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Bending vibration of a rectangular plate with arbitrarily located rectilinear crack
Affiliation:1. Public Health Laboratory of Valencia, Av. Catalunya, 21, 46020, Valencia, Spain;2. Department of Analytical Chemistry, University of Valencia, Doctor Moliner 50, 46100, Burjassot, Spain;3. Foundation for the Promotion of Health and Biomedical Research in the Valencian Region, FISABIO-Public Health, 21, Avenida Catalunya, Valencia, 46020, Spain;4. Research Institute for Pesticides and Water, Avda Sos Baynat s/n, University Jaume I, 12071 Castellón, Spain;1. School of Metallurgy and Chemical Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, Jiang Xi, China;2. Department of Chemical and Biochemical Engineering, National Engineering Laboratory for Green Productions of Alcohols-Ethers-Esters, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China;1. School of Architecture, State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China;2. Chair of Building Construction and Material Science, Department of Architecture, Technical University of Munich, Munich 80333, Bayern, Germany;1. Graduate Program in Cell, Molecular, and Developmental Biology, University of California, Riverside, USA;2. Division of Biomedical Sciences, School of Medicine, University of California, Riverside, USA
Abstract:Harmonic flexural vibration of a rectangular plate with an arbitrarily located rectilinear crack is investigated. Double finite Fourier transformation of discontinuous functions is applied to a plate with arbitrary boundary conditions and subjected to transverse harmonic loading. Natural vibration of a simply supported plate is analyzed as a special case. The unknown amplitudes of discontinuities of the displacement and slope across the crack are determined by satisfying boundary conditions at the crack's edge. The square-root singularities of the bending moment at the crack's tips are built into the solution. The method of reduction is applied to the infinite characteristic determinant of the problem. Numerical values of three lowest frequencies of vibration of a square plate are obtained for a diagonally located crack of changing length.
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