TY - JOUR
T1 - Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations
AU - Liu, Di
AU - Xu, Wei
AU - Xu, Yong
PY - 2013/6
Y1 - 2013/6
N2 - A convenient and universal residue calculus method is proposed to study the stochastic response behaviors of an axially moving viscoelastic beam with random noise excitations and fractional order constitutive relationship, where the random excitation can be decomposed as a nonstationary stochastic process, Mittag-Leffler internal noise, and external stationary noise excitation. Then, based on the Laplace transform approach, we derived the mean value function, variance function and covariance function through the Green's function technique and the residue calculus method, and obtained theoretical results. In some special case of fractional order derivative a, the Monte Carlo approach and error function results were applied to check the effectiveness of the analytical results, and good agreement was found. Finally in a general-purpose case, we also confirmed the analytical conclusion via the direct Monte Carlo simulation.
AB - A convenient and universal residue calculus method is proposed to study the stochastic response behaviors of an axially moving viscoelastic beam with random noise excitations and fractional order constitutive relationship, where the random excitation can be decomposed as a nonstationary stochastic process, Mittag-Leffler internal noise, and external stationary noise excitation. Then, based on the Laplace transform approach, we derived the mean value function, variance function and covariance function through the Green's function technique and the residue calculus method, and obtained theoretical results. In some special case of fractional order derivative a, the Monte Carlo approach and error function results were applied to check the effectiveness of the analytical results, and good agreement was found. Finally in a general-purpose case, we also confirmed the analytical conclusion via the direct Monte Carlo simulation.
KW - Axially moving beam
KW - Fractional derivatives Kelvin constitutive relationship
KW - Residue calculus method
KW - Stationary nonstationary noise
KW - Stochastic response
UR - http://www.scopus.com/inward/record.url?scp=84892993061&partnerID=8YFLogxK
U2 - 10.1007/s10409-013-0029-y
DO - 10.1007/s10409-013-0029-y
M3 - 文章
AN - SCOPUS:84892993061
SN - 0567-7718
VL - 29
SP - 443
EP - 451
JO - Acta Mechanica Sinica/Lixue Xuebao
JF - Acta Mechanica Sinica/Lixue Xuebao
IS - 3
ER -