DYNAMIC AMPLIFICATION OF BRIDGE/VEHICLE INTERACTION: A PARAMETRIC STUDY FOR A SKEWED BRIDGE

2003 ◽  
Vol 03 (01) ◽  
pp. 71-90 ◽  
Author(s):  
HUAN ZENG ◽  
CHARLES W. BERT
Keyword(s):  
Parametric Study ◽  
Superposition Principle ◽  
Ritz Method ◽  
Mode Shapes ◽  
Skew Angle ◽  
Dynamic Amplification Factor ◽  
Traffic Condition ◽  
Analytical Technique ◽  
Contact Points ◽  
Dynamic Amplification

The dynamic amplification of a bridge response due to moving vehicles has been the subject of numerous research efforts. The efforts indicate a common difficulty in treating the dynamic interaction. This paper presents a semi-analytical technique to solve the bridge/vehicle interaction problem. A skew bridge, idealized as a discretely stiffened thin isotropic plate, is considered. The natural frequencies and mode shapes of the bridge are computed by a pb-2 Rayleigh–Ritz method. The mode superposition principle is then applied. The dynamic response of the bridge to moving vehicle excitation is expressed in terms of mode shapes and normal coordinates. A three-dimensional three-axle vehicle model is developed and consists of 11 independent degrees of freedom. The bridge and the vehicle are treated as two separate systems connected only at the time-varying contact points. An iteration technique is used to deal with the true coupling between the bridge and the vehicle and to satisfy the compatibility of forces and displacements at the contact points. At last, a parametric study is conducted to investigate the dynamic amplification factor. The influences of vehicle type, axle spacing, traffic condition, span length, and skew angle are examined.

Ambient and forced-vibration tests of the Beauharnois suspension bridge

2000 ◽  
Vol 27 (6) ◽  
pp. 1162-1172 ◽  
Author(s):  
P Paultre ◽  
J Proulx ◽  
T Bégin
Keyword(s):  
Forced Vibration ◽  
Dynamic Properties ◽  
Suspension Bridge ◽  
Rehabilitation Program ◽  
Mode Shapes ◽  
Experimental Program ◽  
Dynamic Amplification Factor ◽  
Dynamic Amplification ◽  
Vibration Tests ◽  
Steel Trusses

Ambient and forced vibration tests were carried out on the Beauharnois Bridge, a unique, 177-m combined suspension and cable-stayed structure near Montreal. A rehabilitation program was completed on the bridge during which the deck was completely rebuilt with an orthotropic slab on two steel trusses. The rehabilitation program also included the addition of two pairs of stay cables on both towers, creating a hybrid suspension system. The paper presents a series of dynamic tests performed to evaluate the dynamic properties and the dynamic amplification factor (DAF) for the rehabilitated bridge. The experimental program involved the measurement of vertical, transverse, and longitudinal acceleration responses of the deck and tower under ambient and controlled traffic loads. Displacement, strain, and integrated acceleration DAFs were computed under different loading conditions. Modal properties were evaluated and used to correlate a three-dimensional finite element model for the bridge, including nonlinear cable behaviour. The paper discusses the experimental setup and the techniques used to evaluate vibration frequencies, mode shapes, and the DAF. Correlation of numerical dynamic properties and experimental results is also presented. Key words: cable-stayed bridge, dynamic amplification, dynamic testing, numerical correlation, modal analysis, suspension bridge.

Analyse dynamique de l'interaction pont-véhicules pour les ponts routiers. II. Application au pont de Senneterre au Québec

1998 ◽  
Vol 25 (1) ◽  
pp. 174-187 ◽  
Author(s):  
Kamel Henchi ◽  
Martin Talbot ◽  
Mario Fafard
Keyword(s):  
Amplification Factor ◽  
Experimental Tests ◽  
Mode Shapes ◽  
Dynamic Amplification Factor ◽  
The Road ◽  
Beam Elements ◽  
Road Profile ◽  
Specific Loading ◽  
Dynamic Amplification

