preprints.org > engineering > mechanical engineering > doi: 10.20944/preprints202407.0993.v1 (registering DOI)

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 11 July 2024 / Approved: 11 July 2024 / Online: 12 July 2024 (11:09:58 CEST)

The study focuses on the free vibration analysis of beams made of axially functionally graded materials (AFGM) with curvilinear variable cross-sections along their length. The beams encompass various shapes, including concave and convex conic sections, with axial material properties varying according to polynomial and exponential laws. The equations of motion are derived using Hamilton's principle within the framework of Timoshenko beam theory. These governing equations, subjected to various boundary conditions, are solved using the differential transform method (DTM). The proposed solution technique is validated by comparing computed natural frequencies with existing in literature results and those obtained through three-dimensional finite element analysis in ABAQUS. The incorporation of material gradients into the beam finite element models was achieved through the user-defined material subroutine (UMAT). Additionally, a comprehensive study is conducted to examine the influence of various factors on the natural frequencies of functionally graded beams. These factors include parameters of material laws, types of variable beam shapes, slenderness ratio, and specific boundary conditions. This study provides a thorough understanding of the modal dynamics of the considered beams, offering valuable insights into the behavior of FGM structures.

free vibrations; axially functionally graded material; curvilinear tapered beam; differential transform method; ABAQUS

Engineering, Mechanical Engineering

* All users must log in before leaving a comment