Dynamic response of a beam excited by a moving mass

Nonlinear Dynamic Analysis of an Inclined Timoshenko Beam Subjected to a Moving Mass/Force with Beam’s Weight Included

“…To establish verifications of our analysis, we consider the data given in [12] 2 . Based on input above data and developed computer program for the linear analysis, we calculated the maximum deflection of the mid-point of the considered weightless beam as; 5.91 mm, whereas the similar result reported by [29] and [12] are 5.84 mm and 5.78 mm, respectively which show very good agreement between our numerical result and other references. However, as described before, in this study we focus on the nonlinear analysis of coupled longitudinal, transversal and cross-section rotational vibrations of an inclined self-weight beam under the act of a traveling mass.…”

Vehicle-Bridge Dynamic Interaction Using Finite Element Modelling

“…They have zero value outside the interval between adjacent nodes, and for the location of a vehicle wheel j over a bridge node i, A ij (t) and B ij (t) become 1 and 0 respectively, which satisfies u j (t)=w b,i (t). The numerical expression for these auxiliary functions can be found in Cifuentes (1989) and González et al (2008a). The vector of equivalent nodal forces {f b } composed of forces f i (t) and moments M i (t) acting on a bridge node i at time t can also be expressed as a function of the p interaction forces using the auxiliary functions: …”

“…The algorithms to carry out this calculation can be classified in two main groups: (a) those based on an uncoupled iterative procedure where equations of motion of bridge and vehicle are solved separately and equilibrium between both subsystems and geometric compatibility conditions are found through an iterative process (Veletsos & Huang, 1970;Green et al, 1995;Hwang & Nowak, 1991;Huang et al, 1992;Chatterjee et al, 1994b;Wang et al, 1996;Yang & Fonder, 1996;Green & Cebon, 1997;Zhu & Law, 2002;Cantero et al, 2009), and (b) those based on the solution of the coupled system, i.e., there is a unique matrix for the system that is formed by eliminating the interaction forces appearing in the equations of motion of bridge and vehicle, and updated at each point in time (Olsson, 1985;Yang & Lin, 1995;Yang & Yau 1997;Henchi et al, 1998;Yang et al, 1999Yang et al, , 2004aKim et al, 2005;Cai et al, 2007;Deng & Cai, 2010;Moghimi & Ronagh, 2008a). The use of Lagrange multipliers can also be found in the solution of VBI problems (Cifuentes, 1989;Baumgärtner, 1999;González et al, 2008a). A step-by-step integration method must be adopted to solve the uncoupled or coupled differential equations of motion of the system.…”

A general solution to the identification of moving vehicle forces on a bridge

“…Truck and bridge have been modeled with the general-purpose FE package MSc/NASTRAN for Windows [27]. The authors use an approach based on a Lagrange technique that allows for the representation of the compatibility condition at the bridge/vehicle interface through a set of auxiliary functions [28,29]. Accordingly, software has been developed to generate an entry into the assembled stiffness matrix of the vehicle-bridge system provided by MSc/NASTRAN [4].…”