Response of a bridge to a moving vehicle load

2006 ◽  
Vol 33 (1) ◽  
pp. 49-57 ◽  
Author(s):  
J H Lin
Keyword(s):  
Standard Deviation ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Statistical Characteristics ◽  
Roughness Coefficient ◽  
Vehicle Speed ◽  
Moving Vehicle ◽  
Bridge Span ◽  
Pavement Roughness

The determination of the statistical characteristics of bridge deflections due to a load of a vehicle moving across the span of a bridge is frequently a problem of great interest for bridge engineers. Developed herein is a spectral approach for evaluating the variation of bridge deflections due to a vehicle moving at constant speed along a rough bridge surface. Based on the above-mentioned approach, this study presents a closed-form solution for variances of bridge deflections. An example of application of the solution to the estimation of variances of bridge deflections is also presented. The effects of pavement type, vehicle speed, and bridge span on standard deviation of bridge deflections are investigated. The results of numerical examples show that if the effect of engine motions on vehicle vibrations is disregarded, the standard deviation of bridge deflections is proportional to the square root of the pavement roughness coefficient a for a specified vehicle speed.Key words: moving load, bridge deflection, pavement roughness.

Alternative Formulas to Compute Implied Standard Deviation

2009 ◽  
Vol 12 (02) ◽  
pp. 159-176 ◽  
Author(s):  
James S. Ang ◽  
Gwoduan David Jou ◽  
Tsong-Yue Lai
Keyword(s):  
Standard Deviation ◽  
Closed Form ◽  
Asset Price ◽  
Closed Form Solution ◽  
Form Solution ◽  
Call Option ◽  
Present Value ◽  
Underlying Asset ◽  
The Third ◽  
Exercise Price

We assume that the call option's value is correctly priced by Black and Scholes' option pricing model in this paper. This paper derives an exact closed-form solution for implied standard deviation under the condition that the underlying asset price equals the present value of the exercise price. The exact closed-form solution provides the true implied standard deviation and has no estimate error. This paper also develops three alternative formulas to estimate the implied standard deviation if this condition is violated. Application of the Taylor expansion on a single call option value derives the first formula. The accuracy of this formula depends on the deviation between the underlying asset price and the present value of the exercise price. Use of the Taylor formula on two call option prices with different exercise prices is used to develop the second formula, which can be used even though the underlying asset price deviates significantly from the present value of the exercise price. Extension of the second formula's approach to third options value derives the third formula. A merit of the third formula is to circumvent a required parameter used in the second formula. Simulations demonstrate that the implied standard deviations calculated by the second and third formulas provide accurate estimates of the true implied standard deviations.

Closed-Form Representation of Beam Response to Moving Line Loads

2000 ◽  
Vol 68 (2) ◽  
pp. 348-350 ◽  
Author(s):  
Lu Sun
Keyword(s):  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Winkler Foundation ◽  
Line Load ◽  
State Response ◽  
Form Representation ◽  
Mach Numbers ◽  
Moving Line

Fourier transform is used to solve the problem of steady-state response of a beam on an elastic Winkler foundation subject to a moving constant line load. Theorem of residue is employed to evaluate the convolution in terms of Green’s function. A closed-form solution is presented with respect to distinct Mach numbers. It is found that the response of the beam goes to unbounded as the load travels with the critical velocity. The maximal displacement response appears exactly under the moving load and travels at the same speed with the moving load in the case of Mach numbers being less than unity.

scholarly journals Dynamic Analysis of an Infinitely Long Beam Resting on a Kelvin Foundation under Moving Random Loads

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Y. Zhao ◽  
L. T. Si ◽  
H. Ouyang
Keyword(s):  
Fourier Transform ◽  
Random Vibration ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Integration Scheme ◽  
Random Loads ◽  
Numerical Integration Scheme ◽  
Vibration Responses ◽  
The Fourier Transform

