Marcello Vasta

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.

Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process

In this paper the exact stationary solution in terms of probability density function for a restricted class of non-linear systems under both external and parametric non-normal delta-correlated processes is presented. This class has been obtained by imposing a given probability distribution and finding the corresponding dynamical system which satisfies the modified Fokker-Planck equation. The effectiveness of the results has been verified by means of a Monte Carlo simulation.

Stochastic integro-differential and differential equations of non-linear systems excited by parametric poisson pulses

Abstract The connection between stochastic integro-differential equation and stochastic differential equation of non-linear systems driven by parametric Poisson delta correlated processes is presented. It is shown that the two different formulations are fully equivalent in the case of external excitation. In the case of parametric type excitation the two formulation are equivalent if the non-linear argument in the integral representation is related by means of a series to the corresponding non-linear parametric term in the stochastic differential equation. Differential rules for the two representations to find moment equations of every order of the response are also compared.

Parametric identification of systems with non-Gaussian excitation using measured response spectra

The problem of estimating parameters in dynamic systems excited by stochastic processes is addressed. Attention is focused on situations where the response processes are measurable but the excitation processes are non-Gaussian, unmeasurable and known only in terms of parameterised stochastic process models. General techniques for simultaneously estimating system and excitation process parameters are developed, based on the use of both normal, second order spectra and higher order, trispectra. The method is validated through application to some simulated data, relating to an oscillator driven by two specific kinds of non-Gaussian stochastic excitation.

A method for the probabilistic analysis of nonlinear systems

Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an attractive tool for the analysis of a wide class of stochastic systems.

Coupled electro-mechanical models of fiber-distributed active tissues

We discuss a constitutive model for stochastically distributed fiber reinforced tissues, where the active behavior of the fibers depends on the relative orientation of the electric field. Unlike other popular approaches, based on numerical integration over the unit sphere, or on the use of second order structure tensors, for the passive behavior we adopt a second order approximation of the strain energy density of the distribution. The purely mechanical quantities result to be dependent on two (second and fourth order, respectively) averaged structure tensors. In line with the approximation used for the passive behavior, we model the active behavior accounting for the statistical fiber distribution. We extend the Helmholtz free energy density by introducing a directional active potential, dependent on a stochastic permittivity tensor associated to a particular direction, and approximate the total active potential through a second order Taylor expansion of the permittivity tensor. The approximation allows us to derive explicitly the active stress and the active constitutive tensors, which result to be dependent on the same two averaged structure tensors that characterize the passive response. Active anisotropy follows from the distribution of the fibers and inherits its stochastic parameters. Examples of passive and active behaviors predicted by the model in terms of response to biaxial testing are presented, and comparisons with passive experimental data are provided.

Damage Detection on the Z24 Bridge by a Spectral-Based Dynamic Identification Technique

The paper tackles the dynamic identification and the damage detection carried out by a spectral-based method on the well-known Z24 bridge, a three-span pre-stressed concrete bridge located in Switzerland. Before being destroyed, the bridge was progressively damaged and tested in the framework of the Brite Euram project SIMCES. Starting from this benchmark, the presented spectral-based identification technique is validated and the usefulness of this method as a non-destructive tool able to catch the dynamic behavior of a structure and locate the damage is widely discussed. Firstly, a FE model of the bridge was built and calibrated in order to analyze its response to different excitation types (ramp force, triangular pulse, shaker and random vibrations) and several damage scenarios. Secondly, aiming at identifying both the modal parameters and the damage of the bridge, the spectral-based method is applied making use of the power spectral matrix decomposition. Finally, a proper index is defined and applied to this case-study in order to locate the damage.

Viscoelectromechanics modeling of intestine wall hyperelasticity

ABSTRACT Elastic-electroactive biological media are sensitive to both mechanical and electric forces. Their active behavior is often associated with the presence of reinforcing fibers and their excitation-contraction coupling is due to the interplay between the passive elastic tissue and the active muscular network. In this paper we focus on the theoretical framework of constitutive equations for viscous electroactive media. The approach is based on the additive decomposition of the Helmholtz free energy accompanied to the multiplicative decomposition of the deformation gradient in elastic, viscous and active parts. We describe a thermodynamically sound scenario that accounts for geometric and material nonlinearities.

Identification of Uncertain Vibrating Beams through a Perturbation Approach

AbstractUncertainty characterization plays a key role in the safety assessment of many engineering structures. Nevertheless, the inverse problem for structures with uncertain parameters has received less attention than the relevant direct one, since one deals with stochastic structural system identification. This paper discusses the dynamic identification of linear structural systems with random stiffness parameters. Following a perturbation approach, recently proposed by the authors in a discrete framework, an identification technique for transversely vibrating 1-D uncertain continua is proposed. Results for a paradigmatic case, a simply supported beam, are presented and discussed.

Parametric Resonance of Hopf Bifurcation in a Generalized Beck’s Column

A generalized damped Beck’s column under pulsating actions is considered. The nonlinear partial integrodifferential equations of motion and the associated boundary conditions, expanded up to cubic terms, are tackled through a perturbation approach. The multiple scales method is applied to the continuous model in order to obtain the bifurcation equations in the neighborhood of a Hopf bifurcation point in primary parametric resonance. This codimension-2 bifurcation entails two control variables, namely, the amplitude of the static and dynamic components of the follower force, playing the role of detuning and bifurcation parameters, respectively. In the postcritical analysis bifurcation diagrams and relevant phase portraits are examined. Two bifurcation paths associated with specific values of the follower force static component are discussed and the birth of new stable period-2 subharmonic motion is observed. DOI: 10.1115/1.3007905