Dynamic response of bridges under travelling loads

1993 ◽  
Vol 20 (2) ◽  
pp. 287-298 ◽  
Author(s):  
J. L. Humar ◽  
A. M. Kashif
Keyword(s):  
Dynamic Response ◽  
Rational Design ◽  
Weight Ratio ◽  
Experimental Investigations ◽  
Speed Ratio ◽  
Force Model ◽  
Beam Model ◽  
Dynamic Amplification Factor ◽  
Design Procedures ◽  
Dynamic Amplification

In spite of a number of analytical and experimental investigations on the dynamic response of bridges to moving vehicle loads, the controlling parameters that govern the response have not been clearly identified. This has, in turn, inhibited the development of rational design procedures. Based on an analytical investigation of the response of a simplified beam model traversed by a moving mass, the present study identifies the governing parameters. The results clearly show why attempts to correlate the response to a single parameter, either the span length or the fundamental frequency, are unsuccessful. Simple design procedures are developed based on relationships between the speed ratio, the weight ratio, and the dynamic amplification factors; and a set of design curves are provided. Key words: dynamic response of bridges, vehicle–bridge interaction, moving force model, moving sprung mass model, dynamic amplification factor.

scholarly journals Damped dynamic response of strengthened beams by composite coats under moving force by FEM

2018 ◽  
Vol 106 (2) ◽  
pp. 206
Author(s):  
Abdennacer Chemami ◽  
Youcef Khadri ◽  
Sabiha Tekili ◽  
El Mostafa Daya ◽  
Ali Daouadji ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Numerical Study ◽  
Moving Load ◽  
Damping Ratio ◽  
Time Integration ◽  
Superposition Method ◽  
Dynamic Amplification Factor ◽  
Aluminum Composite ◽  
Strengthened Beam ◽  
Dynamic Amplification

This paper presents a numerical study of the free and damped forced vibration of simply-supported beams with composite coats subjected to a moving load by use of finite elements method. Three types of beam configurations, aluminum, composite and strengthened beam are investigated. The equation of motion of the beam is solved using the modal superposition method and integrated by applying the Newmark time integration procedure. Good agreements were achieved between the FEM and analytical solutions. The damped dynamic response, critical velocities and the dynamic amplification factor of the beam are calculated for different parameters such as the thickness ratio, the fiber orientation of the coat and damping ratio.

Dynamic Response of High Steep Rock Slopes Based on Wenchuan Near-Field Seismic Motion Characteristics

2010 ◽  
Vol 168-170 ◽  
pp. 1090-1097
Author(s):  
Shi Guo Xiao ◽  
Wen Kai Feng
Keyword(s):  
Numerical Analysis ◽  
Dynamic Response ◽  
Amplification Factor ◽  
Near Field ◽  
Seismic Load ◽  
Rock Slopes ◽  
Dynamic Amplification Factor ◽  
Seismic Motion ◽  
Dynamic Amplification ◽  
Motion Characteristics

Near-field seismic motion characteristics are analyzed in accordance with records of the 2008 Ms8.0 Wenchuan Earthquake measured at Wolong Station, upon which the determination of seismic load is introduced. Dynamic response features, such as acceleration, displacement and stress, of high steep rock slopes on the banks of Zipingpu Reservoir at a variety of locations resulting from horizontal seismic force are analyzed with a numerical analysis routine. The dynamic amplification factor on the slope top is determined, leading to a characterization of the mode of failure of the high steep slope. Analyses show that the dynamic amplification factor at the top of the slopes is about 1.34; however, dynamic response deformation features and stress state at different positions on the slope vary. Earthquake damage of the high steep rock slopes consists mainly of partial avalanche of the rock mass at the top of the slopes by joint cutting. Field investigations after the earthquake have partially confirmed the numerical analysis results presented in this paper.

Dynamic Behaviour of Minimum Platforms Under Random Seas

2003 ◽  
Author(s):  
Micaela Pilotto ◽  
Beverley F. Ronalds
Keyword(s):  
Dynamic Response ◽  
Dynamic Behaviour ◽  
Amplification Factor ◽  
Finite Element Models ◽  
Dynamic Amplification Factor ◽  
Maximum Value ◽  
Random Seas ◽  
Exponential Stretching ◽  
Structural Configurations ◽  
Dynamic Amplification

This paper describes the dynamic response of minimum facilities with different structural configurations which are subjected to random seas. The finite element models are kept simple with the aim of focusing on the physics of the phenomena involved. The response is studied in terms of the dynamic amplification factor (DAF), representing the ratio between the dynamic and the static response. Two different formulations of the DAF under random seas are compared. The first is defined in terms of standard deviation (DAF1), the second in terms of the most probable maximum value (DAF2). Ringing is observed to be a relevant feature of the dynamic response and to affect primarily the braced monopod configurations. Ringing is detected using DAF2. The paper also addresses the importance of the kinematic representation above the still water level. Different methods of stretching the velocity field in the wave zone (delta, Wheeler and exponential stretching) are shown to have a significant impact on the dynamic response of the platforms.