Nonstationary random vibration analysis of an infinitely long beam resting on a Kelvin foundation subjected to moving random loads is studied in this paper. Based on the pseudo excitation method (PEM) combined with the Fourier transform (FT), a closed-form solution of the power spectral responses of the nonstationary random vibration of the system is derived in the frequency-wavenumber domain. On the numerical integration scheme a fast Fourier transform is developed for moving load problems through a parameter substitution, which is found to be superior to Simpson’s rule. The results obtained by using the PEM-FT method are verified using Monte Carlo method and good agreement between these two sets of results is achieved. Special attention is paid to investigation of the effects of the moving load velocity, a few key system parameters, and coherence of loads on the random vibration responses. The relationship between the critical speed and resonance is also explored.

Probabilistic Representation and Transmission of Nonstationary Processes in Multi-Degree-of-Freedom Systems

1998 ◽  
Vol 65 (2) ◽  
pp. 398-409 ◽  
Author(s):  
S. F. Masri ◽  
A. W. Smyth ◽  
M.-I. Traina
Keyword(s):  
Random Process ◽  
Structural Control ◽  
Extreme Values ◽  
Free Field ◽  
Closed Form Solution ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Statistical Characteristics ◽  
Earthquake Ground Motion ◽  
Process Data

A relatively simple and straightforward procedure is presented for representing non-stationary random process data in a compact probabilistic format which can be used as excitation input in multi-degree-of-freedom analytical random vibration studies. The method involves two main stages of compaction. The first stage is based on the spectral decomposition of the covariance matrix by the orthogonal Karhunen-Loeve expansion. The dominant eigenvectors are subsequently least-squares fitted with orthogonal polynomials to yield an analytical approximation. This compact analytical representation of the random process is then used to derive an exact closed-form solution for the nonstationary response of general linear multi-degree-of-freedom dynamic systems. The approach is illustrated by the use of an ensemble of free-field acceleration records from the 1994 Northridge earthquake to analytically determine the covariance kernels of the response of a two-degree-of-freedom system resembling a commonly encountered problem in the structural control field. Spectral plots of the extreme values of the rms response of representative multi-degree-of-freedom systems under the action of the subject earthquake are also presented. It is shown that the proposed random data-processing method is not only a useful data-archiving and earthquake feature-extraction tool, but also provides a probabilistic measure of the average statistical characteristics of earthquake ground motion corresponding to a spatially distributed region. Such a representation could be a valuable tool in risk management studies to quantify the average seismic risk over a spatially extended area.

Moving Load on a Fluid-Solid Interface: Supersonic Regime

1973 ◽  
Vol 40 (1) ◽  
pp. 137-142 ◽  
Author(s):  
T. C. Kennedy ◽  
G. Herrmann
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
Steady State Response ◽  
Entire Space ◽  
State Response ◽  
Supersonic Regime

The steady-state response of a semi-infinite solid with an overlying semi-infinite fluid subjected at the plane interface to a moving point load is determined for supersonic load velocities. The exact, closed-form solution valid for the entire space is presented. Some numerical results for the displacements at the interface are calculated and compared to the results obtained when no fluid is present.

Exact closed-form solutions for Lamb’s problem—II: a moving point load

2020 ◽  
Vol 223 (2) ◽  
pp. 1446-1459
Author(s):  
Xi Feng ◽  
Haiming Zhang
Keyword(s):  
Point Source ◽  
Closed Form ◽  
High Speed ◽  
Moving Load ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
High Speed Rail ◽  
Lamb’S Problem ◽  
Homogeneous Half Space

SUMMARY In this paper, we report on an exact closed-form solution for the displacement in an elastic homogeneous half-space elicited by a downward vertical point source moving with constant velocity over the surface of the medium. The problem considered here is an extension to Lamb’s problem. Starting with the integral solutions of Bakker et al., we followed the method developed by Feng and Zhang, which focuses on the displacement triggered by a fixed point source observed on the free surface, to obtain the final solution in terms of elementary algebraic functions as well as elliptic integrals of the first, second and third kind. Our closed-form results agree perfectly with the numerical results of Bakker et al., which confirms the correctness of our formulae. The solution obtained in this paper may lay a solid foundation for further consideration of the response of an actual physical moving load, such as a high-speed rail train.

