A. K. Abramian
V. L. Andreyev
D. A. Indejtchev
Acad. of Sci. of Russia, St. Petersburg
Inst. for Problems of Mech. Eng., Bolshoy 61 V.O., St. Petersburg 199178, Russia
The influence of compressible liquid on nonlinear oscillation of a channel back boundary is studied. The back boundary is a beam with a thrust on an elastic bed. The beam is excited by parametric longitudinal compressing forces. Using the Galerkin procedure the starting equation takes the form: W[sub 1]+a(t)W[sub 1]+(epsilon)W[sub 1]=bW[sub 1][sup 3]+cW[sub 1]W[sub 2][sup 2]=0, W[sub 2]+f(t)W[sub 2]+(gamma)W[sub 2][sup 3]+gW[sub 2]W[sub 1][sup 2]=0. The fundamental resonances of the beam are examined by using the multiple-scales averaging analysis. The presence of liquid leads to reduction of the range where stable oscillation of the system is possible. Numerical simulation of the process in the phase space has been conducted and chaotic behavior of the system has been found. Precision algorithms of Runge-Kutta (DOPRI) have been used for the numerical simulation. The numerical simulations are studied in the context of Runge-Kutta simplex methods. Qualitative analysis of process dynamics has been obtained. Lyapunov exponents and fractal dimensionality have been determined; they prove the presence of a strange attractor in the system.