TY - JOUR
T1 - Complete semi-analytical solution for a uniformly moving mass on a beam on a two-parameter visco-elastic foundation with non-homogeneous initial conditions
AU - Dimitrovová, Zuzana
N1 - Sem PDF conforme despacho.
info:eu-repo/grantAgreement/FCT/5876/147353/PT#
This work was supported by FCT, through IDMEC, under LAETA, project UID/EMS/50022/2013.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - In this paper the new semi-analytical solution for the moving mass problem, published by the author of this paper, is extended to account for the non-homogeneous initial conditions. Derivations are presented for infinite homogeneous beams placed on a two-parameter visco-elastic foundation. Methods of integral transforms and contour integration are exploited to obtain the final closed-form solution, which is presented in form of a sum of the truly steady-state part, mass induced harmonic part, initial conditions induced harmonic part and transient vibration. Except for the transient part that is obtained by numerical integration, full evolution of the transversal vibrations can be quickly and accurately obtained by simple evaluation of the presented closed-form results. Newly derived formulas for infinite beams are validated by analysis of long finite beams, where the problem is solved by the eigenmode expansion method. Excellent agreement between the results is obtained validating the new formulas.
AB - In this paper the new semi-analytical solution for the moving mass problem, published by the author of this paper, is extended to account for the non-homogeneous initial conditions. Derivations are presented for infinite homogeneous beams placed on a two-parameter visco-elastic foundation. Methods of integral transforms and contour integration are exploited to obtain the final closed-form solution, which is presented in form of a sum of the truly steady-state part, mass induced harmonic part, initial conditions induced harmonic part and transient vibration. Except for the transient part that is obtained by numerical integration, full evolution of the transversal vibrations can be quickly and accurately obtained by simple evaluation of the presented closed-form results. Newly derived formulas for infinite beams are validated by analysis of long finite beams, where the problem is solved by the eigenmode expansion method. Excellent agreement between the results is obtained validating the new formulas.
KW - Constant and harmonic load
KW - Mass-induced frequency
KW - Moving mass
KW - Non-homogeneous initial conditions
KW - Normal force
KW - Semi-analytical solution
KW - Transverse vibrations
UR - http://www.scopus.com/inward/record.url?scp=85048528262&partnerID=8YFLogxK
U2 - 10.1016/j.ijmecsci.2018.05.055
DO - 10.1016/j.ijmecsci.2018.05.055
M3 - Article
AN - SCOPUS:85048528262
SN - 0020-7403
VL - 144
SP - 283
EP - 311
JO - International Journal of Mechanical Sciences
JF - International Journal of Mechanical Sciences
ER -