Pierfrancesco Cacciola

Monte Carlo simulation in the stochastic analysis of non-linear systems under external stationary Poisson white noise input

A method for the evaluation of the probability density function (p.d.f.) of the response process of non-linear systems under external stationary Poisson white noise excitation is presented. The method takes advantage of the great accuracy of the Monte Carlo simulation (MCS) in evaluating the first two moments of the response process by considering just few samples. The quasi-moment neglect closure is used to close the infinite hierarchy of the moment differential equations of the response process. Moreover, in order to determine the higher order statistical moments of the response, the second-order probabilistic information given by MCS in conjunction with the quasi-moment neglect closure leads to a set of linear differential equations. The quasi-moments up to a given order are used as partial probabilistic information on the response process in order to find the p.d.f. by means of the C-type Gram–Charlier series expansion.

Dynamic response of a rectangular beam with a known non-propagating crack of certain or uncertain depth

In this paper the deterministic behaviour of a beam with a transverse on edge non-propagating crack is first studied. Moreover the stochastic setting pertaining the case in which the crack has an uncertain depth is investigated. The beam is discretized by finite elements in which a so-called closing crack model, with fully open or fully closed crack, is used to describe the damaged element. Once the mathematical model of the beam is defined, the dynamic response is evaluated by applying a numerical procedure based on the philosophy of structural systems with dynamic modification. In the stochastic case the improved perturbation method is modified in order to solve efficiently the stochastic non-linear differential equations.

Vibrating barrier: a novel device for the passive control of structures under ground motion.

A novel device, called vibrating barrier (ViBa), that aims to reduce the vibrations of adjacent structures subjected to ground motion waves is proposed. The ViBa is a structure buried in the soil and detached from surrounding buildings that is able to absorb a significant portion of the dynamic energy arising from the ground motion. The working principle exploits the dynamic interaction among vibrating structures due to the propagation of waves through the soil, namely the structure–soil–structure interaction. The underlying theoretical aspects of the novel control strategy are scrutinized along with its numerical modelling. Closed-form solutions are also derived to design the ViBa in the case of harmonic excitation. Numerical and experimental analyses are performed in order to investigate the efficiency of the device in mitigating the effects of ground motion waves on the structural response. A significant reduction in the maximum structural acceleration of 87% has been achieved experimentally.

Stochastic seismic analysis of large linear structural systems under fully non-stationary spectrum compatible ground motion

Seismic assessment of linear systems is usually performed adopting the well-known modal analysis along with response spectrum technique. Limits of this approach are directly related to the hypothesis of stationary behavior of the response adopted for deriving most common modal combination rules, i.e. SRSS, CQC. Generally, the response of a structure under seismic actions is non-stationary and pertinent analyses have to be performed. In this chapter stationary and non-stationary stochastic models of the seismic action consistent with a given response spectrum will be initially discussed. Furthermore, a technique for determining the non-stationary response through the so-called non-geometric spectral moments will be addressed. Finally a modal correction technique will be proposed in order to make the proposed procedure competitive for coping with the analysis of large structural systems vibrating under random base excitations.

Stochastic analysis of large structural systems under fully non-stationary input

Dynamic analysis of large linear systems is usually performed adopting the well-known modal analysis along with modal truncation of higher modes. However, in the case in which the contribution of higher modes is not negligible, modal correction methods have to be introduced to improve the accuracy of the dynamic response either in the case of deterministic or stochastic excitation. Aim of this paper is to propose a new computationally competitive method for the stochastic analysis of large linear system vibrating under fully non-stationary Gaussian excitations. The method is based on the extension of the mode-acceleration method and its variant, the stochastic mode-acceleration method, for the evaluation of the non-geometric spectral moments of the non-stationary response. Numerical results from the study of a large MDoF structure show the accuracy and the efficiency of the proposed technique.

