Dynamic response of width- and thickness-tapered composite beams using Rayleigh-Ritz method and modal testing

摘要

Tapered composite beams formed by width-taper or by terminating or dropping-off some of the plies from the primary structure provide high stiffness to weight ratios, high modulus to weight ratios, damage tolerance and design tailoring capabilities. Since they are increasingly and widely being used in a variety of engineering applications such as robot arms, lightweight mechanical components, aircraft wings, space structures, helicopter blades and yokes, turbine blades, and civil infrastructures, it is important to ensure that their design is reliable and safe. Study of the dynamic response of the tapered composite beams helps to optimize the design and avoid future investments on repairs. It is, therefore, essential for design engineers to evaluate the dynamic characteristics of tapered composite beams effectively. In the present study, symmetric width-tapered and thickness- and width-tapered laminated composite beams are considered and their free and forced vibration response and the buckling response of tapered composite columns are investigated. Due to the variety of tapered beam configurations and the complexity of partial differential equations that govern their free and forced vibration response and their buckling response, no closed-form analytical solution can be obtained. Therefore, Rayleigh-Ritz method is used based on Kirchhoff one-dimensional laminated beam theory and the efficiency and accuracy are established very systematically. Width-tapered laminated composite beam samples are manufactured using NCT-301 graphite-epoxy composite material. Experimental modal analysis using impact hammer testing is conducted for the determination of coherence function, time and auto-response function and Frequency Response Function (FRF) of width-tapered laminated composite beams. The natural frequencies obtained from experimental modal analysis are validated with that obtained Rayleigh-Ritz method. A detailed parametric study is conducted to investigate the effects of width ratio, taper configuration, taper angle, length ratio, boundary conditions, laminate configurations, static end-axial force, and damping on dynamic response. Free and forced vibration response results obtained using Rayleigh-Ritz method are also compared with that obtained using conventional finite element formulation in a separate but simultaneous study.