Vibration Analysis Of Thin-Walled Box-Beams Considering Distortion

Thin-walled members are widely used in high-rise buildings, long-span bridges, and other important engineering structure. More and more attention is paid on thin-walled members because of their diversity and complexity. Since seismic analysis and dynamic analysis are important in high-rise buildings and long-span bridges, free vibration analysis becomes an important part of analysis of thin-walled members.This paper presents a spline finite member element method considering distortion for free vibration analysis of thin-walled box beams. Starting from the relation between displacement and strain when a beam is deforming, this paper establishes element energy equation for free vibration. Because the displacement of a box beam is a continuous function, equation is difficult to achieve analytical solutions. By using Vlasov generalized coordinates to simulate the cross-section lateral displacements , transformed B3 spline function to simulate the cross-section warping displacements and general displacement solution in static analysis to simulate vibration displacements, this paper gets the element energy equation with 4 lateral displacements and nodes'warping displacements, and gets the global energy equation by finite-element method. Finally an vibration equation is derived from the equation above based on Hamilton Variation Principle. Free vibration frequencies and corresponding modes are achieved by solving the eigen equation.Analysis in this paper gives up the rigid-frame assumption and takes distortion mode of box beams into consideration by adding one unknown displacement variable. It also reflects shear lag effect by considering the shear deformation of the median surface in thin-walled members. Using transformed B3 spline function to simulate cross-section displacements, actual nodes'displacements substitute generalized displacements, so the compatibility of displacement at nodes where walls joint is satisfied. Spline interval and steps may change, which makes the method flexible and simple.Compared with solutions by software MIDAS, solutions of some examples show that the method reflects the distortion of box beams, and is simple in preprocess, convergent and sufficiently accurate.