Period-Doubling Bifurcations in Atomic Force Microscopy

2009 ◽  
Author(s):  
Andrew J. Dick ◽  
Wei Huang
Keyword(s):  
Dynamic Response ◽  
Atomic Force Microscope ◽  
Period Doubling ◽  
Surface Force ◽  
Resonance Excitation ◽  
Force Model ◽  
Beam Model ◽  
Atomic Force ◽  
Local Material ◽  
Local Material Properties

The dynamic response of an atomic force microscope cantilever probe is studied for off-resonance excitation and interactions with a soft silicone rubber material. The dynamic response of the probe is simulated using a three-mode approximation of the Euler-Bernoulli beam model for excitation at two-and-a-half times the probe’s fundamental frequency. These simulations are conducted in order to reproduce the period-doubling bifurcation experimentally observed in the response of the probe of a commercial atomic force microscope. In order to duplicate this behavior, parameters within the surface force model are tuned to account for variations in the characteristics of the sample material. Through this work, the relationship between the sample material’s effective stiffness and the response behavior of the probe are studied in an effort to develop the means to identify the local material properties of a sample by characterize the nonlinear response of the probe.

scholarly journals Effect of temperature and porosities on dynamic response of functionally graded beams carrying a moving load

2017 ◽  
Vol 20 (K2) ◽  
pp. 24-33
Author(s):  
Tuyen Van Bui
Keyword(s):  
Dynamic Response ◽  
Temperature Rise ◽  
Material Properties ◽  
Amplification Factor ◽  
Moving Load ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Element Formulation ◽  
Dynamic Amplification Factor ◽  
Dynamic Amplification

The effect of temperature and porosities on the dynamic response of functionally graded beams carrying a moving load is investigated. Uniform and nonlinear temperature distributions in the beam thickness are considered. The material properties are assumed to be temperature dependent and they are graded in the thickness direction by a power-law distribution. A modified rule of mixture, taking the porosities into consideration, is adopted to evaluate the effective material properties. Based on Euler-Bernoulli beam theory, equations of motion are derived and they are solved by a finite element formulation in combination with the Newmark method. Numerical results show that the dynamic amplification factor increases by the increase of the temperature rise and the porosity volume fraction. The increase of the dynamic amplification factor by the temperature rise is more significant by the uniform temperature rise and for the beam associated with a higher grading index.

scholarly journals Dynamic Response and Robustness Evaluation of Cable-Supported Arch Bridges Subjected to Cable Breaking

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Guotao Shao ◽  
Hui Jin ◽  
Ruinian Jiang ◽  
Yue Xu
Keyword(s):  
Dynamic Response ◽  
Evaluation Method ◽  
Progressive Collapse ◽  
Bending Moment ◽  
Simulation Method ◽  
Dynamic Amplification Factor ◽  
Cable System ◽  
Evaluation Indexes ◽  
Dynamic Amplification ◽  
Arch Bridges

Cable-supported arch bridges have had many cable break accidents, which led to dramatic deck damage and even progressive collapse. To investigate the dynamic response and robustness of cable-supported arch bridges subjected to cable breaking, numerical simulation methods were developed, compared, and analyzed, and an effective and accurate simulation method was presented. Then, the cable fracture of a prototype bridge was simulated, and the dynamic response of the cable system, deck, and arch rib was illustrated. Finally, the robustness evaluation indexes of the cable system, deck, and arch rib were constructed, and their robustness was evaluated. The results show that the dynamic response of the adjacent cables is proportional to the length of the broken cable, while the dynamic response of the deck is inversely proportional to the length of the broken cable. The dynamic amplification factor of the cable tension and deck displacement is within 2.0, while that of the arch rib bending moment exceeds 2.0. The break of a single cable will not trigger progressive collapse. When subjected to cable breaking, the deck system has the least robustness. The proposed cable break simulation procedure and the robustness evaluation method are applicable to both existing and new cable-supported bridges.

Estimation of Equivalent Dynamic Amplification Factor (EDAF) on a Jacket Structure

2013 ◽  
Author(s):  
Gro Sagli Baarholm ◽  
Atle Johansen ◽  
Jørn Birknes ◽  
Sverre Haver
Keyword(s):  
Dynamic Response ◽  
Linear Time ◽  
Limit State ◽  
Wave Model ◽  
Ultimate Limit State ◽  
Static Response ◽  
Dynamic Amplification Factor ◽  
Irregular Wave ◽  
The North ◽  
Dynamic Amplification

Non-linear time domain irregular wave simulations have been performed for the Kvitebjørn jacket platform located in the North Sea with the aim to quantify the dynamic amplification. The jacket is a slender structure installed in about 190m water depth. For each of the selected extreme sea states both quasi-static and dynamic response simulations have been carried out for several wave realizations using different seeds. Based on the quasi-static response and dynamic response, equivalent dynamic amplification factors (EDAFs) were calculated for different response measures in the jacket. EDAF is the factor one has to multiply the q-probability quasi-static response with in order to obtain an adequate estimate of the q-probability dynamic response. The EDAFs are to be used in ultimate limit state (ULS) and accidental limit state (ALS) analyses of the platform. Simulations were performed applying a Gaussian wave with Wheeler stretching and a second-order wave model. This paper focuses on the selection of wave kinematics method and on the establishment of the EDAF analysis procedure.

