Dynamic response of linear structures to a random stream of pulses

Śniady, P.

doi:10.1016/0022-460x(89)90825-0

Cited by 25 publications

(12 citation statements)

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“…Here, the external and internal damping e!ects are assumed to be proportional, respectively, to the mass and sti!ness properties of the beam. That is, (7,8) where and are the proportionality constants. Substituting equations (5), (7), and (8) into equation (1), considering the orthogonality conditions of the normal modes, and carrying out the familiar operations, the di!erential equation of the kth mode of the generalized de#ection or the modal response is expressed as…”

mentioning

confidence: 99%

Vibration Analysis of Beams With General Boundary Conditions Traversed by a Moving Force

Hilal

Zibdeh

2000

Journal of Sound and Vibration

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confidence: 99%

Vibration Analysis of Beams With General Boundary Conditions Traversed by a Moving Force

Hilal

Zibdeh

2000

Journal of Sound and Vibration

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“…Combining (12), (13), and (15), we get the following formulae: Calculating the partial derivative of (15) and setting it to 0, we obtain the equations to estimate parameter values. Many methods can be used, such as maximum likelihood estimation, Bayesian estimation, the method of inference functions for margins, and canonical maximum likelihood.…”

Section: Year Month Data Time Minute Second Axle Type Lane Speed (Km/mentioning

confidence: 99%

Modeling vehicle traffic loads by the 2D compound Poisson process

Liu

et al. 2018

Appl Stoch Models Bus & Ind

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Vehicular loads are an important factor in the fatigue and deterioration of bridges. In this paper, using weight‐in‐motion data from the Nanxi Yangtze river bridge, we propose a novel two‐dimensional (2D) compound Poisson process model of vehicle loads. This model considers the relations between vehicle loads, including vehicle speed and weight, whereby the relationships between these two marginal processes are described by a 2D Lévy copula function. Vehicle loads simulated by the proposed model were then compared with measured vehicle loads. The results show that histograms for vehicle loads simulated by the proposed model are similar to those generated for the measured vehicle loads. Moreover, the theoretical probabilities of vehicle loads are close in value to the empirical probabilities of vehicle loads. In addition, a two‐sample Kolmogorov‐Smirnov test at the significance level of 1% is given, which yields asymptotic p‐values of 3.2966 × 10−4 for vehicle speed and 3.0489 × 10−10 for vehicle weight. These values confirm that the proposed 2D compound Poisson process model is suitable for estimating vehicle loads.

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“…The Poisson process N (t) with parameter λ gives the number of impulses in time (0, t]. The response of the system (1) for Poisson "white noise" has a form of Stielties integral [13,14] …”

Section: Random Dynamic Influence Vectormentioning

confidence: 99%

“…This means that the load process cannot be divided into deterministic and stochastic parts which can be done for a dynamic system with deterministic parameters. Furthermore, such a formulation of the solution enables us to deal with a variety of stochastic loads constituted by stochastic point processes [13,14]. Let the excitation process be Poisson "white noise"…”

Section: Random Dynamic Influence Vectormentioning

confidence: 99%

“…The first one when the excitation is a weakly stationary stochastic process [1] with a given spectral density function or Poisson "white noise" [13,14] and the second one when it is constituted by a nonstationary process with evolutionary spectral density function [15]. The formulas for both cases are derived and a numerical example considering a building structure under wind and earthquake excitation is also presented.…”

Section: Introductionmentioning

confidence: 99%

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