TY - JOUR
T1 - Application of a generalized Senator-Bapat perturbation technique to nonlinear dynamical systems with an irrational restoring force
AU - Lai, S. K.
AU - Xiang, Y.
PY - 2010
Y1 - 2010
N2 - This paper presents an alternative approach for mathematical modeling of an oscillating system with an irrational restoring force. Such a model corresponds to the oscillation of an elastic wire or string. A generalized Senator-Bapat perturbation technique is employed to deal with this nonlinear system. Unlike the conventional perturbation method, it not only solves the nonlinear problem without the requirement of small parameters, but also provides highly accurate solutions for small as well as large amplitudes of motion. Illustrative examples are selected and demonstrated for verifying the accuracy of this approach.
AB - This paper presents an alternative approach for mathematical modeling of an oscillating system with an irrational restoring force. Such a model corresponds to the oscillation of an elastic wire or string. A generalized Senator-Bapat perturbation technique is employed to deal with this nonlinear system. Unlike the conventional perturbation method, it not only solves the nonlinear problem without the requirement of small parameters, but also provides highly accurate solutions for small as well as large amplitudes of motion. Illustrative examples are selected and demonstrated for verifying the accuracy of this approach.
UR - http://handle.uws.edu.au:8081/1959.7/552927
U2 - 10.1016/j.camwa.2010.07.048
DO - 10.1016/j.camwa.2010.07.048
M3 - Article
SN - 0898-1221
VL - 60
SP - 2078
EP - 2086
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 7
ER -