This paper proposes a new damage index for the crack identification of beams made of functionally graded materials (FGMs) by using the wavelet analysis. The damage index is defined based on the position of the wavelet coefficient modulus maxima in the scale space. The crack is assumed to be an open edge crack and is modeled by a massless rotational spring. It is assumed that the material properties follow exponential distributions along the beam thickness direction. The Timoshenko beam theory is employed to derive the governing equations which are solved analytically to obtain the frequency and mode shape of cracked FGM beams. Then, we apply the continuous wavelet transform (CWT) to the mode shapes of the cracked FGM beams. The locations of the cracks are determined from the sudden changes in the spatial variation of the damage index. An intensity factor, which relates to the size of the crack and the coefficient of the wavelet transform, is employed to estimate the crack depth. The effects of the crack size, the crack location and the Young's modulus ratio on the crack depth detection are investigated.
This paper studies the free vibration of size-dependent functionally graded material (FGM) microplates in contact with viscous fluid. The Mori-Tanaka model is applied to formulate the continuous gradual variation of material properties of FGM microplates along thickness direction. A non-classical microplate model is established based on the modified couple stress theory, which considers the size effect by introducing the material length scale parameter. A physical neutral plane is introduced to eliminate the stretching-bending coupling effect. The motion of viscous fluid is defined by Navier-Stokes equations, with which the hydrodynamic loading on microplates is determined with consideration of inertial effect and viscous damping effect. The governing equations for FGM microplates in contact with viscous fluid are derived using the Hamilton's principle and solved by differential quadrature method. Numerical results are obtained to discuss the influences of the aspect ratio, fluid depth, slenderness ratio, fluid viscosity, gradient index, fluid density, and size parameter on the vibration behaviours of microplates in contact with viscous fluid.
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