Dynamic responses of a ribbon floating bridge under moving loads

A Study on Motion Control of Multiple Floating Units

“…(2) and (3) Where m is the mass, and z I is the inertia moment of the floating unit on the fixed z-axis, respectively. Generally, the planar motions of this multi-connected floating units shown in Fig.…”

“…In recent years, a certain number of researchers paid attention to the pontoon floating bridge. S. Fu and W. Cui presented the dynamic analysis of floating bridges [3]. Besides, Hirono et al [4] introduced a new study on measurement system for positional displacement of floating units for pontoon bridges.…”

Numerical and Experimental Investigation of Ribbon Floating Bridges

“…Connections are very important in determining the displacement response of ribbon pontoon floating bridges and may be either rigid-or hinge-connected. The specific connection type determines the response characteristics of the bridge such as natural frequency of vibration as well as the amplitude of vibration (Fu & Cui, 2012).…”

“…Illustration of the nonlinear connector(Fu & Cui, 2012) .............................. 24 Figure 2-5: Numerical vs Experimental results for midpoint displacement at 3m/s, 6m/s and 9m/s vehicle speeds (Fu & Cui, 2012) ..................................................................... 25 Figure 2-6: Vehicle-structure system: (a) schematic illustration and (b) free body diagram (Neves et al, 2012) ........................................................................................................ 26 Figure 2-7: Simply supported beam subjected to moving sprung mass (Neves et al, 2012) ...................................................................................................................................... 26 viii Figure 2-8: Vertical displacement of first sprung mass (Neves et al, 2012) .................... 27 Figure 2-9: Dimensionless Basic Natural Vibration Frequency vs Depth to Length Ratio of Continuous Floating Bridge (Fleischer & Park 2004)................................................. 28 Figure 2-10: Bridge midpoint displacement versus vehicle position at 10 m/s for 6-m, 9m and 12-m water depths ............................................................................................... 29 Figure 2-11: Half-bonded contact element with a) three, b) two, c) one lift-off point (Nguyen & Pham, 2016) ................................................................................................ 30 Figure 2-12: Dynamic Modification Factors for different Foundation Stiffness Parameters (a) K0 = 10, (b) K0 = 20, (c) K0 = 30, (d) K0 = 40. (Nguyen & Pham, 2016) .................... 31 Figure 2-13: Comparative Vehicle Model (Zhang et al,, 2010) ....................................... 32 Figure 3-1: Pontoon Hinged and Rigid Connection details ............................................. 39 Figure 3-2: Rigid Connected Bridge Bending Moments (Harre, 2002) ........................... 40 Figure 3-3: The Beam Element (Logan et al, 2007) ....................................................... 41 Figure 3-4: Vehicle-Bridge Idealization ......................................................................... 43 Figure 3-5: Free Body Diagram of vehicle-bridge dynamic forces ................................. 52 Figure 3-6: Free Body Diagram of floating bridge traversed by single axle (after Humar…”

“…The vehicle(Figure 3-4)is idealized by two unsprung masses each of mass and , representing the rear and front unsprung masses respectively; a sprung mass with mass moment of inertia ; and rear and front suspensions having spring stiffness and damping coefficient , and ,respectively. This vehicle model is simple yet captures the vehicle dynamic characteristics, and has been used by many authors includingHumar & Kashif (1993), Fu & Cui (2012,Nguyen & Pham (2016) andErtekin et al (2001).…”