Analytical Modeling and Vibration Analysis of Partially Cracked Rectangular Plates With Different Boundary Conditions and Loading (original) (raw)
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On Approximate Analytical Solutions for Vibrations in Cracked Plates
Applied Mechanics and Materials, 2006
Recent NATO funded research on methods for detection and interpretation methodologies for damage detection in aircraft panel structures has motivated work on low-order nonlinear analytical modelling of vibrations in cracked isotropic plates, typically in the form of aluminium aircraft panels. The work applies fundamental aspects of fracture mechanics to define an elliptical crack, and the local stress field and loading conditions, arbitrarily located at some point in the plate, and then derives an analytical expression for this that can be incorporated into the PDE for an edge loaded plate with various possible boundary conditions. The plate PDE is converted into a nonlinear Duffing-type ODE in the time domain by means of a Galerkin procedure and then an arbitrarily small perturbation parameter is introduced into the equation in order to apply an appropriate solution method, in this case the method of multiple scales. This is used to solve the equation for the vibration in the crack...
Vibration Analysis of Cracked Aluminium Plates
This research is concerned with analytical modelling of the effects of cracks in structural plates and panels within aerospace systems such as aeroplane fuselage, wing, and tail-plane structures, and, as such, is part of a larger body of research into damage detection methodologies in such systems. This study is based on generating a so-called reduced order analytical model of the behaviour of the plate panel, within which a crack with some arbitrary characteristics is present, and which is subjected to a force that causes it to vibrate. In practice such a scenario is potentially extremely dangerous as it can lead to failure, with obvious consequences. The equation that is obtained is in the form of the classical Duffing equation, in this case, the coefficients within the equation contain information about the geometrical and mass properties of the plate, the loading and boundary conditions, and the geometry, location, and potentially the orientation of the crack. This equation has ...
In this paper, vibration analysis of a rectangular thin isotropic plate with a part-through surface crack of arbitrary orientation and position is performed by using the Kirchhoff plate theory. Simply supported (SSSS), clamped (CCCC) and simply supported–clamped (SCSC) boundary conditions are considered for the analysis. First, the governing differential equation of a cracked plate is formulated. A modified line spring model is then used to formulate the crack terms in the governing equation. Next, by the application of Burger's formulation, the differential equation is transformed into the well-known Duffing equation with cubic and quadratic nonlinearities. The Duffing equation is then solved by the method of multiple scales (MMS) to extract the frequency response curve. Natural frequencies are evaluated for different values of length, angle and position of a part-through surface crack. Some results are compared with the published literature. Amplitude variation with different values of length, angle and position of a part-through surface crack are presented, for all three types of the plate boundary conditions.