Thumbnail
Access Restriction
Subscribed

Author Yaghoubi, Saba Tahaei ♦ Mousavi, S. Mahmoud ♦ Paavola, Juha
Source SpringerLink
Content type Text
Publisher Springer Berlin Heidelberg
File Format PDF
Copyright Year ©2015
Language English
Subject Domain (in DDC) Technology ♦ Engineering & allied operations
Subject Keyword Dynamic analysis ♦ Shear deformable beam ♦ Strain gradient ♦ Velocity gradient ♦ Variational approach ♦ Theoretical and Applied Mechanics ♦ Mechanics
Abstract The strain and velocity gradient framework is formulated for the third-order shear deformable beam theory. A variational approach is applied to determine the governing equations together with initial and boundary conditions. Within the gradient framework, the strain energy is generalized to include strain as well as strain gradient. Furthermore, the kinetic energy is also generalized to include velocity and the velocity gradient. Such approach results in the introduction of the static and kinetic internal length scales. For dynamic analysis of beams, most of the gradient theories do not take the velocity gradient into account. The model developed in this paper depicts the influence of the velocity gradient on the governing equations and initial and boundary conditions of the third-order shear deformable theory. Through the assumption of the velocity gradients, kinematic quantities are distinguished on the microscale and on the macroscale. Finally, Timoshenko and Euler–Bernoulli beam theories are also presented by simplifying the third-order theory.
ISSN 09391533
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2015-02-28
Publisher Place Berlin/Heidelberg
e-ISSN 14320681
Journal Archive of Applied Mechanics
Volume Number 85
Issue Number 7
Page Count 16
Starting Page 877
Ending Page 892


Open content in new tab

   Open content in new tab
Source: SpringerLink