Vibration analysis of a plate with three parallel horizontal cracks

Tiew, Yong Leek (2021) Vibration analysis of a plate with three parallel horizontal cracks. Project Report. Universiti Teknikal Malaysia Melaka, Melaka, Malaysia. (Submitted)

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Abstract

In this report, the equation of motion of vibration analysis of a thin isotropic plate with three parallel horizontal cracks for a given set of boundary conditions is developed. Kirchoff’s classical plate theory is applying to obtain the principles equilibrium and equation motion of an isotropic plate. Crack formulation on the plate is then presented from the application of Line Spring Model (LSM). After, Galerkin’s method is used to find the solution of governing equation by applying weighted residual technique and convert the transverse function into time dependent function. The governing equation is then finalized by applying equation of three boundary conditions. Next, the Berger’s formulation is applied to transverse the deflection terms of in-plane forces into a non-linear ordinary equation. The natural frequency of the plate is then become a variable by parameters of half crack length, length of plate, boundary conditions and number of cracks (single and multiple). The mathematical model result is presented in term of natural frequency are totally affect by half crack length and number of cracks and the result is validated by comparison with finite element analysis result

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