Further Refinement of the Subsonic Doublet-Lattice Method

The doublet-lattice method (DLM) is in use worldwide for e utter and dynamic response analyses of aircraft at subsonic speeds. The present paper develops a further ree nement to extend its frequency limits for applications to higher frequency e utter, e.g., for aeroservoelastic systems with high-frequency control surfaces, and dynamic response, e.g., for short wavelength gusts. The DLM is an aerodynamic e nite element method for modeling oscillating interfering lifting surfaces in subsonic e ows. It reduces to the vortex-lattice method at zero-reduced frequency. The number of e nite elements (boxes) required for accurate results depends on aspect ratio and reduced frequency, among other parameters. At high reduced frequency, the chordwise dimension of the boxes must be small. However, an approximation in the method, viz., that the variation of the numerator of the incremental oscillatory kernel function is parabolic across the span of the box bound vortex, restricts the box aspect ratio to about 3. Hence, high-frequency requirements bring an associated requirement for a large number of boxes in the aerodynamic ideali- zation. If a higher-order approximation is used for the spanwise variation of the numerator of the incre- mental oscillatory kernel, the limitation on box aspect ratio can be relaxed and the number of spanwise divisions required in high-frequency analyses will be reduced signie cantly, leading to a reduction in the total number of boxes. This paper replaces the original parabolic approximation by a quartic approxi- mation. The quartic curve-e tting coefe cients are determined for the planar and nonplanar kernels, and the new integrals for the planar and nonplanar normalwash factors are evaluated. The ree nement is incorporated into a DLM code previously known as N5KA, and convergence studies on typical cone gu- rations are presented that attempt to specify a higher limit for practical box aspect ratios.