Antonina Pirrotta

Time delay induced effects on control of linear systems under random excitation

Recursive formulas in terms of statistics of the response of linear systems with time delay under normal white noise input are developed. Two alternative methods are presented, in order to capture the time delay effects. The first is given in an approximate solution obtained by expanding the control force in a Taylor series. The second, available for the stationary solution (if it exists) gets the variance of the controlled system, with time delay in an analytical form. The efficacy loss in terms of statistics of the response is discussed in detail.

The mechanically based non-local elasticity: an overview of main results and future challenges

The mechanically based non-local elasticity has been used, recently, in wider and wider engineering applications involving small-size devices and/or materials with marked microstructures. The key feature of the model involves the presence of non-local effects as additional body forces acting on material masses and depending on their relative displacements. An overview of the main results of the theory is reported in this paper.

Stochastic response analysis of nonlinear systems under Gaussian inputs

Abstract In this paper the extension of Itos rule for the case of vector real valued functions of the response of nonlinear systems excited by zero-mean Gaussian white noise processes is presented. A suitable particularization of the vector function, in order to obtain the statistical moments of every order to the response, is treated, obtaining the differential equations of the response moments in an elegant and compact form. Polynomial expansion and closure schemes are framed in the context outlined here in order to obtain an effective procedure from a computational point of view. An application to a trigonometric nonlinear system, solved in the literature by the stochastic averaging method, is treated here by the moment equation approach using the polynomial expansion of the nonlinear terms in order to evidence the validity of this approach.

Time delay induced effects on control of non-linear systems under random excitation

Time delay in the active control can be caused by measurements of system states, by physical properties of the equipment used for the control itself. The time delay induced effects on control of linear or non-linear systems may cause unsynchronization in the application of the control forces, efficacy loss and instability as well. In this paper the time delay effects on non-linear systems under normal white noise is studied, an approximated approach based on the Taylor expansion of the control forces is introduced. It is shown that in the case of non-linear systems and non-linear control forces by means of the Taylor expansion the original system excited by external white noise is transformed into another one under parametric type excitation. Numerical studies show the reliability of this technique in the study of time delay effects on control of non-linear systems.

An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems

The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF. It is shown that, for the case of relatively high-dimensional systems, the herein proposed implementation can drastically decrease the associated computational cost by several orders of magnitude, as compared to both the standard WPI technique and an MCS approach. Several numerical examples are included, whereas comparisons with pertinent MCS data demonstrate the efficiency and reliability of the technique.

Direct Derivation of Corrective Terms in SDE Through Nonlinear Transformation on Fokker–Planck Equation

This paper examines the problem of probabilistic characterization of nonlinear systems driven by normal and Poissonian white noise. By means of classical nonlinear transformation the stochastic differential equation driven by external input is transformed into a parametric-type stochastic differential equation. Such equations are commonly handled with Itô-type stochastic differential equations and Itôs rule is used to find the response statistics. Here a different approach is proposed, which mainly consists in transforming the Fokker–Planck equation for the original system driven by external input, in the transformed probability density function of the new state variable. It will be shown that the Wong–Zakay or Stratonovich corrective term and the hierarchy of correction terms in the case of Poissonian white noise arise in a natural way.

Non-linear systems under impulsive parametric input

In this paper the problem of the response of non-linear systems excited by an impulsive parametric input is treated. For such systems the response exhibits a jump depending on the amplitude of the impulse as well as on the value of the state variables immediately before the impulse occurrence. Recently, the jump prediction has been obtained in a series form. Here the incremental rule for any scalar real valued function is obtained in an analytical form involving the jump of the state variables. It is also shown that the formulation for the jump evaluation is also able to give a new step-by-step integration technique.

Fractional Tajimi–Kanai model for simulating earthquake ground motion

The ground acceleration is usually modeled as a filtered Gaussian process. The most common model is a Tajimi–Kanai (TK) filter that is a viscoelastic Kelvin–Voigt unit (a spring in parallel with a dashpot) carrying a mass excited by a white noise (acceleration at the bedrock). Based upon the observation that every real material exhibits a power law trend in the creep test, in this paper it is proposed the substitution of the purely viscous element in the Kelvin Voigt element with the so called springpot that is an element having an intermediate behavior between purely elastic (spring) and purely viscous (dashpot) behavior ruled by fractional operator. With this choice two main goals are reached: (i) The viscoelastic behavior of the ground may be simply characterized by performing the creep (or the relaxation) test on a specimen of the ground at the given site; (ii) The number of zero crossing of the absolute acceleration at the free field that for the classical TK model is

CVBEM Application to a Novel Potential Function Providing Stress Field and Twist Rotation at Once

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