“…Definition of fiber angles, the stiffness coefficients, coupling stiffness, and the mass/inertia terms of the layup are according to our previous study and the details can be found in Ref. [10,13]. After quite burdensome manipulation of formulas, the integral form of equation of motion for the TWB composite twin-engine wing system with CAS configuration is obtained as;…”
Section: Aeroelastic Governing Equation Of Motionmentioning
confidence: 99%
“…In order to have slender and lighter wing structure, advanced composite materials with thin walled beams (TWBs) structure has been developed. Application of TWBs in aircraft wings as a load carrying part of the wing and studying their dynamic behavior has been the topic of many researches [8][9][10][11][12][13]. Librescu [9] thoroughly investigated the theoretical foundations of composite TWBs and derived the necessary relations.…”
Section: Introductionmentioning
confidence: 99%
“…and(2) prime sign denotes differentiation with respect to the direction. ( ) are the primary and secondary warping functions that are given in[10].…”
In the present study, the aeroelastic energy response of a twin-engine composite wing system is optimized based on sequential quadratic programming (SQP) method. The variable stiffness is acquired by constructing laminates of thin wall beam (TWB) with curvilinear fibers having prescribed paths. In order to account the effect of spanwise locations and mass of the engines on the aeroelastic characteristics of TWB, the novel governing equations of motion are obtained using Hamilton's variational principle. The paper aims to exploit desirable fiber paths with improved aeroelastic properties for different twin-engine wing configuration. Ritz based solution methodology is employed to solve the equations with coupled incompressible unsteady aerodynamic model based on Wagner's function. A novel optimization strategy based on the total energy of the aeroelastic system is introduced. The proposed total energy, as a cost function, is minimized in terms of four optimization variables of two engine's locations and wing structure curvilinear fiber angle with two design parameters. The total energy is obtained by integrating responses of kinetic and potential energy in a specific time interval. The minimum total energy is an indication of ideal optimization variables which leads to the optimum flutter performance. Numerical results demonstrate the effectiveness of the optimization variables on the total energy of the aeroelastic system and determine the optimal values of introduced variables in case of minimum total energy and improved aeroelastic characteristics.
“…Definition of fiber angles, the stiffness coefficients, coupling stiffness, and the mass/inertia terms of the layup are according to our previous study and the details can be found in Ref. [10,13]. After quite burdensome manipulation of formulas, the integral form of equation of motion for the TWB composite twin-engine wing system with CAS configuration is obtained as;…”
Section: Aeroelastic Governing Equation Of Motionmentioning
confidence: 99%
“…In order to have slender and lighter wing structure, advanced composite materials with thin walled beams (TWBs) structure has been developed. Application of TWBs in aircraft wings as a load carrying part of the wing and studying their dynamic behavior has been the topic of many researches [8][9][10][11][12][13]. Librescu [9] thoroughly investigated the theoretical foundations of composite TWBs and derived the necessary relations.…”
Section: Introductionmentioning
confidence: 99%
“…and(2) prime sign denotes differentiation with respect to the direction. ( ) are the primary and secondary warping functions that are given in[10].…”
In the present study, the aeroelastic energy response of a twin-engine composite wing system is optimized based on sequential quadratic programming (SQP) method. The variable stiffness is acquired by constructing laminates of thin wall beam (TWB) with curvilinear fibers having prescribed paths. In order to account the effect of spanwise locations and mass of the engines on the aeroelastic characteristics of TWB, the novel governing equations of motion are obtained using Hamilton's variational principle. The paper aims to exploit desirable fiber paths with improved aeroelastic properties for different twin-engine wing configuration. Ritz based solution methodology is employed to solve the equations with coupled incompressible unsteady aerodynamic model based on Wagner's function. A novel optimization strategy based on the total energy of the aeroelastic system is introduced. The proposed total energy, as a cost function, is minimized in terms of four optimization variables of two engine's locations and wing structure curvilinear fiber angle with two design parameters. The total energy is obtained by integrating responses of kinetic and potential energy in a specific time interval. The minimum total energy is an indication of ideal optimization variables which leads to the optimum flutter performance. Numerical results demonstrate the effectiveness of the optimization variables on the total energy of the aeroelastic system and determine the optimal values of introduced variables in case of minimum total energy and improved aeroelastic characteristics.
“…Kandil and Eissa [16] suppressed the two peaks of the positive position feedback (PPF) controller's performance with imposed V-curves by coupling two additional non-linear saturation controllers (NSC) to the rotating blade. Farsadi et al [17] modeled structurally thin-walled beams to study the aeroelastic behavior of the preliminary twisting and the high aspect ratio wings. Kandil and El-Gohary [18,19] studied the effects of time delay on the vibration control performance for reducing the oscillations of a rotating beam via proportional derivative (PD) and NSC controllers.…”
Time delay is an obstacle in the way of actively controlling non-linear vibrations. In this paper, a rotating blade’s non-linear oscillations are reduced via a time-delayed non-linear saturation controller (NSC). This controller is excited by a positive displacement signal measured from the sensors on the blade, and its output is the suitable control force applied onto the actuators on the blade driving it to the desired minimum vibratory level. Based on the saturation phenomenon, the blade vibrations can be saturated at a specific level while the rest of the energy is transferred to the controller. This can be done by adjusting the controller natural frequency to be one half of the blade natural frequency. The whole behavior is governed by a system of first-order differential equations gained by the method of multiple scales. Different responses are included to show the influences of time delay on the closed-loop control process. Also, a good agreement can be noticed between the analytical curves and the numerically simulated ones.
“…They also adopted nite-state induced ow theory of Peters to model the unsteady aerodynamic loads. Farsadi et al [43] geometrically studied the nonlinear aeroelastic behavior of pre-twisted HAR wings. The structure was modeled as thin walled beams and the approximation of the Wagner's function in time domain was used to describe unsteady aerodynamic loads in the incompressible ow regime.…”
The nonlinear dynamic response, Limit Cycle Oscillations (LCOs), of High-Aspect-Ratio (HAR) wings using novel indicial aerodynamics in subsonic ow was investigated. Using the nonlinear beam theory, the structural model was derived with in-plane and out-of-plane bending and torsional motions, all nonlinearities up to cubic order arising from large deformation, mass distribution, and cross-sectional mass imbalance. Based on new approximations of the indicial functions, a comprehensive unsteady aerodynamic model was used. Coupling such indicial aerodynamics to nonlinear structural equations can result in a uni ed nonlinear aeroelastic formulation in both incompressible and subsonic compressible ows. The e ects of ight conditions, wing tip initial disturbances, Sti ness Ratio (SR) between bending modes, and nonlinearity due to inertia and cross-sectional mass imbalance on the characteristics of LCO are discussed. The results showed that compressibility could a ect the LCO boundary up to 12 percent, which implied that appropriate Mach-dependent aerodynamics was required to achieve a more reasonable and realistic description of dynamic behavior of the system. It was observed that the presence of LCO before the linear utter speed depended on the initial disturbances as well as wing characteristics.
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