Browsing by Subject "Aeroelasticity -- Mathematical models"
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Item Numerical and experimental investigation of coupled beam and pendulum oscillator(Texas Tech University, 1992-12) Cuvalci, OlkanA large number of aerospace structures and large flexible mechanical structures may be modeled as a large flexible beam with a tip-mass. Sometimes, under certain conditions (high excitation amplitude, etc.), large deformation may be produced in the structure. In the field of design, the developments have led to the use of lightweight and high strength materials in these structures. Hence, modern structures are lighter, more flexible, and provide much lower energy dissipation, leading to an intense vibration response. A vibrating (oscillating) system has a maximum response amplitude at the resonance conditions; as a result, the system should work before or beyond the resonance case. Otherwise, it has a maximum response amplitude, which may cause the system to fail. In this research, a flexible beam with an appendage, which consists of a mass-pendulum attached to its tip, is investigated. Such an appendage can be located anywhere along the beam. However, in this research, only a tip appendage is considered. The pendulum which is considered as an auto-parametric vibration absorber. The equations of the motion of a system are obtained using D'Alembert's principle. The partial differential equations are reduced to a set of ordinary differential equations using the Galerkin method. The equations are nonlinear since the analysis is based on large deflection and also coupling exists between the beam and the pendulum. Numerical simulations are performed in order to obtain frequency response curves of the beam and the pendulum. The simulations are performed for different damping coefficients, both beam and pendulum, around primary resonance and under different forcing amplitudes. Experiments are conducted for two different lengths of the beam. The longer beam is used for uninverted pendulum motion, and the shorter beam for the inverted pendulum motion. Four different pendulums are considered for the uninverted pendulum case, and one pendulum for the inverted pendulum case. The results show that an energy exchange between the beam and pendulum, and also chaotic motion, is observed for some parameters of the beam and pendulum. Hence, the pendulum may be considered as a suitable auto-parametric vibration absorber.Item Random modal interaction of a non-linear aeroelastic structure(Texas Tech University, 1985-08) Hedayati, ZhianThe modal interaction of an aeroelastic structure subjected to random wide band excitation is investigated. An analytical model, represented by three degrees of freedom, is adopted. The equations of motion are derived by employing Lagrange's equation. The Fokker-Planck equation approach is used to generate the statistical dynamic moment equations of the response. Linear and non-linear modal interactions are obtained for various system parameters. The linear modal analysis involves the determination of the normal mode eigenvalues in terms of the system parameters. The main objective of this standard analysis is to define the critical regions of internal resonance of the sum type ω3 = ω1 + ω2, where o)i are the system eigenvalues. Analytical solutions are obtained for the mean square response of the linearized system with constant and randomly varying stiffnesses. The results provide mean square stability criteria for the linear case with random stiffness. The linear response statistics are used as a reference to measure the departure of the non-linear system response in the neighborhood of the internal resonance condition. For the non-linear case the differential equations of the response moments are found to form an infinite coupled set which is closed via a cumulant-neglect scheme. The resulting closed first and second order moment equations, 27 in total, are solved by numerical integration. The response at the critical internal resonance demonstrates a deviation from the corresponding linear response. The results indicate that the autoparametric interaction takes place in the form of energy transfer between the three modes, and large amplitude motion of one mode associated with suppression of the other two modes.