Closed-form solutions for the evolutionary frequency response function of linear systems subjected to separable or non-separable non-stationary stochastic excitations

Muscolino, G.; Alderucci, Tiziana

doi:10.1016/j.probengmech.2015.02.001

Cited by 32 publications

(14 citation statements)

References 29 publications

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“…Unfortunately, the solution of this problem has not been derived in exact form, even in the simplest case of the stationary response of a Single-Degree-of-Freedom (SDoF) linear oscillator under zero mean Gaussian white noise. In the framework of approximate methods, for zero-mean Gaussian non-stationary input, the evaluation of the so-called Non-Geometric Spectral Moments (NGSMs) is required [12][13][14][15][16]. Therefore the j-th NGSMs, , () ii uu t , is a complex quantity whose real part can be evaluated as the cross-covariance between the response process and the response velocity process of the same linear system subjected to a non-stationary input whose stationary counterpart is proportional to its Hilbert transform.…”

Section: Explicit Solutions For the Ngsmsmentioning

confidence: 99%

“…where, for j=k, , the vector , j t Y represents the modal evolutionary frequency response vector function in terms of state variables and can be evaluated in closed form solutions as recently proposed by the authors [16]. It has to be emphasized that, thanks' to the proposed approach, the computation of any Hilbert transform is avoided.…”

Section: Explicit Solutions For the Ngsmsmentioning

confidence: 99%

“…In this section in order to verify the accuracy of the proposed procedure the benchmark quiescent classically damped linear MDOFs [16] is analysed; this frame has a uniform story height 320 cm H and a bay width 600 cm L , as shown in Figure 7. The steel columns are made of European HE340A wide flange beams with moment of inertia along the strong axis .…”

Section: Numerical Applicationmentioning

confidence: 99%

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Response Statistics of Structural Systems Subjected to Fully Non-Stationary Spectrum Compatible Excitation

Alderucci¹,

Muscolino²

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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The probabilistic analysis of structural systems subjected to seismic excitations requires the spectral characterization of both the input excitation and the structural response; in order to reproduce the typical characteristics of real earthquakes ground-motion time history, the seismic excitation should be modelled as a non-stationary stochastic process. Once the characterization of the ground motion acceleration is done, it is possible to analyze the safety of structural systems subjected to those excitations; in particular, the largest absolute value peak of stochastic response is a useful design information. In order to define the statistics of the maximum of the stochastic response of structures, it is necessary to evaluate the Non-Geometric Spectral Moments (NGSMs).In this paper the fully non-stationary spectrum compatible model has been adopted to define the ground motion acceleration process. Then the evaluation of the NGSMs is performed. The main steps of the proposed approach are: i) the study of a set of real earthquakes to catch their most important features; ii) the introduction of the fully non-stationary spectrum compatible process; iii) the definition of the NGSMs, in the time domain; iv) the evaluation of the mean frequency; v) the validation with the Monte Carlo Simulation. 305

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Section: Explicit Solutions For the Ngsmsmentioning

confidence: 99%

Section: Explicit Solutions For the Ngsmsmentioning

confidence: 99%

Section: Numerical Applicationmentioning

confidence: 99%

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Response Statistics of Structural Systems Subjected to Fully Non-Stationary Spectrum Compatible Excitation

Alderucci¹,

Muscolino²

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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“…In recent studies [20,21], the senior authors, have evaluated in explicit form, for both classically and non-classically damped structural systems, the time-frequency varying response function.…”

Section: Introductionmentioning

confidence: 99%

Response Sensitivity of Structural Systems Subjected to Fully Non-Stationary Random Processes

Alderucci¹,

Genovese²,

Muscolino³

2019

Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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A method for the evaluation of the statistics of response sensitivity of both classically and non-classically damped discrete linear structural systems under fully non-stationary stochastic seismic processes is presented. To do this the evolutionary frequency response function, also referred in literature as the time-frequency varying response function, plays a central role in the evaluation of the spectral characteristics of non-stationary response. The proposed approach requires the following items: a) to write governing motion equations in state-variables, which are very suitable to evaluate the statistics of the response of both classically and non-classically damped discrete linear structural systems by an unified approach; b) to evaluate in explicit closed form solutions the derivatives of time-frequency response vector functions with respect to the parameters that define the modified structural model; c) to obtain the sensitivity of the structural response statistics by frequency domain integrals. A numerical application shows that the proposed approach is suitable to cope with practical problems of engineering interest.

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“…The power spectral method representing the energy distribution with respect to frequencies is a widely accepted method in random vibration field [29,30]. For a moving random load problem the frequency-domain method based on the spectral analysis theory of random vibration is extremely attractive for evaluation of the response statistics.…”

Section: Introductionmentioning

confidence: 99%

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

Zhao

Ouyang

2017

Shock and Vibration

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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.

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Closed-form solutions for the evolutionary frequency response function of linear systems subjected to separable or non-separable non-stationary stochastic excitations

Cited by 32 publications

References 29 publications

Response Statistics of Structural Systems Subjected to Fully Non-Stationary Spectrum Compatible Excitation

Response Statistics of Structural Systems Subjected to Fully Non-Stationary Spectrum Compatible Excitation

Response Sensitivity of Structural Systems Subjected to Fully Non-Stationary Random Processes

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

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