The normal mode interaction of a two degree-of-freedom structural system subjected to random external and parametric excitations is investigated. The analysis is confined to the linear dynamic coupling for which the normal mode frequencies and mode shapes are obtained in terms of the system parameters. The equations of motion are written in terms of the normal coordinates. However, these equations are found to be coupled through random parametric coefficients in the presence of external forcing terms. The excitations are modeled as Gaussian "physical" white noise processes for which the response can be represented as a Markov process. In this case, both the Ito stochastic calculus or the Fokker-Planck equation can be applied. Both methods lead to a set of deterministic differential equations for the joint moments of the response. The stationary response of the system is obtained and closed form expressions for the response mean squares are derived. In the neighborhood of the system uncoupled frequency Ratio ω{sub}11/ω{sub}22≈1.0(ω{sub}11 is the natural frequency of the wing alone, and ω{sub}22 is the natural frequency of the fuel storage structure) the mean square of the wing response is suppressed while the coupled storage structure exhibits large mean squares. The analysis reveals that for certain system parameters internal resonance condition ω{sub}2 = 2ω{sub}1 (where ω{sub}1 and ω{sub}2 are the normal mode frequencies of the system) is satisfied. Under this condition the structure random response must be analyzed by considering the non-linear coupling of the normal modes. The non-linear analysis is currently undertaken by the authors.
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