Variational Iteration Method for Free Vibration Analysis of a Timoshenko Beam under Various Boundary Conditions

Vibration analysis of FGM cylindrical shells under various boundary conditions

In this paper, a unified analytical approach is proposed to investigate vibrational behavior of functionally graded shells. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stokes transformation. Material properties are assumed to be graded in...

Free vibration analysis of a rotating Timoshenko beam by differential transform method

Purpose – To perform the flapwise bending vibration analysis of a rotating cantilever Timoshenko beam. Design/methodology/approach – Kinetic and potential energy expressions are derived step by step. Hamiltonian approach is used to obtain the governing equations of motion. Differential transform method (DTM) is applied to solve these equations. Findings – It is observed that the rIVu term which...

The variational iteration method for a class of tenth-order boundary value differential equations

Free and Forced Vibration Analysis of Composite Laminated Conical Shells under Different Boundary Conditions Via Galerkin Method

In this paper, natural frequency and response of forced vibration of composite laminated conical shells under different boundary conditions are investigated. To this end, equations of Donnell's thin shell theory are used as governing equations. The analytical Galerkin method together with beam mode shapes as weighting functions is employed to solve the problem. Due to importance of boundary con...

Free Vibration Analysis of Functionally Graded Piezoelectric Material Beam by a Modified Mesh Free Method

A mesh-free method based on moving least squares approximation (MLS)  and weak form of governing equations including two dimensional equations of motion and Maxwell’s equation is used to analyze the free vibration of functionally graded piezoelectric material (FGPM) beams. Material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the...

Vibration analysis of a rotating closed section composite Timoshenko beam by using differential transform method

This study introduces the Differential Transform Method (DTM) in the analysis of the free vibration response of a rotating closed section composite, Timoshenko beam, which features material coupling between flapwise bending and torsional vibrations due to ply orientation. The governing differential equations of motion are derived using Hamilton’s principle and solved by applying DTM. The natura...