Sharif Digital Repository

Natural frequencies and mode shapes of two joined isotropic conical shells are presented in this study. The joined conical shells can be considered as the general case for joined cylindrical-conical shells, joined cylinder-plates or cone-plates, conical and cylindrical shells with stepped thicknesses and also annular plates. Governing equations are obtained using thin-walled shallow shell theory of Donnell and Hamilton's principle. The continuity conditions at the joining section of the cones are appropriate expressions among stress resultants and deformations. The equations are solved assuming trigonometric response in circumferential and series solution in meridional directions and all... 

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... 

Free vibration analysis of moderately thick rectangular FG plates on elastic foundation with various combinations of simply supported and clamped boundary conditions are studied. Winkler model is considered to describe the reaction of elastic foundation on the plate. Governing equations of motion are obtained based on the Mindlin plate theory. A semi-analytical solution is presented for the governing equations using the extended Kantorovich method together with infinite power series solution. Results are compared and validated with available results in the literature. Effects of elastic foundation, boundary conditions, material, and geometrical parameters on natural frequencies of the FG... 

Free vibration analysis of simply supported FG cylindrical shells for four sets of in-plane boundary conditions is performed. The material properties are assumed to be temperature-dependant and gradually changed in the thickness direction of the shell. The effects of temperature rise are investigated by specifying arbitrary high temperature on the outer surface and the ambient temperature on the inner surface of the cylinder. Distribution of temperature across the shell thickness is found from steady state heat conduction only in the thickness direction. The equations of motion are based on Love's shell theory and the von Karman-Donnell-type of kinematic nonlinearity. The static analysis is... 

In this paper, a continuous model for vibration analysis of a beam with an open edge crack including the effects of shear deformation and rotary inertia is presented. A displacement field is suggested for the beam and the strain, and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton's principle. The equation of motion is solved with a modified Galerkin method and the natural frequencies and mode shapes are obtained. A good agreement has been observed between the results of this research and the results of previous work done in this fiels. The results are also compared to results of a similar model with Euler-Bernoulli assumptions to... 

In this study, the homotopy analysis method is used to obtain an accurate analytical solution for fundamental non-linear natural frequency and corresponding displacement of tapered beams. Comparison between the obtained results and numerical solutions shows that the first-order approximation of present study leads to accurate solutions with a maximum relative error less than 0.5%  

In this paper, a continuous model for flexural vibration of beams with a vertical edge crack including the effects of shear deformation and rotary inertia is presented. The crack is assumed to be an open-edge crack perpendicular to the neutral plane. A quasi-linear displacement filed is suggested for the beam, and the strain and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton principle. The equation of motion is solved with a modified weighted residual method, and the natural frequencies and mode shapes are obtained. The results are compared to the results of similar model with Euler–Bernoulli assumptions and finite element model... 

In this study, sandwich beam model (SM) is proposed for free vibration analysis of bilayer graphene nanoribbons (BLGNRs) with interlayer shear effect. This model also takes into account the intralayer (in-plane) stretch of graphene nanoribbons. The molecular dynamics (MD) simulations using the software LAMMPS and Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential are done to validate the accuracy of the sandwich model results. The MD simulation results include the two first frequencies of cantilever BLGNRs with different lengths and two interlayer shear moduli, i.e., 0.25 and 4.6GPa. These two interlayer shear moduli, 0.25 and 4.6GPa, can be obtained by sliding a small... 

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential... 

Free vibrations and the transverse response of sandwich plates with viscoelastic cores under wide-band random excitation is studied with special attention to the so-called pumping, thickness-shear and stretching modes. The quadratic displacement field is adopted for all displacement components of the core to accurately capture the higher modes excited by the wide-band excitation. The Love-Kirchhoff plate theory is used for the face layers. The viscoelastic behavior of the core is modeled by the Golla-Hughes-McTavish method. An analytical solution using the normal mode method is provided for the simply supported boundary conditions by including a different family of modes. The effects of some... 

In this paper, nonlinear thermo-mechanical free vibration analysis of functionally graded (FG) beams investigated. Euler-Bernoulli assumptions together with Vo n Karman's strain-displacement relation are employed to derive the nonlinear governing partial differential equation (PDE) of motion. He's variational method is employed to obtain a simple and efficient approximate closed form solution of the nonlinear governing equation. Comparison between results of the present work and those available in literature shows the accuracy of presented technique. Some new results for the nonlinear natural frequencies of the FG beams such as the effect of vibration amplitude, material inhomogeneity and... 

