptical Plates
Proceedings of the 2010 International Conference on Mechanical, Industrial, and Manufacturing Technologies (MIMT 2010)
Vibration of Plates
Design of Plate and Shell Structures
A New Exact Analytical Approach for In-Plane and Transverse Vibration of Thick Laminated Plates
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3