Geodesic
Oscillatory chain with elastic supports and bending stiffness under conditions close to acoustic vacuum
Russian journal of nonlinear dynamics, Tome 12 (2016) no. 3, pp. 311-325

Voir la notice de l'article provenant de la source Math-Net.Ru

We present results of analytical and numerical investigation of the nonstationary planar dynamics of a string with uniformly distributed discrete masses without preliminary tension and taking into account the bending stiffness. Each mass is coupled to the ground by lateral springs without tension which have (effectively) a characteristic that is nonlinearizable in the case of planar motion. The most important limiting case corresponding to low-energy transversal motions is considered taking into account geometrical nonlinearity. Since such excitations are described by approximate equations where cubic elastic forces contribute the most, oscillations take place under conditions close to the acoustic vacuum. We obtain an adequate analytical description of resonant nonstationary processes in the system under consideration, which correspond to an intensive energy exchange between its parts (clusters) in the domain of low frequencies. Conditions of energy localization are given. The analytical results obtained are supported by computer numerical simulations. The system considered may be used as an energy sink of enhanced effectiveness.
Keywords: nonlinear dynamics, nonlinear normal mode, limiting phase trajectory, energy exchange, localization. 
@article{ND_2016_12_3_a1,
     author = {I. P. Koroleva (Kikot) and L. I. Manevich},
     title = {Oscillatory chain with elastic supports and bending stiffness under conditions close to acoustic vacuum},
     journal = {Russian journal of nonlinear dynamics},
     pages = {311--325},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2016_12_3_a1/}
}
TY  - JOUR
AU  - I. P. Koroleva (Kikot)
AU  - L. I. Manevich
TI  - Oscillatory chain with elastic supports and bending stiffness under conditions close to acoustic vacuum
JO  - Russian journal of nonlinear dynamics
PY  - 2016
SP  - 311
EP  - 325
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2016_12_3_a1/
LA  - ru
ID  - ND_2016_12_3_a1
ER  - 
%0 Journal Article
%A I. P. Koroleva (Kikot)
%A L. I. Manevich
%T Oscillatory chain with elastic supports and bending stiffness under conditions close to acoustic vacuum
%J Russian journal of nonlinear dynamics
%D 2016
%P 311-325
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2016_12_3_a1/
%G ru
%F ND_2016_12_3_a1
I. P. Koroleva (Kikot); L. I. Manevich. Oscillatory chain with elastic supports and bending stiffness under conditions close to acoustic vacuum. Russian journal of nonlinear dynamics, Tome 12 (2016) no. 3, pp. 311-325. http://geodesic.mathdoc.fr/item/ND_2016_12_3_a1/