caa a22 4500 445360291 CHVBK 20180317142913.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s11071-010-9859-3 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9859-3 On primary resonances of weakly nonlinear delay systems with cubic nonlinearities [Elektronische Daten] [Mohammed Daqaq, Khaled Alhazza, Yousef Qaroush] We implement the method of multiple scales to investigate primary resonances of a weakly nonlinear second-order delay system with cubic nonlinearities. In contrast to previous studies where the implementation is confined to the assumption of linear delay terms with small coefficients (Hu et al. in Nonlinear Dyn. 15:311, 1998; Ji and Leung in Nonlinear Dyn. 253:985, 2002), in this effort, we propose a modified approach which alleviates that assumption and permits treating a problem with arbitrarily large gains. The modified approach lumps the delay state into unknown linear damping and stiffness terms that are functions of the gain and delay. These unknown functions are determined by enforcing the linear part of the steady-state solution acquired via the method of multiple scales to match that obtained directly by solving the forced linear problem. We examine the validity of the modified procedure by comparing its results to solutions obtained via a harmonic balance approach. Several examples are discussed demonstrating the ability of the proposed methodology to predict the amplitude, softening-hardening characteristics, and stability of the resulting steady-state responses. Analytical results also reveal that the system can exhibit responses with different nonlinear characteristics near its multiple delay frequencies. Springer Science+Business Media B.V., 2010 Delay systems nationallicence Primary resonance nationallicence Peak frequency nationallicence Method of multiple scales nationallicence Daqaq Mohammed Nonlinear Vibrations and Energy Harvesting Lab (NOVEHL), Department of Mechanical Engineering, Clemson University, 29634, Clemson, SC, USA aut Alhazza Khaled Kuwait University, Kuwait City, Kuwait aut Qaroush Yousef Nonlinear Vibrations and Energy Harvesting Lab (NOVEHL), Department of Mechanical Engineering, Clemson University, 29634, Clemson, SC, USA aut Nonlinear Dynamics Springer Netherlands 64/3(2011-05-01), 253-277 0924-090X 64:3<253 2011 64 11071 https://doi.org/10.1007/s11071-010-9859-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9859-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Daqaq Mohammed Nonlinear Vibrations and Energy Harvesting Lab (NOVEHL), Department of Mechanical Engineering, Clemson University, 29634, Clemson, SC, USA aut NATIONALLICENCE 700 1- Alhazza Khaled Kuwait University, Kuwait City, Kuwait aut NATIONALLICENCE 700 1- Qaroush Yousef Nonlinear Vibrations and Energy Harvesting Lab (NOVEHL), Department of Mechanical Engineering, Clemson University, 29634, Clemson, SC, USA aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 64/3(2011-05-01), 253-277 0924-090X 64:3<253 2011 64 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer