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An Analytical Approach to Nonlinear Vibrations of a Three-Layered Sandwich Beam with a Viscoelastic Core, under the Effects of Internal Resonance, Employing MMS
PashaJavid, Babak | 2014
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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 45326 (45)
- University: Sharif University of Technology
- Department: Aerospace Engineering
- Advisor(s): Haddadpour, Hassan
- Abstract:
- Vibrations with high amplitudes in continuous systems and models with multiple degrees of freedom, in specific conditions, is concomitant with a phenomenon called internal resonance. In the presence of this phenomenon, energy is transferred from one directly excited mode to the other vibrating modes of the structure results in response of the structure to be combination of the excited modes. In that situation occurrence of the internal resonance may decrease the level of undesired vibrations of the structure. This behavior is of interest especially in sandwich structures with viscoelastic cores that are designated to improve the damping characteristics of the structure and the property may be used in optimized design problems. To assess the mentioned objectives, is the core aim of the current thesis. To fulfill the goal, nonlinear vibrations of a three-layered sandwich beam with a viscoelastic mid-layer and elastic outer layers subjected to two different types of simply supported boundary conditions are studied utilizing Galerkin technique along with direct integration and also method of multiple scales (MMS). Then the results are validated using the model developed in ANSYS software environment. In this study, the nonlinear governing equations of the system are derived applying the Hamilton approach and considering the fully nonlinear strain-displacement relations. The problem is analyzed for structural conditions that let the internal resonance to happen and possibility of the further vibration attenuation is concluded employing this phenomenon
- Keywords:
- Analytical Method ; Internal Resonance ; Nonlinear Vibration ; Viscoelastic Beam ; Sandwich Beam
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