Sharif Digital Repository

The present study aims at the free vibration analysis of double tapered columns. Foundation is assumed to be elastic and the effects of self-weight and tip mass with significant moment of inertia are considered. The governing equation of motion is obtained using the Hamilton principle, based on both the Euler-Bernoulli and Timoshenko beam models. Applying the power series method of Frobenius, the base solutions of the governing equations are obtained in the form of a power series via general recursive relations. Applying the boundary conditions, the natural frequencies of the beam/column are obtained using both models. The obtained results are compared with literature and a very good... 

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is... 

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is... 

In this study, the instability of spinning cylindrical shells partially filled with viscous liquid is investigated. Based on the Navier-Stokes equations for the incompressible flow, a 2D model is developed for liquid motion at each section of the cylinder. The governing equations of the cylinder vibrations are obtained based on the first-order shear deformable shell theory. The nonpenetration and no-slip boundary conditions of the flow on the wetted surface of the cylinder relate the liquid motion to the shell vibrations. Also the liquid pressure exerted on the cylinder wall combines the vibrations of the rotary cylinder to the liquid motion. By using the obtained coupled liquid-structure... 

In this paper, the static stability of the variable cross section columns, subjected to distributed axial force, is considered. The presented solution is based on the singular perturbation method of Wentzel-Kramers-Brillouin and the column is modeled using Euler-Bernoulli beam theory. Closed-form solutions are obtained for calculation of buckling loads and the corresponding mode shapes. The obtained results are compared with the results in the literature to verify the present approach. Using numerous examples, it is shown that the represented solution has a very good convergence and accuracy for determination of the instability condition  

This paper deals with the determination of free vibration characteristics and instability conditions of flexible spinning cylinders partially filled with fluid. Using the linearized Navier-Stokes equations for the incompressible, inviscid flow, a 2D model is developed for fluid motion at each section of the cylinder. The forces exerted on the cylinder wall as a result of the fluid motion are calculated as functions of lateral acceleration of the cylinder axis in the Laplace domain. Applying the Hamilton principle, the governing equations of flexural motion of the cylinder are derived and then combined with the equations describing the fluid forces to obtain the coupled field equations of the...