In this paper, nonlinear vibration of a micro cantilever exposed to a constant velocity flow is studied. In order to obtain vibration frequency and time response of the micro beam the variational iteration method is used as a novel tool for solving nonlinear differential equations. Results of the analytical solution are compared with those obtained by Runge-Kutta method which shows very good agreement between them. Results confirm that frequency of vibration depends on the flow velocity. Also, the high sensitivity of the vibration frequency to the flow velocity means that it can be an effective indicator of velocity  

Free vibration of multilayered composite cylinder which volume fraction of fiber varies according to power law in longitudinal direction has been studied. Rule of mixture model and reverse of that are employed to represent elastic properties of this fibrous functionally graded composite. Straindisplacement relations employed are based on Reissner- Naghdi-Berry's shell theory. The displacement finite element model of the governing equations of motion is derived by writing weak form of them. The Lagrangian shape functions for in-plane displacements and Hermitian shape functions for displacement in normal direction to the surface of mid-plane are utilized by defining a conformal quadrilateral... 

In this paper, nonlinear vibration analyses of Euler-Bernoulli, Rayleigh, Shear and Timoshenko beams with simple end conditions are presented using homotopy analysis method (HAM). Closed form solutions for natural frequencies, beam deflection, post-buckling load-deflection relation, and critical buckling load are presented. The calculated natural frequencies for all four cases were verified against some available results in the literature and very good agreement observed. Furthermore, obtained results for deflection, buckling, and post-buckling of each beam are presented and the effects of some parameters, such as slenderness ratio, the rotary inertia, and the shear deformation are examined  

In this paper a nonlinear dynamic model for drill string in inclined well drilling is developed. Effects of drilling mud flow rate, weight on bit, angular velocity along with viscous damping on stability and vibration of the drill string are studied. Findings indicate the nonlinear effects are significant on the results. The effects of drilling mud flow rate and weight on bit on the natural frequencies and time responses are evaluated. Enhancement of drilling mud flow rate results in decreasing of natural frequencies and vibrational amplitude, while increasing the weight on bit, leads to decrease of the natural frequencies and increase the vibrational amplitude. © JVE INTERNATIONAL LTD  

Natural frequencies are important dynamic characteristics of a structure. Therefore, the exact solution pertaining to free vibration of stepped circular plate elastically restrained against rotation, translation, and internal elastic ring support resting on an arbitrary variable elastic foundation using Green Function is presented in this paper. Thus, an accurate and direct modeling technique is introduced for modeling stepped circular plate on an arbitrary variable elastic foundation with arbitrary boundary conditions and internal elastic ring support. The effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and... 

The free vibration analysis of rotating axially functionally graded nanobeams under an in-plane nonlinear thermal loading is provided for the first time in this paper. The formulations are based on Timoshenko beam theory through Hamilton’s principle. The small-scale effect has been considered using the nonlocal Eringen’s elasticity theory. Then, the governing equations are solved by generalized differential quadrature method. It is supposed that the thermal distribution is considered as nonlinear, material properties are temperature dependent, and the power-law form is the basis of the variation of the material properties through the axial of beam. Free vibration frequencies obtained are... 

Laminated composite beams with variable thickness are being widely used in many engineering applications. To enhance the dynamic behavior of structures subject to random loading, tapered laminated beams incorporated with magnetorheological (MR) fluids (MR-tapered beam) are proposed. A finite element model has been developed for random vibration analysis of MR-tapered beam based on layerwise displacement theory. The effects of thickness ratios of tapered beam, magnetic fields, statistical properties, correlation and autocorrelation on dynamic behaviors of structures have been investigated. The proposed structural element significantly enhances the dynamic response of MR-tapered beam under... 

The vibration characteristics, including fundamental frequencies and loss factors, of a sandwich conical shell with constrained viscoelastic layer is presented. The mechanical properties of viscoelastic core is modeled using Zener fractional order model. The equations of motion are derived employing Donnell representation of classical shell theory and solved using Raighly-Ritz method. The results are compared with other investigations and the effects of geometric parameters including the length to radius, radius to thickness and core to facing thickness on fundamental frequencies and loss factors are studied. © 2019 Elsevier Ltd