TY - JOUR
T1 - Response probability density functions of Duffing-Van der Pol vibro-impact system under correlated Gaussian white noise excitations
AU - Li, Chao
AU - Xu, Wei
AU - Feng, Jinqian
AU - Wang, Liang
PY - 2013/3/15
Y1 - 2013/3/15
N2 - This paper aims to investigate the stationary probability density functions (PDFs) of a Duffing-Van der Pol vibro-impact system excited by correlated Gaussian white noise. With the help of non-smooth transformation, the stationary PDFs are formulated analytically by the stochastic averaging of energy envelope. The analytical results are verified by numerical simulation results. Stochastic bifurcations for different parameters are considered, and several special PDF forms are observed in this paper. The first form is the shape of the PDF of total energy can be similar to a crater, which has a minimum and a maximum. The second one is the shape of the joint PDF with three peaks, that is to say, the section of joint PDF has three maximum and two minimum. In addition, the influence of the degree of the correlation of Gaussian white noises is explored.
AB - This paper aims to investigate the stationary probability density functions (PDFs) of a Duffing-Van der Pol vibro-impact system excited by correlated Gaussian white noise. With the help of non-smooth transformation, the stationary PDFs are formulated analytically by the stochastic averaging of energy envelope. The analytical results are verified by numerical simulation results. Stochastic bifurcations for different parameters are considered, and several special PDF forms are observed in this paper. The first form is the shape of the PDF of total energy can be similar to a crater, which has a minimum and a maximum. The second one is the shape of the joint PDF with three peaks, that is to say, the section of joint PDF has three maximum and two minimum. In addition, the influence of the degree of the correlation of Gaussian white noises is explored.
KW - Correlated Gaussian white noise
KW - Non-smooth transformation
KW - Stationary PDFs
KW - Stochastic averaging
KW - Stochastic bifurcation
KW - Vibro-impact system
UR - http://www.scopus.com/inward/record.url?scp=84872308878&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2012.11.053
DO - 10.1016/j.physa.2012.11.053
M3 - 文章
AN - SCOPUS:84872308878
SN - 0378-4371
VL - 392
SP - 1269
EP - 1279
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 6
ER -