Vibration mode localization in rectangular plates with V-shaped through cracks

Vibration mode localization caused by V-shaped through cracks in rectangular plates is discussed in this work. A solution method is presented for the free vibration analysis of rectangular plates containing V-shaped through cracks. A domain decomposition technique is employed in combination with two sets of modified Fourier series. The Rayleigh-Ritz method is used to determine the natural frequencies, and the mode shapes are then constructed by superposition of the admissible functions. Finally, this method is applied to determine the modal characteristics of plates with V-shaped cracks by focusing on the effects of various crack parameters on frequencies and mode localization. The degree of localization is evaluated quantitatively through a localization scalar parameter. It is found that the frequencies and mode shapes are more affected by longer crack lengths and smaller included angles, and that mode localization is more likely to occur under these conditions.