DYNAMIC CHARACTERISTICS OF PARTIAL COMPOSITE BEAMS

2008 ◽  
Vol 08 (04) ◽  
pp. 665-685 ◽  
Author(s):  
C. W. HUANG ◽  
Y. H. SU
Keyword(s):  
Fundamental Frequency ◽  
Dynamic Characteristics ◽  
Composite Beam ◽  
Moving Load ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Time History ◽  
Composite Beams ◽  
Form Solution ◽  
Superposition Method

This paper is concerned with the dynamic characteristics of composite beams with partial shear connections. The governing equations of motion for partial composite beams are derived from the one-dimensional partial composite beam theory. By solving the corresponding characteristic equation, the natural frequencies and modal shapes for simple partial composite beams are obtained. The orthogonality condition between the natural modes is utilized to decouple the equations of motion. Closed-form solution for the simple partial composite beam subjected to a moving load is derived by the modal superposition method. Key parameters that govern the fundamental frequency and deflection impact factor of simple partial composite beams are identified. Numerical results show that the former is controlled by the composite connection and section combination parameters, and the latter by the fundamental frequency ratio. It was observed that the time-history response of a partial composite beam may differ significantly from that of a full composite beam in terms of amplitude, period, and overall shape, depending on the composition connection.

Internal Resonance of Finite Beams on Nonlinear Foundations Traversed by a Moving Load

2008 ◽  
Author(s):  
Masoud Ansari ◽  
Ebrahim Esmailzadeh ◽  
Davood Younesian
Keyword(s):  
Nonlinear Vibration ◽  
Internal Resonance ◽  
Multiple Scales ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Resonance Effects ◽  
Frequency Responses ◽  
Railway System ◽  
Multiple Scales Perturbation Method

Vibration analysis of beams traversed by moving load is an old and well known topic in structural mechanics, and has been of great interest for researchers of different fields, such as mechanical, railway and civil engineering. Many researchers have conducted different investigations in this field. In the present research, the nonlinear vibration of the system is studied and consequently the response of the system to a moving load is determined as a closed form solution. Furthermore, the effects of load amplitude on the response of the system are investigated. Galerkin’s method is first utilized to truncate the governing equation of motion and then MMS (Method of Multiple Scales) perturbation method is applied to study the nonlinear vibration of the system, in the presence of the internal resonance. Effects of damping of the foundation as well as magnitude of the moving load on the frequency responses are investigated. The proposed methodology and obtained results can be used to investigate the behavior several systems among which railway system shows a good compatibility.

scholarly journals A New Approach on the Response of Non-Uniform Prestressed Timoshenko Beams on Elastic Foundation Subjected to Harmonic Loads

2021 ◽  
Vol 4 (2) ◽  
pp. 66-87
Author(s):  
O.K. Ogunbamike
Keyword(s):  
Elastic Foundation ◽  
Moving Load ◽  
Closed Form Solution ◽  
Complete Information ◽  
Form Solution ◽  
Mode Shapes ◽  
Accurate Information ◽  
Timoshenko Beams ◽  
Beams On Elastic Foundation ◽  
Vibration Responses

The dynamic response of the Timoshenko beam resting on an elastic foundation subjected to harmonic moving load using modal analysis (MA) was investigated. The method of MA was employed to obtain a closed form solution to this class of dynamical systems. In order to use MA, accurate information is needed on the natural frequencies, mode shapes and orthogonality of the mode shapes. A thorough literature survey reveals that the method has not been reported in existing literature to solve non-prestressed Timoshenko beams. Thus, we present complete information on how to use MA to derive the forced vibration responses of a simply thick beam subjected to harmonic moving loads. The effects of axial force and foundation parameters on the dynamic characteristics of the beams are studied and described in detail. In order to validate the accuracy of this method, we compare the frequency parameter with the existing literature which appears to compare favorably.

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