Free Dry Vibration of Low-Aspect-Ratio Cantilever Wing: SemiAnalytical and Numerical Analysis With Experimental Verification

Abstract

The free vibration of a low-aspect cantilever wing is studied by semianalytical, numerical, and experimental means. The wing is modeled as a two-way tapered, hollow Kirchhoff's plate, with the chord-wise section as symmetrical NACA0018 aerofoil. The chord length and the thickness taper from root to tip, over the span. The semianalytical approach is based on Galerkin's method, which includes the modal superposition of two orthogonal beam modeshapes (free-free beam in chord-wise direction and cantilever beam in span-wise direction). The free vibration is also studied numerically using ANSYS. The results have been compared with an experimental study, performing the dry impact hammer test. A model scale wing has been constructed from a 3-mm-thick metal sheet, with a length-scale ratio of 1:10. Comparative studies have been done among the three methods. The feasibility of modeling a low-aspect-ratio wing as a plate has been investigated. 1. Introduction Lifting surfaces commonly occur in engineering structures: fans, steam and gas turbine blades, impeller blades, wind turbine blades, helicopter fans, airplane wings, marine propeller blades, marine rudders and skegs, and other control surfaces like hydrofoils and wings in high-speed marine crafts. The lifting surface is typically a cantilever, with one edge welded to the main structure (root), and the other end free (tip). The span-wise geometry is tapered, for greater strength at the root and lighter weight at the tip. The chord-wise cross section is an aerofoil, which acts as a lifting surface to the incoming flow at varying angles of attack. The aspect ratio of the lifting surface, i.e., the ratio of the span length to the mean chord length, may vary from 0.4 to 0.6 in a turbine blade to 12 to 15 in an airplane wing/wind turbine. This work focuses on a low-aspect-ratio lifting surface, whose usual span-to-chord ratio is 1.5–2.