TY - JOUR
T1 - Dynamics of a micro scale Timoshenko beam subjected to a moving micro particle based on the modified couple stress theory
AU - Jafari-Talookolaei, R. A.
AU - Abedi, M.
AU - Şimşek, M.
AU - Attar, M.
PY - 2018/2/1
Y1 - 2018/2/1
N2 - In this study, the free and forced vibration analysis of a micro scale Timoshenko beam resting on a Pasternak elastic foundation and subjected to a moving micro particle is presented. Based on the modified couple stress theory and employing Hamilton’s principle, the governing equations along with the boundary conditions are derived. A semi-analytical solution is obtained for the free vibration of the problem by expressing the dynamic lateral displacement and cross-section rotation in terms of the series of Legendre polynomials and extremizing the objective functional of the problem with respect to the unknown displacements and Lagrange multipliers. Correspondingly, the computed eigenvalue information of the system is utilized in the modal expansion technique to obtain the transient dynamic response. For comparison purposes, the free vibration frequencies of the micro beam and the dynamic deflections using the classical Timoshenko beam theory are compared with previously published studies and very good agreements have been observed. Furthermore, more numerical examples for natural frequencies and dynamic deflection of the beam are presented and the effects of some parameters, such as the material length scale parameter, the velocity of micro particle, the Pasternak elastic foundation parameters, shear deformation effects and boundary conditions are examined.
AB - In this study, the free and forced vibration analysis of a micro scale Timoshenko beam resting on a Pasternak elastic foundation and subjected to a moving micro particle is presented. Based on the modified couple stress theory and employing Hamilton’s principle, the governing equations along with the boundary conditions are derived. A semi-analytical solution is obtained for the free vibration of the problem by expressing the dynamic lateral displacement and cross-section rotation in terms of the series of Legendre polynomials and extremizing the objective functional of the problem with respect to the unknown displacements and Lagrange multipliers. Correspondingly, the computed eigenvalue information of the system is utilized in the modal expansion technique to obtain the transient dynamic response. For comparison purposes, the free vibration frequencies of the micro beam and the dynamic deflections using the classical Timoshenko beam theory are compared with previously published studies and very good agreements have been observed. Furthermore, more numerical examples for natural frequencies and dynamic deflection of the beam are presented and the effects of some parameters, such as the material length scale parameter, the velocity of micro particle, the Pasternak elastic foundation parameters, shear deformation effects and boundary conditions are examined.
KW - Microbeam
KW - modified couple stress theory
KW - moving micro particle
KW - semi-analytical solution
KW - Timoshenko theory
UR - http://www.scopus.com/inward/record.url?scp=85040828288&partnerID=8YFLogxK
U2 - 10.1177/1077546316645237
DO - 10.1177/1077546316645237
M3 - Article
AN - SCOPUS:85040828288
VL - 24
SP - 527
EP - 548
JO - Journal of Vibration and Control
JF - Journal of Vibration and Control
SN - 1077-5463
IS - 3
ER -