Non-linear Free Vibration Analysis of Stepped Beams under Gravity by Transfer Matrix Method

Free Vibration Analysis of Functionally Graded Materials Non-uniform Beams

In this article, nonuniformity effects on free vibration analysis of functionally graded beams is discussed. variation in material properties is modeled after Powerlaw and exponential models and the non-uniformity is assumed to be exponentially varying in the width along the beams with constant thickness. Analytical solution is achieved for free vibration with simply supported conditions. It is...

A Study on Non-linear Free Vibration of Cantilever Beams

Non-linear flexural vibration of beams with various boundary conditions such as hinged–hinged, clamped–clamped and clamped–hinged has been extensively studied using analytical approaches and numerical methods like FEM. A detailed review has been brought out by Rosenberg [1] and Satyamoorthy [2]. However, the investigation pertaining to the cantilever case, which is also of practical interest, i...

Free Vibration Analysis of Functionally Graded Beams with Cracks

This study introduces the free vibration analysis of multilayered symmetric sandwich Timoshenko beams, made of functionally graded materials with two edge cracked, using the finite element method and linear elastic fracture mechanic theory. The FG beam consists of 50 layers, located symmetrically to the neutral plane, whose material properties distribution change along the beam thickness, accor...

Analysis of Free Vibration of Triangular Plates with Non-Uniform Linear Thickness and Arbitrary Boundary Conditions

Free Vibration Analysis of Quintic Nonlinear Beams using Equivalent Linearization Method with a Weighted Averaging

In this paper, the equivalent linearization method with a weighted averaging proposed by Anh (2015) is applied to analyze the transverse vibration of quintic nonlinear Euler-Bernoulli beams subjected to axial loads. The proposed method does not require small parameter in the equation which is difficult to be found for nonlinear problems. The approximate solutions are harmonic oscillations, whic...