Analytical and Experimental Random Vibration of Nonlinear Aeroelastic Structures

摘要

The analytical part deals with the nonlinear response of a three degree of freedom aeroelastic structural model in the neighborhood of combination internal resonance condition. The Fokker Planck equation approach is used to derive a general differential equation for the response statistical joint moments. The equations are solved by using numerical integration. The solution shows that the response coordinates are non-stationary random processes and the three normal modes are in complete nonlinear interaction. The interaction is found to be very strong at a region of internal detuning which is shifted from the exact internal resonance condition. This result is under further investigation by using a non-gaussian closure scheme. The experimental investigation is conducted out on a two degree of freedom model. When the first normal mode is externally excited by a band-limited random excitation, the system mean square response is found to be linearly proportional to the excitation spectral density level up to a certain level above which the two normal modes exhibit discontinuity governed mainly by the internal detuning parameter and the system damping ratios. The results are completely different when the second normal mode is excited. For small levels of excitation spectral density the response is dominated by the second normal mode. For higher levels of excitation spectral density the first normal mode attends and interacts nonlinearly with the second mode in a form of energy exchange.