Abstract
In this study, simple and manageable closed form expressions are obtained for the mean value, the spectral density function, and the standard deviation of the deflection induced by stochastic moving loads on bridge‐like structures. As a basic case, a simply supported beam is considered, loaded by a sequence of concentrated forces moving in the same direction, with random instants of arrival, constant random crossing speeds, and constant random amplitudes. The loads are described by three stochastic processes, representing an idealization of vehicular traffic on a bridge in case of negligible inertial coupling effects between moving masses and structure. System’s responses are analytically determined in terms of mean values and power spectral density functions, yielding standard deviations, with the possibility to easily extend the results to more refined models of single span bridge‐like structures. Potential applications regard structural analysis, vibration control, and condition monitoring of traffic excited bridges.
Highlights
Closed form expressions are obtained for the mean value, spectral density function, and standard deviation of the deflection induced by stochastic moving loads on bridge-like structures
A supported beam is considered, loaded by a sequence of concentrated forces moving in the same direction, with random instants of arrival, constant random crossing speeds, and constant random amplitudes. e loads are described by three stochastic processes, which represent an idealization of traffic on a bridge, in the case in which the relative magnitude of moving masses introduces negligible coupling effects with the structure
Possible applications are in the fields of structural analysis, vibration control, and condition monitoring of structures excited by stochastic moving loads, like traffic-excited bridges
Summary
A straight homogeneous beam is considered, supported at both ends as represented in Figure 1. e Euler–Bernoulli beam model is adopted, loaded by a sequence of concentrated forces moving in the same direction, with random instants of arrival, constant random crossing speeds, and constant random intensities. Erefore, modal shapes can be expressed in any case on the basis of the sine function, and this allows the validity of the adopted model to be extended to a more general case. In case of more complicated, realistic single span bridge-like structures, either a spectral approach or the results of a finite element analysis may be taken into account In the former case, modal shapes may be expressed directly as linear combinations of sine functions due to Ritz–Galerkin expansions. 4. Mean Value of the Response e n-th modal force acting on the system at any instant t > TN can be expressed by adding the contributions of each concentrated moving force by means of stochastic Stieltjes integrals [10]. Which amplitude is modulated in z by modal shapes (linear combinations of sine functions, as already discussed regarding the model of the structure)
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