A State-Space Viscoelastic Model of Double-Beam Systems toward the Dynamic Analysis of Wind Turbine Blades

Abstract

A novel state-space formulation is presented for the dynamic analysis of rotating doublebeam systems, consisting of two elastic beams continuously joined by viscoelastic springs. Although very simple, the proposed model lends itself to be used in studying the transverse vibration of wind turbine blades provided with a viscoelastic core. An efficient numerical scheme of solution is proposed, which can be further extended to include the effects of shear strain within the core, along with geometrical and material nonlinearities. INTRODUCTION A very effective strategy for mitigating dynamic effects on wind turbine blades is the inclusion of a viscoelastic layer between the outer plies (Manwell et al., 2002; Chaviaropoulos et al., 2006; Hansen et al., 2006). This sandwich configuration is usually analyzed relying on somehow equivalent values of elastic stiffness and viscous damping for the viscoelastic components (Johnson and Kienholz, 1982; Rao and He, 1993). Although straightforward, this approach may overestimate the actual dissipation provided by the viscoelastic materials, as demonstrated by recent investigations on the vibration of viscoelastically damped structures (Palmeri et al., 2003; Palmeri and Ricciardelli, 2006). These studies have also pointed out that enlarged state-space models allow overcoming the traditional concepts of equivalent stiffness and damping, and lend themselves to be implemented in computationally efficient time-domain numerical schemes. The latter feature can be very useful in the fatigue analysis of rotor blades, when cycle counting techniques require time histories of internal forces at critical points for a number of operational conditions (Fuglsang and Madsen, 1999; Ragan and Manuel, 2007; Hansen, 2008). Within this framework, a novel state-space formulation is presented for studying the transverse vibration of double-beam systems, made of two outer elastic beams continuously joined by an inner viscoelastic layer. As apposite to other methods available in the literature (Vu et al., 2000; Oniszczuk, 2000 and 2003), the proposed technique enables one to considerer beams with varying cross section and rate-dependent constitutive law for the inner layer, as typical in the case of rotor blades. Although the double-beam representation is quite crude for actual systems, the proposed state-space approach proves to be accurate and versatile, and is well suited to be extended to more sophisticated models for wind turbine applications. 1973 Earth and Space 2010: Engineering, Science, Construction, and Operations in Challenging Environments © 2010 ASCE