TY - JOUR
T1 - Free vibration analysis of a structural system with a pair of irrational nonlinearities
AU - Lai, S. K.
AU - Wu, B. S.
AU - Lee, Y. Y.
PY - 2017/5/1
Y1 - 2017/5/1
N2 - An alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented. This system can be used to represent mathematical models in various engineering problems. Prior to solving the problem, a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation. Analytical solutions are then obtained using the combination of the harmonic balance method and Newton's method. This approach shows that lower-order analytical procedures can yield highly accurate and exact solutions that are difficult to obtain with an analytical expression.
AB - An alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented. This system can be used to represent mathematical models in various engineering problems. Prior to solving the problem, a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation. Analytical solutions are then obtained using the combination of the harmonic balance method and Newton's method. This approach shows that lower-order analytical procedures can yield highly accurate and exact solutions that are difficult to obtain with an analytical expression.
KW - Analytical approximate solutions
KW - Harmonic balance method
KW - Irrational nonlinearities
KW - Newton's method
KW - Rational approximation
UR - http://www.scopus.com/inward/record.url?scp=85019625613&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85019625613&origin=recordpage
U2 - 10.1016/j.apm.2017.01.017
DO - 10.1016/j.apm.2017.01.017
M3 - 21_Publication in refereed journal
VL - 45
SP - 997
EP - 1007
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
SN - 0307-904X
ER -