Effects of Supporting Member on the Nonlinear Parametric Resonance of a Cable

2016 ◽  
Vol 16 (02) ◽  
pp. 1450096
Author(s):  
Shi Cong Hong ◽  
Du Jian Zou ◽  
Ming Hai Wei ◽  
Kun Lin
Keyword(s):  
Multiple Scales ◽  
Coupled Model ◽  
Parametric Vibration ◽  
Beam Model ◽  
Mass Ratio ◽  
Dynamic Amplification Factor ◽  
Proposed Model ◽  
Large Amplitude Motions ◽  
Dynamic Amplification ◽  
Inclined Angle

The cables in cable-supported structures are commonly subjected to potentially damaging large amplitude motions mainly arising from parametric vibrations of the cables. This paper presents an analysis of the effects of supporting member on the nonlinear parametric vibration of a cable using a coupled cable-beam model. The proposed model considers the parameters of the beam and geometric nonlinearities of the cable. First, the multiple scales method is applied directly to the model, and by using the first-order equation, the frequency response and stability conditions are obtained. The effects of the mass ratio, stiffness ratio, and inclined angle of the coupled model are then evaluated. Then, the effects of these parameters on the parametric vibration characteristics of cable are investigated in terms of the maximum mid-span displacement and dynamic amplification factor. The results obtained represent an extension of the previous studies, which provide some useful insights into the design of cable-supported structures.

Dynamic Response of Fractionally Damped Viscoelastic Plates Subjected to a Moving Point Load

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Rajendra Kumar Praharaj ◽  
Nabanita Datta ◽  
Mohammed Rabius Sunny
Keyword(s):  
Dynamic Response ◽  
Fractional Derivative ◽  
Dynamic Behavior ◽  
Moving Load ◽  
Viscoelastic Model ◽  
Point Load ◽  
Dynamic Amplification Factor ◽  
Modal Summation ◽  
Liouville Fractional Derivative ◽  
Dynamic Amplification

Abstract The dynamic response of fractionally damped viscoelastic plates subjected to a moving point load is investigated. In order to capture the viscoelastic dynamic behavior more accurately, the material is modeled using the fractionally damped Kelvin–Voigt model (rather than the integer-type viscoelastic model). The Riemann–Liouville fractional derivative of order 0 < α ≤ 1 is applied. Galerkin's method and Newton–Raphson technique are used to evaluate the natural frequencies and corresponding damping coefficients. The structure is subject to a moving point load, traveling at different speeds. The modal summation technique is applied to generate the dynamic response of the plate. The influence of the order of the fractional derivative on the free and transient vibrations is studied for different velocities of the moving load. The results are compared with those using the classical integer-type Kelvin–Voigt viscoelastic model. The results show that an increase in the order of the fractional derivative causes a significant decrease in the maximum dynamic amplification factor, especially in the “dynamic zone” of the normalized sweep time. The dynamic behavior of the plate is verified with ansys.

scholarly journals Dynamic Response of Long Rectangular Floors Subjected to Periodic Force Excitation

Materials ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1417 ◽  
Author(s):  
Zsuzsa B. Pap ◽  
László P. Kollár
Keyword(s):  
Dynamic Response ◽  
Amplification Factor ◽  
Damping Ratio ◽  
Effective Width ◽  
Rectangular Plates ◽  
Dynamic Amplification Factor ◽  
Periodic Force ◽  
Static Loads ◽  
Dynamic Amplification ◽  
Force Excitation

Since damping in lightweight floors is usually low, dynamic amplification can be rather high. Long rectangular plates subjected to concentrated loads are often investigated by a replacement beam with a so called “effective width”. Although this approach is a reliable tool for static loads, the steady-state dynamic response of beams and long plates subjected to periodic loads are significantly different. The maximum displacements and accelerations of beams (and of not-long rectangular plates) are obtained by using a dynamic amplification factor, which in the case of resonance is equal to 1 / 2 ξ , where ξ is the damping ratio. For long plates (and for not-long orthotropic rib-stiffened plates), as discussed in the paper, the response and the amplification factor are substantially different from those of beams. Hence, design based on effective width may lead to 2–4 times higher acceleration than the real values. In an economic design, to avoid unnecessary damping enhancement, this effect must be taken into account.

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