Dynamic Analysis of an Annular Plate Resting on the Surface of an Elastic Half-Space with Distributive Properties

This work gives a semi-analytical approach for the dynamic analysis of a plate of annular shape resting on the surface of an elastic half-space with distributive properties. Such calculations have been associated with significant mathematical challenges, often leading to unrealizable computing processes. Therefore, the dynamic analysis of beams and plates interacting with the surfaces of elastic foundations has to date not been completely solved. To advance this work, the deflections of the plate are determined by the Ritz method, and the displacements of the surface of elastic half-space are determined by studying Green's function. The coupling of these two studies is achieved by a mixed method, which allows determination of reactive forces in the contact zone and, hence, the determination of other physical magnitudes. Natural frequencies, natural shapes, and the dynamic response of a plate due to external harmonic excitation are determined. Validation with a Winkler problem illustrates the distributive property effects on the results of the dynamic analysis

Dynamic amplification of a multi-span orthotropic bridge deck under vehicular movement

The response of a multi-span, continuous orthotropic bridge deck during truck loading is investigated to better understand the dynamic interaction between moving vehicles and highway bridge decks. The present study is based on a recently published, semi-analytical approach for free vibration in which the modal superposition method incorporates intermodal coupling. Herein, the bridge deck is modeled as a jointless, multi-span, orthotropic plate, and the vehicle is modeled as a dynamic, multi-body system. The road surface roughness randomness is modeled as a normal, stationary, random process described by its Power Spectral Density (PSD). The coupled equations of the motion vehicle/bridge deck are solved by Newmark’s method. An iterative process in each time step is performed to find the equilibrium between the bridge deck and vehicle tires using an uncoupled algorithm previously developed by other authors. Two numerical application examples are presented: an isotropic and an orthotropic, three-span bridge deck both crossed by an AASHTO-based vehicle model. In example one, the intermodal coupling affects the dynamic deflection of bridge deck but only slightly. Example two demonstrates that the loading mode and the vehicle speed have a significant influence on the Dynamic Amplification Factor. However, the most important parameter to affect the dynamic vehicle/bridge deck interaction force is the road’s surface roughness, as has been shown for other bridge types under various load conditions

Extension of semi-analytical approach to determine natural frequencies and mode shapes of multi-span orthotropic bridge deck

This paper extends a single equation, semi-analytical approach for three-span bridges to multispan ones for the rapid and precise determination of natural frequencies and natural mode shapes of an orthotropic, multi-span plate. This method can be used to study the dynamic interaction between bridges and vehicles. It is based on the modal superposition method taking into account intermodal coupling to determine natural frequencies and mode shapes of a bridge deck. In this paper, a four- and a five-span orthotropic roadway bridge decks are compared in the first 10 modes with a finite element method analysis using ANSYS software. This simplified implementation matches numerical modeling within 2% in all cases. The paper verifies that applicability of single formula approach as a simpler alternative to finite element modeling.Deposited by bulk impor

Homogenization of a Composite, Multi-Girder Bridge Deck as an Equivalent Orthotropic Plate

3rd International Conference on Composite Materials and Structures, University of Sciences and Technology of Oran, Oran, Algeria, 2 - 3 December 2014Most bridge decks are orthotropic, because of the orthotropic nature of their component parts (e.g. isotropic slabs, grillages, T-beam bridge decks, multi-beam bridge decks, multi-cell boxbeam bridge, and slabs stiffened with ribs of box section). Thus, the orthotropic plate theory plays an important role in the static and dynamic analysis of bridges. For example, a multicellular Fiber Reinforced Polymer (FRP) composite bridge deck can be modeled as an orthotropic plate with equivalent stiffnesses that account for the size, shape, and constituent materials of the cellular deck. Thus, the complexity of material anisotropy of the panels and orthotropic structure of the deck system can be reduced to an equivalent orthotropic plate with global elastic properties in two orthogonal directions – parallel and transverse to the longitudinal axis of the deck cell. This paper investigates a homogenization of composite, orthotropic, three-span, multi-girder bridge to explore the concept of the volumetric and mass fractions of a reinforced composite material. This homogenization takes into account all properties of this composite structure (deck slab, girders and diaphragms). From those, all the equivalent orthotropic plate properties were obtained. The work is highly relevant with respect to evaluating the dynamic interaction between bridges and vehicles

Dynamic response of a multi-span, orthotropic bridge deck under moving truck loading with tandem axles

In this paper, a new three-dimensional vehicle with tandem axels at the rear is developed to determine dynamic response of bridge deck under load applying truck. The vehicle is modeled by a three-axle dynamic system with 9 degrees of freedom to accurately simulate the disposition and the intensity of loads on the bridge deck. The bridge deck is modeled by a thin, orthotropic, multi-span plate. The road surface irregularities are modeled by a random function characterized by a spectral roughness coefficient and power spectral density. The modal method is used to solve the equation of motion of the bridge deck. Equations of motion of the vehicle are obtained using the virtual work principle. The coupled equations of motion vehicle/bridge deck are integrated numerically by Newmark’s method. A computational algorithm in FORTRAN is then elaborated to solve the integrated equations of motion in a decoupled, iterative process. A numerical example of an orthotropic, three-span bridge deck, excited by a 9 degree of freedom truck is presented. The resulting distribution of the Dynamic Amplification Factor (DAF) on the bridge deck does not reflect any particular trend, because high values can be obtained at points where the vertical displacement is small. The DAF is significant only under the interaction force. Thus, the road surface roughness was shown to have a significant influence on the dynamic vehicle/bridge deck interaction forces

Dynamic Analysis of an Annular Plate Resting on the Surface of an Elastic Half-Space with Distributive Properties

This work gives a semi-analytical approach for the dynamic analysis of a plate of annular shape resting on the surface of an elastic half-space with distributive properties. Such calculations have been associated with significant mathematical challenges, often leading to unrealizable computing processes. Therefore, the dynamic analysis of beams and plates interacting with the surfaces of elastic foundations has to date not been completely solved. To advance this work, the deflections of the plate are determined by the Ritz method, and the displacements of the surface of elastic half-space are determined by studying Green's function. The coupling of these two studies is achieved by a mixed method, which allows determination of reactive forces in the contact zone and, hence, the determination of other physical magnitudes. Natural frequencies, natural shapes, and the dynamic response of a plate due to external harmonic excitation are determined. Validation with a Winkler problem illustrates the distributive property effects on the results of the dynamic analysis

Free vibration analysis of multi-span orthotropic bridge deck with rubber bearings

In this paper, a semi-analytical approach is proposed for free vibration analysis of a multi-span, orthotropic bridge deck with rubber bearings. This allows more realistic modeling of vibration transmission from a bridge’s deck to its supports. The approach is based on modal superposition incorporating intermodal coupling. The bridge deck was modeled as a continuous, multi-span, orthotropic rectangular plate with equivalent rigidities. The rubber bearings were inserted between the girders and rigid supports to absorb traffic induced vibrations. The rubber bearing was modeled by linear elastic, vertical supports as very flexible in rotation and highly rigid in the vertical direction. The method’s efficacy was validated against two numerical examples. The absolute error was less than 10%