Aeroservoelastic Study of a Delta Wing with Actuators of Variable Stiffness

Abstract

The primary focus of the proposed work is to carry out dynamic aeroelastic analysis on the delta wing, considering the actuator stiffness. It is envisaged that the variation in the actuator stiffness, induces the changes in the resonant frequencies and the corresponding mode shapes. This, in turn adversely affects the aeroelastic parameters, while the wing is interacting with the surrounding air loads. Hence, there is a need to carry out dynamic aeroelastic flutter analysis for varying velocities at different altitudes, to identify the flutter critical velocity. Here, frequency domain flutter analysis is carried out to identify the onset of flutter, using MSC-NASTRAN / PATRAN. However, the aerodynamic modelling, required to compute the unsteady air loads, uses the Doublet Lattice Method (DLM) formulation in the subsonic regime. In DLM, the Mach number and reduced frequency pairs are of prime concern, wherein the values are calculated and tabulated based on the modal frequencies of concern. In the proposed work, the frequency domain analyses utilize the MSC-NASTRAN solver incorporating the p-k method of flutter analysis. Subsequently, the flight velocities considered here are of higher subsonic and close to the supersonic regimes, while the flying altitudes range from sea-level to twelve kilometers. Here, the variation in control stiffness is in decreasing steps of 10 starting from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">15</sup> N/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> N/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The requisite frequency domain flutter analyses study resulted in different flutter modes while considering the subsonic and supersonic flight regimes. It was observed that the decrease in control surface actuator stiffness had major influence on the overall stiffness of wing, which caused increase in flutter frequency and gradual decrease in flutter velocity. However, the control stiffness, when decreased beyond 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> N/m2, exhibited minimal effect on the flutter results. This quiescence of critical flutter velocity variation suggests that the reduction of actuator stiffness beyond a particular value inhibits the effects of aerodynamic force redistribution on mode shapes. Simultaneously, the time domain analyses with the first five modes and sixteen reduced frequencies are considered in the state-space formulation in the MATLAB environment. To interpret the unsteady aerodynamics as continuous functions of rational polynomials, Pade's and minimum-state approximation methods are utilized. Finally, the flutter velocities resulting from the time domain analysis are validated with reference to the NASTRAN results, with an error of <8%.