Stochastic response of a double hinged articulated leg platform under wind and waves Mohd Moonis Zaheer a,n , Nazrul Islam b a CES, University Polytechnic, AMU Aligarh 202002, India b Department of Civil Engineering, Jamia Millia Islamia, New Delhi 110025, India article info Article history: Received 15 April 2011 Received in revised form 14 August 2012 Accepted 23 August 2012 Available online 23 October 2012 Keywords: Articulated leg platform Offshore structures Compliant towers Random wind Dynamic response abstract The displacement response of an articulated leg platform (ALP) is mainly governed by its rigid body mode of vibration which has a very low frequency. Since the fluctuating component of the wind velocity has very low frequency energy content, the wind induced vibration of the platform may be significant. In this paper, the response of an ALP to wave alone, wind alone, and correlated wind and waves are investigated. The fluctuating component of the wind is modeled by Simiu’s spectrum, while the sea state is characterized by Pierson–Mosokowitz (P–M) spectrum. Random wind and waves are simulated by Monte Carlo simulation technique. For comparative studies of the platform responses, wind spectra suggested by Kareem, Davenport and API-RP2A are employed. The nonlinear dynamic equations of motion are derived by Lagrangian approach considering nonlinearities due to variable submergence, instantaneous tower orientation and drag force. The response of ALP is determined by a time domain iterative method using Newmark’s- b integration scheme. It is concluded that response estimates based on the Davenport spectrum are lower than those based on the Simiu, Kareem and API RP 2A spectra due to higher energy available in these spectra at low frequencies. Furthermore, average hinge rotation of the platform under all cases is within permissible limits for platform operations. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction The fundamental frequency of an articulated leg platform (ALP) is designed to be well below the commonly occurring frequency range of waves to avoid dynamic amplification. How- ever, such platforms are more susceptible to low frequency excitation of winds. Since most of the energy in wind lies in the low frequency range, such towers may have significant dynamic response due to wind gustiness. The magnitude of vibration depends upon the exposed area of the platform to wind and its velocity of approach. The wind induced vibration of ALPs is a complicated phenom- enon due to fluid structure interaction effects. As such, there is lack of a comprehensive study conducted to investigate the wind and wave induced vibration of ALPs. Some studies related to these vibrations are available for other compliant platforms such as TLPs and guyed towers (Qi et al., 1991; Vickery, 1995; Ahmad, 1996; Ahmad et al., 1997; Bisht and Jain, 1998; and Zeng et al., 2006). Jain and Kirk (1981) presented an analysis of the dynamic response of a double hinged articulated tower to non-collinear waves and current. Datta and Jain (1990) analyzed the response of a single hinged ALP to random wind alone and to the combined effect of wind, wave and current forces. Sellers and Niedzwecki (1992) furnished valuable inputs on a general mathematical model of multi hinged articulated tower. Islam and Ahmad (2003) analyzed the results of a double pendulum articulated tower under long crested and directional random seas. McNeilly and Will (2006) described the design and installation of Benguela–Belize compliant piled tower in Angola. In one of the studies, Deepak and Datta (2008) presented the probabilistic response of a single leg articulated tower using stochastic aver- aging procedure together with weighted residual error minimiz- ing technique. Islam et al. (2009) compared the responses of a single and double hinged articulated tower under various ocean environments. They observed that studies of wind were found to be imperative for double hinged articulated towers to serve and survive in the hostile offshore environment. The response of an ALP under different ocean environments is an important phenomenon to study because of the complex hydrodynamic and aerodynamic interactions. The behavior of double hinged articulated tower under different wind spectra found no reporting in the literature. Kareem (1985) compared tension leg platform (TLP) responses under Davenport, Harris and Kaimal spectra. The study highlights the superiority of Kaimal spectrum due to the presence of higher energy in the meso scale Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jweia Journal of Wind Engineering and Industrial Aerodynamics 0167-6105/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jweia.2012.08.005 n Corresponding author. Tel. þ91 9911697968. E-mail addresses: mooniszaheer@rediffmail.com (M. Moonis Zaheer), nazrulislam.jmi@gmail.com (N. Islam). J. Wind Eng. Ind. Aerodyn. 111 (2012) 53–60