caa a22 4500 445360879 CHVBK 20180317142914.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s11071-010-9820-5 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9820-5 Improved reduced order solution techniques for nonlinear systems with localized nonlinearities [Elektronische Daten] [I. PraveenKrishna, C. Padmanabhan] This paper examines the modeling and solution of large-order nonlinear systems with continuous nonlinearities which are spatially localized. This localization is exploited by a combined component mode synthesis (CMS)—dynamic substructuring approach for efficient model reduction. Anew ordering method for the Fourier coefficients used in the Harmonic Balance Method (HBM) is proposed. This allows the calculation of the slave dynamic flexibility matrix, using simple analytical expressions thus saving considerable computational effort by avoiding inverse calculation. This procedure is also capable of handling proportional damping. Ahypersphere-based continuation technique is used to trace the solution, and hence track bifurcations since it has the advantage that the augmented Jacobian matrix remains square. The reduced system is also solved using a time-variational method (TVM) which generates sparse Jacobian matrices when compared with HBM. Several systems including those with parametric excitation and internal resonances are solved to demonstrate the capability of the proposed schemes. Acomparison of these techniques and their effectiveness in solving extremely strong nonlinear systems with continuous nonlinearities is discussed. Springer Science+Business Media B.V., 2010 Large nonlinear systems nationallicence Mode superposition nationallicence Dynamic condensation nationallicence Component mode synthesis nationallicence Harmonic balance nationallicence Time variational method nationallicence QR nationallicence LU nationallicence SVD nationallicence Powell hybrid method nationallicence Continuation nationallicence Hypersphere nationallicence PraveenKrishna I. Machine Design Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, 600036, Chennai, India aut Padmanabhan C. Machine Design Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, 600036, Chennai, India aut Nonlinear Dynamics Springer Netherlands 63/4(2011-03-01), 561-586 0924-090X 63:4<561 2011 63 11071 https://doi.org/10.1007/s11071-010-9820-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9820-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- PraveenKrishna I. Machine Design Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, 600036, Chennai, India aut NATIONALLICENCE 700 1- Padmanabhan C. Machine Design Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, 600036, Chennai, India aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 63/4(2011-03-01), 561-586 0924-090X 63:4<561 2011 63 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer