caa a22 4500 445361174 CHVBK 20180317142915.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s11071-010-9796-1 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9796-1 Multiple scales analysis of wave-wave interactions inacubically nonlinear monoatomic chain [Elektronische Daten] [Kevin Manktelow, Michael Leamy, Massimo Ruzzene] The interaction of waves in nonlinear media is of practical interest in the design of acoustic devices such as waveguides and filters. This investigation of the monoatomic mass-spring chain with a cubic nonlinearity demonstrates that the interaction of two waves results in different amplitude and frequency dependent dispersion branches for each wave, as opposed to a single amplitude-dependent branch when only a single wave is present. A theoretical development utilizing multiple time scales results in a set of evolution equations which are validated by numerical simulation. For the specific case where the wavenumber and frequency ratios are both close to 1:3 as in the long wavelength limit, the evolution equations suggest that small amplitude and frequency modulations may be present. Predictable dispersion behavior for weakly nonlinear materials provides additional latitude in tunable metamaterial design. The general results developed herein may be extended to three or more wave-wave interaction problems. Springer Science+Business Media B.V., 2010 Nonlinear stiffness nationallicence Wave propagation nationallicence Dispersion nationallicence Bandgap materials nationallicence Metamaterials nationallicence Wave interactions nationallicence Manktelow Kevin George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, 30332-0405, Atlanta, GA, USA aut Leamy Michael George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, 30332-0405, Atlanta, GA, USA aut Ruzzene Massimo George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, 30332-0405, Atlanta, GA, USA aut Nonlinear Dynamics Springer Netherlands 63/1-2(2011-01-01), 193-203 0924-090X 63:1-2<193 2011 63 11071 https://doi.org/10.1007/s11071-010-9796-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9796-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Manktelow Kevin George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, 30332-0405, Atlanta, GA, USA aut NATIONALLICENCE 700 1- Leamy Michael George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, 30332-0405, Atlanta, GA, USA aut NATIONALLICENCE 700 1- Ruzzene Massimo George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, 30332-0405, Atlanta, GA, USA aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 63/1-2(2011-01-01), 193-203 0924-090X 63:1-2<193 2011 63 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer