Estimation of the divergence characteristics of a jet transport aircraft wing using numerical method.

Abstract

The goal of the present paper work is to demonstrate the use of numerical matrix iteration technique to obtain the divergence speed of a jet transport aircraft wing by employing aerodynamic strip theory. Aerodynamics strip theory is employed to obtain the divergence speeds for a finite (Three Dimensional) wing and for an infinite (Two dimensional) wing by matrix iteration technique. The aircraft wing is divided in to a number of Multhopp’s stations. The elastic property of the wing of a typical jet transport is considered for this analysis. Assuming a straight elastic axis, the matrix of torsional influence coefficients associated with Multhopp’s stations has been computed. A MATLAB code is used to iterate the matrix to arrive at the required convergent approximate solution. The solution converges about after ten iterations of the matrix. It is observed that torsional divergence speed estimated on the basis of strip theory without finite span correction is about 18% lower than the divergence speed estimated on the basis of strip theory with finite span correction. Two-dimensional torsional divergence analysis based on strip theory yields conservative torsional divergence speed. A tentative increase of 20 % in torsional stiffness resulted in about 15.5 percent increase in torsional divergence speed of a three-dimensional wing. This shows that divergence speed of a wing is directly proportional to the square root of torsional stiffness. This corroborates the result obtained for a two-dimensional wing. The result of the findings will be mandatory to high performance modern airplane designers for aeroelastic analysis.

Divergence Structural Analysis of an Aircraft Tapered-Unswept Wing Using Aerodynamic Strip Theory for the Case of Flight at Sea Level

“…The dynamic pressure q d with the least Eigen value, which is derived from equilibrium equation in its homogeneous-integral form, are used to calculate the torsional divergence speed of a 3-D wing [5]. Equation (20)'s homogeneous form is:…”

“…Experiments on airplane structures demonstrated that, within certain limitations, force and deflection are linearly connected. Even if the material that makes up the wing structure is stressed at a low level, elastic buckling in the skin of an aircraft wing structure can cause a discontinuity in the force deflection diagram [5]. As a result, the wing structure's elastic properties are presented in the range under the elastic buckling point.…”

“…At some point, the elastic restoring torque is only barely enough to counterbalance the twisting moment, and equilibrium is only attained with the wing breaking point. This is a critical speed known as wing torsional divergence speed [5]. Once the wing's torsional divergence speed is attained, the increase in aerodynamic moment of torsional caused by an arbitrary increase in twist angle equals the increase in elastic restoring torque.…”

“…The wing is statically unstable if the speed arrives at the torsional divergence speed, in which, the increase in the aerodynamic torsional moment exceeds the increase in the elastic restoring torque. Any rise in speed over this value will lead to structural collapse, and the wing will break off [5].…”

“…Setting a given aerodynamic problem into 2-D crosswise direction in comparison with that of longitudinal one. The strip theory is based on the assumption that the 2-dimensional aerodynamic coefficients for added weight for each strip may be calculated and then integrated throughout the length of the body to yield 3-Dimention coefficients [5].…”