In this paper, an application of the algorithm for the dynamic analysis of bridge-vehicles interaction that the authors developed in the preceeding paper is presented. The numerical results are compared to the results obtained from experimental tests of frequencies and mode shapes and from forced vibrations carried out on the Senneterre bridge located in Quebec. The numerical model of the bridge is obtained by tridimensional finite element modeling, using shell and beam elements, and taking into account bridge-vehicles interaction and the road profile in a realistic way. The numerical vehicle model used in the province of Quebec is represented in a discrete form based on mechanical parameters calibrated and adjusted according to experimental results. A parametric study was then carried out. The results of this study allow us to present some recommendations with regard to bridge resistance to dynamic effects and the determination of a dynamic amplification factor based on the specific loading conditions of the bridge. Key words: shell, dynamic, finite elements, interaction, bridge, roughness, vehicle, amplification factor, experimental tests.[Journal translation]

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

Analysis of test blanket module attachments under electromagnetic loads by using a dynamic amplification factor envelope

2018 ◽  
Vol 136 ◽  
pp. 1247-1251
Author(s):  
Raúl Muñoz ◽  
Francisco J. Calvo ◽  
Sergio Sádaba ◽  
Ana M. Gil ◽  
Javier Rodríguez ◽  
...  
Keyword(s):  
Amplification Factor ◽  
Dynamic Amplification Factor ◽  
Dynamic Amplification

scholarly journals Evaluation of Stiffness and Dynamic Properties of a Mine Shaft Steelwork Structure through In Situ Tests and Numerical Simulations

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 664
Author(s):  
Jacek Jakubowski ◽  
Przemysław Fiołek
Keyword(s):  
Numerical Simulations ◽  
Dynamic Properties ◽  
Vertical Motion ◽  
Load Test ◽  
Mode Shapes ◽  
Dynamic Amplification Factor ◽  
In Situ Tests ◽  
Mine Shaft ◽  
Numerical Investigations

A mine shaft steelwork is a three-dimensional frame that directs the vertical motion of conveyances in mine shafts. Here, we conduct field and numerical investigations on the stiffness and dynamic properties of these structures. Based on the design documentation of the shaft, materials data, and site inspection, the steelwork’s finite element model, featuring material and geometric non-linearities, was developed in Abaqus. Static load tests of steelwork were carried out in an underground mine shaft. Numerical simulations reflecting the load test conditions showed strong agreement with the in situ measurements. The validated numerical model was used to assess the dynamic characteristics of the structure. Dynamic linear and non-linear analyses delivered the natural frequencies, mode shapes, and structural response to dynamic loads. The current practices and regulations regarding shaft steelwork design and maintenance do not account for the stiffness of guide-to-bunton connections and disregard dynamic factors. Our experimental and numerical investigations show that these connections provide considerable stiffness, which leads to the redistribution and reduction in bending moments and increased stiffness of the construction. The results also show a high dynamic amplification factor. The omission of these features implicates an incorrect assessment of the design loads and can lead to over- or under-sized structures and ultimately to shortened design working life or failure.

Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials As Assumed Shape Functions

1991 ◽  
Author(s):  
C. Rajalingham ◽  
R. B. Bhat ◽  
G. D. Xistris
Keyword(s):  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Polar Coordinate System ◽  
Free Boundaries ◽  
Natural Modes ◽  
Polar Coordinate ◽  
Boundary Characteristic

Abstract The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on its symmetrical or antisymmetrical property about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.

Analysis of In-Plane Modal Characteristics of an Annular Disk With Multiple Point Supports

2009 ◽  
Author(s):  
S. Bashmal ◽  
R. Bhat ◽  
S. Rakheja
Keyword(s):  
Finite Element ◽  
Orthogonal Polynomials ◽  
Ritz Method ◽  
Element Model ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Multiple Point ◽  
Annular Disk ◽  
Free Boundary Conditions ◽  
Boundary Characteristic

In-plane free vibrations of an isotropic, elastic annular disk constrained at some points on the inner and outer boundaries are investigated. The presented study is relevant to various practical problems including disks clamped by bolts along the inner and outer edges or the railway wheel vibrations. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the frequency parameters and the associated mode shapes. The boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while artificial springs are used to realize clamped conditions at discrete points. The frequency parameters for different point constraint conditions are evaluated and compared with those computed from a finite element model to demonstrate the validity of the proposed method. The computed mode shapes are presented for a disk with different point constraints at the inner and outer boundaries to demonstrate the free in-plane vibration behavior of the disk. Results show that addition of point supports causes some of the modes to split into two different frequencies with different mode shapes. The effects of different orientations of multiple point supports on the frequency parameters and mode shapes are also discussed.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

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