Nonlinear frequency response of parametrically excited functionally graded Timoshenko beams with a crack

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

1 Scopus Citations
View graph of relations


  • J. Yang
  • T. Yan


Original languageEnglish
Article number12061
Journal / PublicationIOP Conference Series: Materials Science and Engineering
Issue number1
Publication statusPublished - 2014


Title9th World Congress on Computational Mechanics, WCCM 2010, Held in Conjuction with the 4th Asian Pacific Congress on Computational Mechanics, APCOM 2010
Period19 - 23 July 2010


This paper investigates the nonlinear dynamic frequency response of a Timoshenko beam made of functionally graded materials (FGMs) with an open edge crack. The beam is clamped and subjected to an axial parametric excitation consisting of a static compressive force and a harmonic excitation force. Theoretical formulations are based on Timoshenko shear deformable beam theory, von Karman type geometric nonlinearity and rotational spring model. Hamilton's principle is used to derive the nonlinear partial differential equations which are transformed into nonlinear ordinary differential equation by using the Least Squares method and Galerkin technique. The nonlinear natural frequencies and excitation frequency-amplitude response curves are obtained by employing Runge-Kutta method and multiple scale method, respectively. A parametric study is conducted to study the effects of material property distribution, crack depth, crack location, excitation frequency, and slenderness ratio on the nonlinear dynamic characteristics of parametrically excited, cracked FGM Timoshenko beams.