Affiliations: Mechanical and Aerospace Engineering Department,
Science and Research Branch, Islamic Azad University, Tehran, Iran | Mechanical Engineering Department, Sharif University
of Technology, Tehran, Iran
Note: [] Corresponding author: Ahmad Mamandi, Ph.D. of Aerospace Engineering, Design of
Aerospace Structures, Post Doctoral Research Fellow. E-mail:
am_2001h@yahoo.com
Abstract: In this study, the nonlinear vibrations analysis of an inclined
pinned-pinned self-weight Timoshenko beam made of linear, homogenous and
isotropic material with a constant cross section and finite length subjected to
a traveling mass/force with constant velocity is investigated. The nonlinear
coupled partial differential equations of motion for the rotation of warped
cross section, longitudinal and transverse displacements are derived using the
Hamilton's principle. These nonlinear coupled PDEs are solved by applying the
Galerkin's method to obtain dynamic responses of the beam. The dynamic
magnification factor and normalized time histories of mid-point of the beam are
obtained for various load velocity ratios and the outcome results have been
compared to the results with those obtained from linear solution. The influence
of the large deflections caused by a stretching effect due to the beam's fixed
ends is captured. It was seen that existence of quadratic-cubic nonlinear terms
in the nonlinear governing coupled PDEs of motion causes stiffening (hardening)
behavior of the dynamic responses of the self-weight beam under the act of a
traveling mass as well as equivalent concentrated moving force. Furthermore, in
a case where the object leaves the beam, its planar motion path is derived and
the targeting accuracy is investigated and compared with those from the rigid
solution assumption.
