H. Asadigorji, A. Karami Mohammadi,
Volume 40, Issue 1 (9-2021)
Abstract
Complex nonlinear behaviors such as chaotic motion have devastating effects on dynamic systems. In this study, nonlinear behavior of simply supported rectangular viscoelastic plates was examined during supersonic aerodynamics and compared with the nonlinear elastic plate. Classical plate theory was used to obtain the plate equations, and Von- Kármán strain-displacement relations were used to consider the nonlinear geometric effects. The Kelvin Voigt model was also used to describe the viscoelastic properties and the “first-order piston theory" was used for supersonic aerodynamic flow. The equations of motion of the rectangular plate were extracted using the Lagrangian method and then, discretized by the Rayleigh-Ritz method. Solution of the equations was performed using fourth order Runge Kutta method. To investigate the dynamic behavior of the plates, the eigenvalues of the system, time history curves, phase portraits, Poincaré maps, and bifurcation diagrams were studied and analyzed. The results show that in some aspect ratios, the threshold for the occurrence of the flutter in the viscoelastic plate will be lower than that in the elastic plate. On the other hand, when the control parameter increases, complex nonlinear behavior such as chaos in the elastic plate goes simpler in the viscoelastic plate, such as periodic motion.
