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This paper presents an investigation on the vibration behaviour of rectangular Mindlin plates with one or more preexisting through cracks. The moving least square element (MLS-element) method recently developed by the authors is further extended to carry out this study. The shape functions of an element for the displacement fields can be derived ba...
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Context 1
... 2 is depicted to illustrate the procedure to model a horizontal side crack in a plate. The plate is divided into four elements and the crack occurs at the edge between two elements as shown in Fig. 2. As it is a through crack, the displacement fields and are all discontinued at the cracked edge. It is seen in Fig. 2 that the two elements do not share an edge at the cracked location. It ensures that no connectivity is imposed at the points between the two elements at the cracked edge. ...
Context 2
... 2 is depicted to illustrate the procedure to model a horizontal side crack in a plate. The plate is divided into four elements and the crack occurs at the edge between two elements as shown in Fig. 2. As it is a through crack, the displacement fields and are all discontinued at the cracked edge. It is seen in Fig. 2 that the two elements do not share an edge at the cracked location. It ensures that no connectivity is imposed at the points between the two elements at the cracked edge. ...
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Citations
... Thus, numerical methods are developed and used to provide approximate solutions. The numerical methods, which have many successful applications in vibration cracked plate, employ a set of basis functions to solve natural frequencies include extended finite element method [10][11][12][13], spline finite strip method [14,15], Galerkin approach [16,17], meshless methods [18][19][20][21][22][23][24][25] and Rayleigh-Ritz methods [26][27][28]. Torabi and Ansari [29] studied the phase-field vibration analysis of the cracked functionally graded graphene platelets-reinforced composite plates considering stationary cracks via the variational finite difference method. ...
In this work, moving least squares differential quadrature scheme is employed to formulate and solve the free vibration analysis of cracked plates resting on the Winkler–Pasternak elastic foundation. Two types of cracks as a part-through surface and internal crack are studied in a rectangular plate. Formulation of the problem is dependent on transverse shear deformation theory and line spring model. Also, continuous weight functions around the crack are produced by diffraction method. Boundary conditions are augmented in the equation of motion and the problem is converted to a discrete eigenvalue problem. The accuracy and efficiency of the present results is validated by comparing with exact, experimental and numerical results. Moreover, the effects of different boundary conditions, crack length, crack depth and foundation parameters on the vibration frequencies and mode shapes are examined in detail. The obtained results may be used for structural health monitoring.
... The accuracy of the current approach is investigated by simulating in ABAQUS software package. Zhou and Xiang [18] investigated the vibration behavior of rectangular Mindlin plates with one or more pre-existing through cracks. The moving least square element (MLS-element) method developed by them is further extended to carry out this study. ...
... Values for coefficient ܥ ሺሻ[18]. ...
In this study, flutter, limit cycle oscillation, and different nonlinear oscillations analyses of rectangular panels with all-over part-through crack are presented. These analyses are carried out for panels in according to first order shear deformation or Mindlin plate theory. The effects of crack’s depth and location on various aeroelastic characteristics of moderately thick rectangular panels are accurately studied. These analyses show that for much of crack’s depths and locations, the amplitude of nonlinear vibrations are increased. But there are some crack’s locations, for them panel has lower amplitude of vibrations with respect to its intact counterpart. With changing the location and depth of crack, the maximum limit cycle oscillation amplitude will be different from intact counterpart. Also cracked panel may exhibit complex oscillations, other than limit cycle oscillation of intact panel. From these analyses, it can be shown that crack has significant influence on flutter boundary, and amplitude of limit cycle oscillation.
