A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable Acceleration

Abstract

In this paper, a new modified finite element method that can be used in the analysis of transverse and lateral vibrations of the thin beams under a point mass moving with a variable acceleration and constant jerk is presented. Jerk is the change in acceleration over time. In this method, the classical finite element of the beam is modified by the inclusion of the inertial effects of the moving mass. This modification is made using the relations between nodal forces and nodal deflections and shape functions of six DOF beam element. The mass, stiffness, and damping matrices of the modified finite element are determined by forces caused by the corresponding transverse and lateral accelerations and jerks, and transverse Coriolis and centripetal accelerations and jerks, respectively. This method was first applied on a simply supported beam plate to provide a comparison with the previous studies in literature, and it was proved that the results were within acceptable limits. Secondly, it was applied on a CNC type box-framed beam to analyse the dynamic response of the beam in terms of variable acceleration and jerk as well as constant velocity and mass ratios.

An Efficient Local Artificial Boundary Condition for Infinite Long Finite Element Euler–Bernoulli Beam

“…Te ABC for the widely used fnite element method (FEM) beam model is seldom discussed. Te biggest diference between FEM and FDM beams is that the former involves rotational degrees of freedom (DOF) (e.g., [27,28]). In this work, we propose a new ABC for FEM Euler-Bernoulli beam, which is local, efcient, accurate, and easy to implement.…”

Numerical methods and their application in dynamics of structures

“…Problems from dynamics of structures have been solved by numerical methods in numerous papers, e.g. (Wu, 2008;Bamer et al, 2021;Esen, 2017;Tapia Andrade & Torres Berni, 2021).…”

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.…”