Linear and autoparametric modal analysis of aeroelastic structural systems



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Texas Tech University


This investigation deals with the linear modal analysis and autoparametric interaction of aeroelastic systems such as an airplane fuselage and wing with fuel storage. The mathematical modeling is derived by applying Lagrange's equations taking into consideration the Christoffel symbol of the first kind to account for the nonlinear coupling of the system coordinates, velocities, and accelerations.

The linear modal analysis will be obtained by considering the linear, conservative portion of the equations of motion. The normal mode frequencies and the associated mode shapes are obtained in terms of the system parameters. The main objective of the linear analysis is to explore the critical regions of autoparametric (or internal) resonance conditions, £kiwi=0 (where ki are integers and wi are the normal mode frequencies). The results show that for certain system parameters the condition of internal resonance is satisfied.

The dynamic behavior of the structure in the neighborhood of internal resonance conditions is obtained by considering the nonlinear coupling of the normal modes. The asymptotic approximation technique due to Struble is employed. Three groups of internal and normal resonance conditions are obtained from the secular terms of the first-order perturbational equations. The transient and steady-state responses cure obtained numerically by using the IBM Continuous System Modeling Program (CSMP) with double precision Milne integration. The transient response shows a build up in the interacted modes to a level which exceeds the steady-state response. In addition, the excited mode is suppressed by virtue of the nonlinear feedback of other modes. Under certain conditions, the steady-state response is derived analytically.

It is concluded that the nonlinear modal analysis reveals certain types of response characteristics which cannot be interpreted within the framework of the linear theory of small oscillations.



Continuous system modeling program (CSMP), Resonance, Aeroelasticity, Degree of freedom, Pendulum