Prediction of the vibration characteristics of a full-size structure from those of a scale model Jia-Jang Wu a, * , M.P. Cartmell b , A.R. Whittaker b a Department of Marine Engineering, National Kaohsiung Institute of Marine Technology, No. 142 Hai-Chuan Road, Nan-Tzu, Kaohsiung, Taiwan 811, Taiwan, ROC b Department of Mechanical Engineering, James Watt Building, University of Glasgow, Glasgow G12 8QQ, UK Received 29 October 2001; accepted 4 May 2002 Abstract The dynamic characteristics of a three-dimensional full-size crane structure are predicted for the system when it is subjected to multiple two-dimensional time-dependent moving loads using the relevant features of a scale model and the associated scaling laws. In order to establish the procedure the dynamic responses of a full-size uniform beam and its scale model, both elastically supported at each end and subjected to a moving force, are investigated. Both free and forced vibration characteristics are used to validate the scaling laws. From the premises established in this example certain derived scaling laws are then applied to the gantry crane problem. Ó 2002 Elsevier Science Ltd. All rights reserved. 1. Introduction The objective of this paper is to predict the structural vibrations of a full-size gantry crane by means of a laboratory model. This work is based on previous re- search into the dynamics and control of mobile gantry crane lifting gear, and utilises an existing 1/10 scale laboratory model, as shown in Fig. 1. Recent work on the structural dynamics of this class of machinery has been reported by Wu and co-workers [1,2] and forms the foundation for the research discussed in this paper. In practice mobile gantry cranes are used in dockside and container yard locations and are massive wheeled structures with principal actuated degrees of freedom driven by electric or electro-hydraulic motors. In addi- tion to this mobile gantry cranes are capable of signifi- cant flexural motions within the structural members themselves, and it is this aspect of their behaviour which is analysed within this paper. For reasons of pragmatism the 1/10 scale model has had to be fixed to the floor of the laboratory, with the gantry motion replaced by an additional, orthogonal, trolley motion. This has led to a structure which is composed of two parts, the stationary framework, as shown by the dotted lines in Fig. 1, and a moving substructure comprising two mobile transverse rails, denoted by P, and a moving trolley carrying the lifting frame, or spreader. The moving substructure runs on two longitudinal rails, denoted by Q and fixed to the top of the stationary framework. On this basis the trolley moves transversely along P in the  x direction and the whole substructure runs along Q in the longitudinal ( y ) direction. In addition to this the spreader can lower or hoist in the  z direction (relative to the motion of the trolley). In this way the spreader can be located at any point within a large three-dimensional workspace within the framework of the scale model. Wu et al. [2] devel- oped a mathematical model to represent the stationary framework of the scale crane model and then used this for calculating the dynamic response of the same struc- ture under the influence of appropriate moving loads. Notwithstanding the conceptual structural differ- ences between the laboratory scale model and typical machines operating in the field, it is generally the case that the vibration characteristics of one will not relate meaningfully to the other without the application of Computers and Structures 80 (2002) 1461–1472 www.elsevier.com/locate/compstruc * Corresponding author. Tel.: +886-7-361-7141x3207; fax: +886-6-280-8458. E-mail address: jjangwu@mail.nkimt.edu.tw (J.-J. Wu). 0045-7949/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0045-7949(02)00095-0