Giuseppe Ricciardi

Stationary and Non Stationary Probability Density Function for Non Linear Oscillators

A method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the probability density function of the response in terms of C-type Gram-Charlier series expansion. By applying the weighted residual method, the Fokker-Planck equation is reduced to a system of non-linear first order ordinary differential equations, where the unknowns are the coefficients of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived.

Improved dynamic analysis of structures with mechanical uncertainties under deterministic input

This paper addresses the dynamic analysis of linear systems with uncertain parameters subjected to deterministic excitation. The conventional methods dealing with stochastic structures are based on series expansion of stochastic quantities with respect to uncertain parameters, by means of either Taylor expansion, perturbation technique or Neumann expansion and evaluate the first- and second-order moments of the response by solving deterministic equations. Unfortunately, these methods lead to significant error when the coefficients of variation of uncertainties are relatively large. Herein, an improved first-order perturbation approach is proposed, which considers the stochastic quantities as the sum of their mean and deviation. Comparisons with conventional second-order perturbation approach and Monte Carlo simulations illustrate the efficiency of the proposed method. Applications are discussed in order to investigate the influence of mass, damping and stiffness uncertainty on the dynamic response of the system.

Seismic metamaterials based on isochronous mechanical oscillators

This Letter introduces a seismic metamaterial (SM) composed by a chain of mass-in-mass system able to filter the S-waves of an earthquake. We included the effect of the SM into the mono dimensional model for the soil response analysis. The SM modifies the soil behavior and in presence of an internal damping the amplitude of the soil amplification function is reduced also in a region near the resonance frequency. This SM can be realized by a continuous structure with inside a 3d-matrix of isochronous oscillators based on a sphere rolling over a cycloidal trajectory.

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.

Probability density function of MDOF structural systems under non-normal delta-correlated inputs

Abstract A method to approximate the probability density function of MDOF linear systems under non-normal delta-correlated input is presented. The method requires: (i) the evaluation of the response cumulants up a given order, by solving the set of cumulant differential equations; (ii) the evaluation of the quasi-moments of the response by means of recursive relationships, once the response cumulants are known; (iii) the evaluation of the coefficients of the C-type Gram-Charlier series expansion of the response probability density function, by solving a set of linear algebraic equations, whose known terms depend on the quasi-moments of the response up to a given order. The numerical application shows the versatility and the accuracy of the proposed method.

A novel local stochastic linearization method via two extremum entropy principles

The classical Gaussian stochastic linearization method for non-linear random vibration problems is reinterpreted on the basis of the maximum entropy principle. Starting from this theoretical result, the maximum entropy principle allows to formulate a local stochastic linearization method, based on the substitution of the original non-linear system by an equivalent locally linear one. The expressions of the equivalent coefficients are derived. The equivalence of this method with a non-Gaussian closure based on the maximum entropy method for stochastic dynamics is evidenced. In addition, an alternative stochastic linearization method is proposed, based on the minimum cross-entropy principle. Numerical applications show the superiority of the two proposed local stochastic linearization methods over the Gaussian one.

Dynamic Behavior of Stay Cables with Rotational Dampers

Vibration reduction in stay cables by means of viscous dampers is of great interest in cable damage prevention and serviceability of structural system supported by such cables. This paper presents a study on the effectiveness, as well as the limits, of rotational viscous dampers and springs inserted at the 2 ends of a bending-stiff taut cable; influence of rotational stiffness of the springs is also studied. After a nondimensional expression of the equation of motion has been obtained, as in other cases of nonproportionally damped continuous structures, complex modal analysis is pursued, obtaining complex eigenvalues and eigenfunctions. Comparison with intermediate dampers, widely used in bridge engineering, is performed showing the range of nondimensional parameters for which the proposed approach is of interest. Finally, a numerical technique based on complex mode superposition is presented in order to evaluate time domain responses for transversal distributed excitation. As an example, the procedure is applied to a wind-exposed cable.

DYNAMICS OF SHALLOW CABLES UNDER TURBULENT WIND: A NONLINEAR FINITE ELEMENT APPROACH

In classic cable theory, vibrations are usually analyzed by writing the equations of motion in the neighborhood of the initial equilibrium configuration. Furthermore, a fundamental difference exists between out-of-plane motions, which basically corresponds to the linear behavior of a taut string and in-plane motion, where self-weight determines a sagged initial profile. This work makes use of a continuous approach to establish the initial shape of the cable when it is subjected to wind or fluid flow arbitrarily directed and employed a novel nonlinear finite element technique in order to investigate the dynamics present around the initial equilibrium shape of the cable. Stochastic solutions in the frequency domain are derived for a wind-exposed cable after linearization of the problem. By applying the proper orthogonal decomposition (POD) technique with the aim of reducing computational effort, an approach to simulate modal wind forces is proposed and applied to the nonlinear equations of motion.

Failure by corrosion in PC bridges: a case history of a viaduct in Italy

Purpose – The purpose of this paper is to illustrate a viaduct collapse due to corrosion phenomena. Moreover, a contribution to the issues related to both the control of existing structures and design methods to be followed for the construction of new buildings is provided. Design/methodology/approach – The objectives were achieved by in situ observations and numerical analyses. The effects of corrosion phenomena are investigated, and the progressive collapse analysis is provided to be helpful in this case. Findings – The damages induced by corrosion phenomena have caused the collapse of the viaduct taken into account. The performed numerical analyses were able to reproduce the effects of corrosion in terms of reduction of wires diameter. Research limitations/implications – The research is limited to prestressed concrete viaduct with post-tensioned cables. Practical implications – A monitoring plan, subdivided in several phases, is suggested, to avoid critical situations as these described. Originality/value – The case study brought useful information on the effects of corrosion on the decks section, showing how the technology in post-tensioned cables is usually insidious and prone to the issues relating to corrosion of the wires.

Earthquake Protection of Existing Structures with Limited Seismic Joint: Base Isolation with Supplemental Damping versus Rotational Inertia

Existing civil engineering structures having strategic importance, such as hospitals, fire stations, and power plants, often do not comply with seismic standards in force today, as they were designed and built based on past structural guidelines. On the other hand, due to their special importance, structural integrity of such buildings is of vital importance during and after earthquakes, which puts demands on strategies for their seismic protection. In this regard, seismic base isolation has been widely employed; however, the existing limited seismic joint between adjacent buildings may hamper this application because of the large displacements concentrated at the isolation floor. In this paper, we compare two possible remedies: the former is to provide supplemental damping in conventional base isolation systems and the latter consists in a combination of base isolation with supplemental rotational inertia. For the second strategy, a mechanical device, called inerter, is arranged in series with spring and dashpot elements to form the so-called tuned-mass-damper-inerter (TMDI) directly connected to an isolation floor. Several advantages of this second system as compared to the first one are outlined, especially with regard to the limitation of floor accelerations and interstory drifts, which may be an issue for nonstructural elements and equipment, in addition to disturbing occupants. Once the optimal design of the TMDI is established, possible implementation of this system into existing structures is discussed.