Ince düzgünsüz plakaların titreşim analizi için Heaviside Fonksiyonları kullanarak Modelleme

Plate structures are utilized in many engineering applications where advanced techniques are used to improve their dynamic properties. These techniques may include attaching discrete patches and/or spatially varying the stiffness and mass properties of the plates. For example, piezoelectric transducers can be attached to the laminated plates to perform shunt damping for efficiently reducing the vibrations of the host plate. The vibration analysis of these non-uniform structures requires efficient and reliable mathematical modeling tools. This work focuses on semi-analytical modeling of plate structures having discrete and/or continuous non-uniformities and electroelastic modeling of laminated plates integrated with piezo-patches where it is utilized for analyzing the shunt damping performance of the whole system. There are many analytical and numerical models developed for the vibration analysis of the plates with attached discrete patches. In parallel, several studies are performed on the vibration analysis of the variable-stiffness laminates where their stiffness and mass properties can be spatially varied. However, there is no analytical model that enables the analysis of plates having discrete(possibly off-axis or rotated) and/or continuous non-uniformities. Considering these needs, the first part of this study aims to address these problems by developing a mathematical model for vibration analysis of plates having different kinds of non-uniformities. A semi-analytical model is developed for the vibration analysis of the plates having discrete (possibly off-axis) and/or continuous non-uniformities where Heaviside step functions are used to represent the discontinuities. Kinematic relations of the plate are based on the Classical Laminated Plate Theory (CLPT) and Rayleigh-Ritz method is used for modal analysis. For modeling rotated discontinuities, a numerical technique is proposed and incorporated into the model. Natural frequencies and mode shapes are calculated for the non-rotated/rotated discrete patch con gurations and validated with finite element simulations. It is shown that the rotation of the patch has a significant effect on the natural frequencies and mode shapes which is captured by the developed model. Finally, the modal analysis is performed on the variable-stiffness composite laminates and the natural frequencies obtained by the developed model are validated with the results from the literature. In the second part of this thesis, the model is extended such that it can be used for the design and analysis of laminated composite plates with surface-bonded piezo-patches in bimorph con gurations. The coupled electromechanical equations are derived to obtain the frequency response functions for displacement and voltage variables under the transverse harmonic point force. The developed model considers mass and stiffness contribution of the piezo-patches and the two-way electromechanical coupling effect. Moreover, an accelerated solution technique is developed for reducing the computation time for solving the coupled differential equations that represent the system dynamics. Several case studies are presented to observe the combined effects of the ply angle and size of the piezo-patches on the natural frequencies and corresponding mode shapes of the host structure. The results are validated by system-level simulations in finite-element software ANSYS. Then, utilizing the developed model, a thorough investigation is performed to determine the system parameters that significantly affect the electromechanical coupling and the shunt damping performance of the overall system. The system parameters such as the host plate ply angle, piezo-patch thickness, size and material, and their combined effects are investigated on the electromechanical coupling coefficient (EMCC). Finally, the shunt damping performance is shown for three confi gurations of weakly, medium and strongly-coupled systems.