Sensitivity of the Stochastic Response of Structures Protected by the Vibrating Barrier Control Device

The sensitivity of the stochastic response of a novel passive control device named Vibrating Barrier (ViBa) developed for reducing the seismic response of structures to earthquake excitation is scrutinized. The Vibrating Barrier (ViBa) is a massive structure, hosted in the soil, calibrated for protecting structures by exploiting the structure-soil-structure interaction effect. The soil is modelled as a linear elastic medium with hysteretic damping by resorting to the Boundary Element Method in the frequency domain. In order to accomplish efficient sensitivity analyses, a reduced model is determined by means of the Craig-Bampton procedure. Moreover, a lumped parameter model is used for converting the hysteretic damping soil model rigorously valid in the frequency domain to the approximately equivalent viscous damping model in order to perform conventional time-history analysis. The sensitivity is evaluated by determining a semi-analytical method based on the dynamic modification approach for the case of multi-variate stochastic input process. A non-stationary zero mean Gaussian random process is considered as stochastic input. The paper presents the sensitivity of the maximum response statistics to the design parameters of the ViBa in protecting a model of an Industrial Building. Comparisons with pertinent Monte Carlo Simulation will show the effectiveness of the proposed approach.

Generation of artificial earthquake accelerograms compatible with mean and mean ± standard deviation

The sustained dissemination of database of recorded accelerograms along with the increasing number of strong-motion networks installed worldwide revealed that the current methodologies for simulating artificial earthquakes possess the drawback that the simulated time-histories do not manifest the variability observed for natural accelerograms. As a consequence, the dispersion of resulting structural response analysis can be underestimated. In order to take into account the natural variability of earthquakes, a methodology for simulating artificial earthquake accelerograms matching mean and mean ± standard deviation response spectra is proposed in this paper. This dispersion can be determined from attenuation relationships or evaluated from selected accelerograms of a strong-motion database. The procedure requires the definition of an evolutionary response-spectrum-compatible power spectral density function with random parameters. The simulated ground motion time-histories will manifest variability so that one observed in natural records.

Stochastic seismic analysis in the Messina strait area

After 1908 Messina earthquake significant progresses have been carried out in the field of earthquake engineering. Usually seismic action is represented via the so called elastic response spectrum or alternatively by time histories of ground motion acceleration. Due the random nature of the seismic action, alternative representations assume the seismic action as zero‐mean Gaussian process fully defined by the so‐called Power Spectral Density function. Aim of this paper is the comparative study of the response of linear behaving structures adopting the above representation of the seismic action using recorded earthquakes in the Messina strait area. In this regard, a handy method for determining the power spectral density function of recorded earthquakes is proposed. Numerical examples conducted on the existing space truss located in Torre Faro (Messina) will show the effectiveness of stochastic approach for coping with the seismic analysis of structures.

Steady-State Dynamic Response of Preisach Hysteretic Systems

The goal of this paper is to study the steady-state dynamic response of an oscillator with a hysteretic component to harmonic excitations. This is accomplished by using the Preisach formalism in the description of the contribution of the hysteretic part. Two cases are considered. In the first the hysteretic component is modeled using a series of Jenkin’s elements, while in the second the same component is modeled by a zero-memory plus a purely hysteretic term. The steady-state amplitude of the response is determined analytically by using the equivalent linearization technique which involves input-output relationships for the equivalent linear system the stiffness and damping coefficients of which are response-amplitude dependent. The derived results are compared with pertinent numerical data obtained by integrating the nonlinear equation of motion of the oscillator. The analytical and numerical results are found in excellent agreement, and supplement the analytical findings of certain previous studies.Copyright

A reanalysis technique for structures under white noise excitation

Publisher Summary This chapter presents a procedure for the reanalysis of the dynamic response of linear systems subjected to a white-noise input process. The procedure allows to evaluate the stochastic response of topologically modified structures effectively. In particular, the modified response is retrieved by the knowledge of the Eigen-properties and the transition matrix of the original structure utilizing the method of dynamic modification and Ritz vectors. The proposed procedure is computationally very effective, because it does not require any Eigen-solution for the modified structure and leads to very accurate results as shown in the numerical application.