Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets

Abstract

International audienceVibrations of non-uniform and functionally graded (FG) beams with various boundary conditions and varying cross-sections are investigated using the Euler–Bernoulli theory and Haar matrices. It is assumed that the cross-section and material properties vary along the beam in the axial direction. The system of the governing equations is transformed with the aid of a set of simplest wavelets. To validate the present results, the non-homogeneity of the beams is discussed in detail and the calculated frequencies are compared with those of the existing literature. The results show that the Haar wavelet approach is capable of calculating frequencies for the beams with different shapes, rigidity, mass density, small or large translational and rotational boundary coefficients. The advantage of the novel approach consists in its simplicity, accuracy and swiftness

Transverse vibration analysis of FGM plates with in-plane exponentially non-homogeneous material

“…Vibration analysis of structures with directionally -but not through the thickness -FGM structures is of significance importance. This has been addressed by in [7][8][9] for axially graded Euler-Bernoulli and Timoshenko beams. It has also been fully discussed for radially FGM circular plates by Sahraee [10], Shariyat and Alipour [11] and Hosseini-Hashemi et al [12], [13].…”

Free vibration of axially functionally graded Euler-Bernoulli beams

“…The presented analysis concerns the FG beams assuming a simple power law of a change of the material distribution through the thickness or the longitudinal direction. Hein and Feklistova [2] present an application of the Haar wavelet approach to free vibrations of FG beams with various boundary conditions and varying cross-sections. In paper [3] by Anandrao et al the finite element system of equations to free vibration analysis of the FG beams is derived.…”

“…The free vibrations of FG beams was analyzed by using various methods in papers [1][2][3][4][5]. The finite element method to the free vibration problem of a FG beams was applied by Alshorbagy et al in paper [1].…”

Free Vibration of Axially Inhomogeneous Beams that are Made of Functionally Graded Materials

“…16 The free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams have been studied by Shahba and Rajasekaran 17 through solving the governing differential equations based on the differential transform element method. Based on the EulerBernoulli theory and Haar wavelet approach, Hein and Feklistova 18 investigated the free vibration nonuniform and functionally graded beams with various boundary conditions and varying cross sections. The free vibration and stability analysis of axially functionally graded tapered Timoshenko beams were carried out using the finite element approach.…”