Studies of structural vibrations have always been a concern for researchers and engineers
because it may cause the structure fatigue or failure. This study considered a free-free beam
with cubic nonlinearities, which subjected to the distributed load with the wind pressure and its
associated unsteady aerodynamic force. There is a wide range of applications of this study such as
rocket structure, satellite, etc.Thepurpose of thisresearch is to find whether there is an internal
resonance (I.R.) in the system. We analyzed this nonlinear system by the method of multiple scales
(a perturbationtechnique);the equations of motion in different time scales were transferred into
linear equations. Wethen utilized thefixed point plots (steady state frequency response) to
examinethe internal resonance of the system. From the results of the fixed point plots, we found that
there exists energy transferbetween y and zdegree of freedom (DOF) of the beam in
specific conditions, as shown in Fig. 1. This phenomenon might cause the system occur primary
resonance (P.R.), which was the special case of the internal resonance. Fig. 1 shows that when the
dimensionless wind pressure q~ equals 8(Mach number = 2), the primary resonanceoccurs. When the
y-DOF is excited, the z-DOF has larger response amplitude than the y-DOF. Finally, we used the
numerical method, fourth-order Runge-Kutta method, to verify the results of frequency response and the internal resonance.
Relation:
The 4th International Conference in Aerospace for Young Scientists (2019)
