Roberta Santoro

A novel exact representation of stationary colored Gaussian processes (fractional differential approach)

A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic differential equations whose solution is a weighted sum of fractional Brownian motions. The exact form of the weighting coefficients is given and it is shown that it is related to the fractional moments of the target spectral density of the colored noise.

Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution

An extension of the path integral to non-linear systems driven by a Poissonian white noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov— Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Diracs deltas occurrences are performed and results are compared with analytical solutions (when available) and Monte Carlo simulation.

Ship Roll Motion under Stochastic Agencies Using Path Integral Method

The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamical models and then applied for ship roll dynamics under random impulsive white noise excitation.

SOME CONVENTIONAL AND UNCONVENTIONAL EDUCATIONAL COLUMN STABILITY PROBLEMS

Two interesting problems are considered for enriching the curriculum of the Strength of Materials course, in the light of recently developed functionally graded materials (FGMs), characterized with the smooth variation of the elastic modulus. These are problems associated with buckling of columns with variable flexural rigidity along the axis of the column. A simple semi-inverse method is proposed for determining closed-form solutions of axially inhomogeneous columns. In order for the presentation to be given in one package, the conventional problems are also recapitulated along with the novel ones. The main approach adopted here is the use of the second-order differential equation, instead of the fourth-order one, obtained by integrating twice and having a physical meaning, since it could be derived based on moment equilibrium. This is essentially the same idea as utilized in the textbook by Timoshenko and Gere;1 the difference is that this paper develops a semi-inverse formulation.

Stochastic Sensitivity Analysis of Structural Systems With Interval Uncertainties

Interval sensitivity analysis of linear discretized structures with uncertain-but-bounded parameters subjected to stationary multi-correlated Gaussian stochastic processes is addressed. The proposed procedure relies on the use of the so-called Interval Rational Series Expansion (IRSE), recently proposed by the authors as an alternative explicit expression of the Neumann series expansion for the inverse of a matrix with a small rank-r modification and properly extended to handle also interval matrices. The IRSE allows to derive approximate explicit expressions of the interval sensitivities of the mean-value vector and Power Spectral Density (PSD) function matrix of the interval stationary stochastic response. The effectiveness of the proposed method is demonstrated through numerical results pertaining to a seismically excited three-storey frame structure with interval Young’s moduli of some columns.Copyright

RESPONSE OF BEAMS WITH CRACK OF UNCERTAIN-BUT BOUNDED DEPTH SUBJECTED TO DETERMINISTIC OR STOCHASTIC LOADS

Abstract. Detection of cracks in structural components and identification of their size for structures having beam form is of crucial importance in many engineering applications. For damaged structures the dynamic response changes with respect to the undamaged ones due to the changes produced on their mechanical properties by the presence of the crack. In this paper the deterministic behavior of a beam with a transverse on edge non-propagating crack is first studied. Moreover the deterministic and stochastic setting pertaining the case in which the crack has an uncertain depth is investigated. Undamaged elements of the beam are modeled by Euler-type finite elements. The uncertain crack depth is modeled as an interval variable and the cracked beam is subjected to both deterministic and zero-mean nonstationary Gaussian random excitations. In the latter case the equation governing the evolution of the main statistics of the response are derived by means of Kronecker algebra. Once the mathematical model of the beam is defined, the dynamic response is evaluated by applying a numerical procedure based on the philosophy the Improved Interval Analysis via Extra Unitary Interval. In particular the proposed procedure is based on the following main steps: i) to define a finite element model of the beam in which the model of fully open crack is used to represent the damaged element; ii) to model the crack depth as an interval variable; iii) to evaluate in time domain the response for deterministic and stochastic excitation, by adopting an unified approach.

Interval Fractile Levels for Stationary Stochastic Response of Linear Structures With Uncertainties

In the framework of stochastic analysis, the extreme response value of a structural system is completely described by its CDF. However, the CDF does not represent a direct design provision. A more meaningful parameter is the response level which has a specified probability, p, of not being exceeded during a specified time interval. This quantity, which is basically the inverse of the CDF, is referred to as a fractile of order p of the structural response. This study presents an analytical procedure for evaluating the lower bound and upper bound of the fractile of order p of the response of linear structures, with uncertain stiffness properties modeled as interval variables subjected to stationary stochastic excitations. The accuracy of the proposed approach is demonstrated by numerical results concerning a wind-excited truss structure with uncertain Young’s moduli. This article is available in the ASME Digital Collection at http://dx.doi.org/10.1115/1.4030455.

RELIABILITY ASSESSMENT OF INTERVAL UNCERTAIN STRUCTURAL SYSTEMS SUBJECTED TO SPECTRUM COMPATIBLE SEISMIC EXCITATIONS

Abstract. The present paper deals with reliability assessment of linear structures with uncertain parameters subjected to seismic excitations modeled as stationary spectrum compatible random Gaussian processes. Structural uncertainties are described by applying the interval model, stemming from the interval analysis. Under the Vanmarcke assumption that the upcrossings of a specified threshold occur in clumps, an efficient procedure for the evaluation of the bounds of the interval reliability function of the generic response process is presented. The key idea is to consider the interval re iability function as depending on the zero-, firstand second-order interval spectral moments of the stationary response rather than on the interval structural parameters. This allows to determine the bounds of the interval r liability function for a given barrier level as the minimum and maximum among the values pertaining to the eight combinations of the bounds of the interval spectral moments of the response. The effectiveness of the proposed approach lies in the evaluation of the bounds of the interval spectral moments of the response in approximate explicit form. To this aim, the so-called Interval Rational Series Expansion is applied in conjunction with the improved interval analysis . For validation purposes, numerical results concerning the region of the interval reliability function of a spatial structure with interval stiffness properties subjected to stationary spectrum compatible seismic excitation are presented.