چكيده به لاتين
The aim of this thesis is the linear and nonlinear analysis of a cracked isotropic plate in contact with fluid inside an acoustical cavity. The crack is considered as a type of surface crack with an arbitrary angle, length, and position. Herewith, the line spring model is utilized in order for the crack to be modeled. Firstly, the governing equations related to the free vibration of the cracked plate using the Von-Karman theory and the aforementioned model for crack are derived. Then, the governing equation is also extended for the analysis of a cracked plate-cavity system. In the next step, the Euler equation is introduced to establish the relationship between the fluid and solid surface. As a result of considering three different boundary conditions as well as using the Euler equation, the coupling between the acoustic terms and plate displacement is eliminated. Afterward, the partial differential equation is converted to a nonlinear ordinary differential equation in the time domain, using the Galerkin method. In the first investigation, by eliminating the nonlinear part of the mentioned equation and considering the linear part, the linear natural frequencies associated with the system are obtained. Also, the effect of different crack parameters is evaluated. In the second analysis, the nonlinear study of the vibrational equation related to the system is conducted. Therefore, by introducing variational iteration method as a semi-analytical method and applying such a method to analyze nonlinear vibration of an intact plate-enclosure, the precision of the introduced method is proved in comparison with other numerical methods. Subsequently, by employing the proposed method for the cracked system, the convergence of the nonlinear natural frequencies is achieved with performing four iterations. Finally, by presenting three and four-dimensional plots, the effective parameters, such as length, orientation, and position related to the crack, on the nonlinear to linear natural frequency ratio are inspected for all modes and boundary conditions. Evaluating various crack parameters will show that the maximum and minimum influence on the nonlinear frequencies are related to the angle and length of the crack, respectively.
