Sharif Digital Repository

In this thesis, the nonlinear vibrations of the circular plate is examined using multiple scale methods and experimental tests. At first step, the nonlinear equations governing the problem are written using von Karman's assumption. In the next step, to solve nonlinear equations and calculate natural frequency, the problem is solved using multiple scale method and frequency charts are extracted as a function of the amplitude of vibration. . The design of the setup has been done in such a way that it is possible to simulate the boundary conditions. In the first phase, experimental tests was performed on a 0.3 mm thick aluminum sheet, which did not produce the desired results due to the... 

Shape Memory Polymers (SMPs) are a class of smart materials capable of remembering multiple shapes, and transitioning between them in response to an external stimulus such as thermal or magnetic induction. SMPs have attracted significant attention of both industrial and academic researchers due to their useful and attractive functionality. This thesis aims to analytically develop Euler-Bernoulli, Timoshenko and von Karman theories for beam bending in small strain regime considering SMP constitutive equations. To properly introduce analytical solution for the problem of beam bending, the constitutive model proposed by Baghani et al. (2012) has been used. For this purpose, three dimensional... 

Nonlinear forced vibrations of thin functionally graded circular and elliptical plates under classical boundary conditions are investigated based on the classical plate theory. The von Kármán strain-displacement relations is employed to include geometrical nonlinearity caused by large transverse displacements of the plate thickness order, and modal expansion in polar and elliptical coordinate along with the perturbation method of multiple scale is used to solve the governing equations. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. Transverse forcing is supposed to be harmonic with angular... 

In this study, based on Donnel’s shell theory and the theory of third-order shear deformation, and taking into consideration von Karman non-linearity terms, the analysis of buckling of functionally graded (FG) and multi-layered cylindrical shell with transversely isotropic layers, subjected to different loadings, was done. Along this line, first using the principle of minimum total potential energy, and based on the Donnel’s shell theory and the theory of third-order shear deformation, five couple equilibrium equations for cylindrical shell were produced. Next these five coupled equilibrium equations were reduced to three uncoupled equilibrium equation which are, in terms of transverse... 

The purpose of this study is to develop the reduced order nonlinear modeling of single cell closed section thin walled composite beams. In this way, global behavior of one dimensional beam under axial load, bending and torsional moment is produced. This model is based on the classical lamination theory, and the nonlinear model is developedby usingthe von-karman strains. In this process the effects of material anisotropy and axial warping are considered. Numerical results are obtained for thin-walledcomposites box beams, addressing the effects of fiber angle and laminate stacking sequence. The nonlinear model is compared with theoretical results of homogeneous beams and the natural... 

The purpose of this study is aeroelastic stability analysis and nonlinear aeroelastic vibration of composite wing with nonlinear 1D beam model. Wing’s structure modelled as thin-walled composite single box beam in linear and nonlinear conditions. Thin-walled composite box beam developed by classical lamination theory and structural nonlinearity is von karman strain. Unsteady aerodynamic of wing modelled with modified strip theory. Aeroelastic equations of wing obtained from modal expansion (assumed mode) and Hamilton’s Principle. In order to stability analysis of wing, the linear aeroelastic equations in state space must be calculated and so with eigenvalue analysis instability speed will be... 

Von-Karman vortex shedding is a transient aerodynamic instability which occurs in laminar flows over a bluff body in a certain condition. When this phenomenon occurs, vortices take form on upper and lower parts of the bluff body and begin to shed into an oscillatory manner affecting a significant part of the flow domain. This research focuses on Karman vortex shedding control by using two thin oscillating splitter plates. Length ratio of plates to cylinder diameter is 1 (L⁄D=1) and plates are attached at ±55 degrees (trigonometric angle). Plates are forced to oscillate at different ratios of natural vortex shedding frequencies (0.75, 1, 1.25, 1.5 and 2) for diffenet amplitudes. Simulations... 

Various public transportation types, e.g., Trains, Buses, and Airplanes, are susceptible to damages made by the impacts of the external objects, which are typically classified as low to medium velocity impacts. This problem reveals the significance of investigating the effects of impact on thin-walled structures, which are the main components of these vehicles' bodies. Owing to the controllable rheological properties of the Magnetorheological fluid with respect to the magnetic field, it can be utilized to control the structure exposed to impact adaptively and minimize the damages. Due to this purpose, sandwich structures such as sandwich beams and plates, thanks to their extended response...