caa a22 4500 445812184 CHVBK 20180317145215.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00419-010-0465-0 doi (NATIONALLICENCE)springer-10.1007/s00419-010-0465-0 Construction of approximate analytical solutions to strongly nonlinear damped oscillators [Elektronische Daten] [B. Wu, W. Sun] An analytical approximate method for strongly nonlinear damped oscillators is proposed. By introducing phase and amplitude of oscillation as well as a bookkeeping parameter, we rewrite the governing equation into a partial differential equation with solution being a periodic function of the phase. Based on combination of the Newton's method with the harmonic balance method, the partial differential equation is transformed into a set of linear ordinary differential equations in terms of harmonic coefficients, which can further be converted into systems of linear algebraic equations by using the bookkeeping parameter expansion. Only a few iterations can provide very accurate approximate analytical solutions even if the nonlinearity and damping are significant. The method can be applied to general oscillators with odd nonlinearities as well as even ones even without linear restoring force. Three examples are presented to illustrate the usefulness and effectiveness of the proposed method. Springer-Verlag, 2010 Damped oscillators nationallicence Transient responses nationallicence Strong nonlinearity nationallicence Linearization nationallicence Harmonic balance nationallicence Analytical approximations nationallicence Wu B. Department of Mechanics and Engineering Science, School of Mathematics, Jilin University, 130012, Changchun, People's Republic of China aut Sun W. Department of Mechanics and Engineering Science, School of Mathematics, Jilin University, 130012, Changchun, People's Republic of China aut Archive of Applied Mechanics Springer-Verlag 81/8(2011-08-01), 1017-1030 0939-1533 81:8<1017 2011 81 419 https://doi.org/10.1007/s00419-010-0465-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-010-0465-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wu B. Department of Mechanics and Engineering Science, School of Mathematics, Jilin University, 130012, Changchun, People's Republic of China aut NATIONALLICENCE 700 1- Sun W. Department of Mechanics and Engineering Science, School of Mathematics, Jilin University, 130012, Changchun, People's Republic of China aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/8(2011-08-01), 1017-1030 0939-1533 81:8<1017 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer