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Modeling aeroelastic effects for an airbreathing hypersonic vehicle is challenging due to its tightly integrated airframe and propulsion system that leads to significant deflections in the thrust vector caused by flexing of the airframe. These changes in the orientation of the thrust vector in turn introduce low-frequency oscillations in the flight-path angle, which make control system design a challenging task. The airbreathing hypersonic vehicle considered here is assumed to be a thin-walled structure, where deformations due to axial, bending, shear, and torsional loads are modeled using the six independent displacements of a rigid cross section. Complex interactions between the airframe and the associated hypersonic flowfield may introduce lightly damped highfrequency modes. Such high-frequency free vibration modes are computed accurately using a previously developed novel scheme. The nonlinear equations of motion for the flexible aircraft are derived; these equations are then linearized about a computed cruise condition, and a selective modal analysis is carried out on the linearized system. Furthermore, a linear quadratic regulator is designed to compensate for perturbations in initial conditions, where a novel and practical approach is used to populate the weighting matrices of the linear quadratic regulator objective function. [ABSTRACT FROM AUTHOR]

Motivated by the need for high-fidelity modeling and accurate control of future hypersonic vehicles subjected to complex aerothermomechanical loads and many other such applications, a novel scheme is proposed to accurately compute higher modes of vibration for one-dimensional structures by coupling the classic Ritz method as a predictor and the linear two-point boundary value problem solver SUPORE as a corrector. The Ritz method is used to compute a preliminary estimate of the natural frequencies for the desired modes. These estimates are then used as initial guesses by SUPORE, which employs superposition and reorthonormalization to accurately solve the governing boundary value problem. Compared to a high-fidelity Ritz approximation or a highly refined finite element modeling procedure, this is a simple, computationally less expensive, and yet highly accurate method to compute mode shapes for applications that require higher modes. This scheme is used to compute mode shapes within an absolute and relative error tolerance of 10-6 for the idealized case of a free-free Euler-Bernoulli beam and a typical air-breathing hypersonic vehicle modeled as a thin-walled structure and taking into account deformations due to bending, shear, and torsion. [ABSTRACT FROM AUTHOR]