1,721,023 research outputs found
Exact Stationary Solution for a Class of Nonlinear Systems Driven by Non- Normal Delta Correlated Processes
No full textClosed form solutions for the time variant spectral characteristics of non stationary random processes
No full textSpectral characteristics are important quantities in describing stationary and non-stationary random processes. In this paper, the spectral characteristics for complex-valued random processes are evaluated and closed-form solutions for the time-variant statistics of the response of linear single-degree-of-freedom (SDOF) and both classically and non-classically damped multi-degree-of-freedom (MDOF) systems subjected to modulated Gaussian colored noise are obtained. The time-variant central frequency and bandwidth parameter of the response processes of linear SDOF and MDOF elastic systems subjected to Gaussian colored noise excitation are computed exactly in closed-form. These quantities are useful in problems which require the use of complex modal analysis, such as random vibrations of non-classically damped MDOF linear structures, and in structural reliability applications. Monte Carlo simulation has been used to confirm the validity of the proposed solutions
Fiber distributed hyperelastic modeling of biological tissues
No full textIn view of a more realistic description of the spatial distribution of the collagen fibers in soft biological tissues, for example the human cornea, we propose a material model alternative to the one based on generalized structure tensors, proposed by Gasser et al. (2006). We assume that the strain energy function depends on the mean value and on the variance of the pseudo-invariant (I) over bar (4) of the distribution of the fibers. Indeed, the mean value was the only term considered in the original generalized structure tensor model. We derive the expression of the stress and of the consistent tangent stiffness of the new model and compare its mechanical response with the one of the original model for standard uniaxial, shear and biaxial tests. The comparisons are made with reference to the response of the exact fiber dispersed model, based on the direct integration of the contribution of the fibers
An approximate technique for the probability density function of the response of a linear oscillator to Erlang renewal random impulse processes
No full textIn this paper, the effect of non Gaussian, non Poissonian impulsive process on linear structural
systems response is considered. The particular impulsive process herein considered is the Erlang renewal
process, useful for traffic load modelling. In (Iwankievicz, 2005) it was shown that, to take advantage from
the well established Poisson differential stochastic calculus, the original Erlang impulse process can be exactly
converted into a Poisson driven process with the aid of a jump process regarded as an auxiliary variable.
Characterizing the reponse process by a chain of k Markov states and making us of the Chapman-
Kolmogorov equation, the evolutionary k equations of the response joint probability density function were derived.
The first of this set of equations is integro-differential while all others are partial differential. These
equations are transformed to first-order partial differential equations and an approximate solution technique is
devised by considering the evolution of the response during small time intervals. Using the method of characteristic,
as shown in (Vasta and Luongo, 2004), is then possible to numerically integrate these equations, and
an explicit solution can be found. It is shown that numerical integration of these equations confirm the consistency
of the theory for different parameters value of the system and of the excitation process, as well as a
good agreement between Markov state modeling and direct computational approach
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