In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.
Stiffened plates are employed in various engineering structures including aerospace, civil, naval, etc. These structures may be subjected to harmonic loads. Therefore, it is essential to understand the harmonic response of a cracked stiffened structure. This study presents the effects of the crack location on the free vibration and harmonic response of the stiffened plates. For this purpose, horizontal and vertical cracks are modelled throughout the fixed from two-side structure. The analyses are performed via the Finite Element Method and the Mode Superposition technique. The natural frequencies and the displacement responses of the cracked and healthy structures are obtained and interpreted. It is concluded that a horizontal crack can decrease the third natural frequency by 60% as it is located in the center of the stiffened plate that is fixed from its nonstiffened edges. Thus, the displacement response of the stiffened structures is increased by 18% in the presence of the side horizontal or vertical cracks, which are located at the free ends of the stiffened structures no matter which boundary condition is considered.
This study presents the effect of vertical and horizontal oriented cracks on free vibration response for circular and annular thin plates. To investigate the dynamic behavior of the damaged circular structures the cracks are modeled separately considering horizontal/vertical orientations, ten different locations, and four crack sizes. For annular thin plates, vertical and horizontal oriented cracks are placed in the middle between the outer and inner edges to investigate the effect of crack directions. The first five resonant frequencies, and the corresponding mode shapes of the cracked circular and annular plates, are obtained by employing the Finite Element Method. The free vibration analyses are conducted considering clamped boundary conditions for circular plates and clamped-clamped, clamped-free, and free-clamped boundary conditions for annular plates. The results are presented and interpreted considering the differences in the non-dimensional frequencies and the mode shapes of those structures. According to the findings, it is seen that depending on its location and size, a crack can change the mode shapes by accumulating the bending regions around it. Besides, a crack may also change the number of bending regions that occurred in the mode shapes of the circular or annular structures.
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