Finite element formulation and analysis of a functionally graded Timoshenko beam subjected to an accelerating mass including inertial effects of the mass

Abstract

This study describes a new finite element method that can be used to analyse transverse and axial vibrations of a Functionally Graded Material (FGM) beam under an accelerating / decelerating mass. The differential equations of the FGM beam are obtained using First-order Shear Deformation Theory (FSDT). In these equations, the interaction terms of mass inertia are derived from the second-order exact differentiation of displacement functions with respect to mass contact point. The FGM beam is made of two different materials (Steel and Alumina Al2O3), which vary in thickness with a power law. Including the effects of neutral axis shift and mass inertia, the proposed method can be used when the dynamic behaviour of the FGM Timoshenko beams is to be analysed in transverse and axial directions, depending on the interaction with the acceleration of the moving loads. After validating this work with literature studies, new investigations and findings are presented for both moving load and mass assumptions. In addition, the obtained results of Timoshenko Beam (TBT) and Euler Bernoulli beam theory (EBT) are compared for FGM beams with various speeds and accelerations of moving mass.

Dynamic response of damaged rigid-frame bridges subjected to moving loads using analytical based formulations

“…Besides the studies focusing on beam-like structures under moving load problem discussed above, the moving mass motion was also considered in the area of the defense technology elements such as tank barrels during fire position (Esen and Koç, 2015) and functionally graded (FG) beams on elastic foundation which are common elements in aerospace and automotive engineering applications (Esen, 2019a). FG Timoshenko beams under accelerating moving mass with inertia effects were investigated in several studies (Esen et al ., 2018; Esen, 2019b). Moving finite element approach was noted as an effective method to obtain the dynamic response of beams subjected to accelerating mass (Esen, 2011).…”

Vibration analysis of functionally graded microbeams with a moving mass based on Timoshenko beam theory

“…In [11], vibration of FG Euler-Bernoulli beam due to a moving mass was studied using the DQM. Esen et al [12] examined the influence of acceleration and deceleration of a moving mass on dynamic behavior of FG beams by using a two-node Timoshenko beam element. The modified continuum mathematical model was presented by Esen et al [13] for vibration study of perforated microbeam under a moving mass.…”

Response characteristics of a beam‐mass system with general boundary conditions under compressive axial force and accelerating masses

“…A large volume of studies has been devoted to this class of problems in literatures. Among these are the works of Low et al who studied experimental and analytical investigations of vibration frequencies for center‐loaded beams, Low and Dubey who considered a note on the fundamental shape function and frequency for beams under off center load, Esen who worked on a new finite element for transverse vibration of rectangular thin plates under a moving mass, Low who investigated a comparative study of the eigenvalue solutions for mass‐loaded beams under classical boundary conditions, Esen who studied a modified FEM for transverse and lateral vibration analysis of thin beams under a mass moving with a variable acceleration, Tso et al who treated circular wave motions in a plate composed of transversely isotropic materials and Esen et al who scrutinized finite element formulation and analysis of a functionally graded Timoshenko beam subjected to an accelerating mass including inertial effects of the mass. In almost all these aforementioned studies, applications of the solution techniques and the theories proposed are limited to the cases when the velocity or the acceleration of the traveling mass is held constant throughout its motion on the structural member it traverses.…”