Search results for " Nonlinear"

LPV models: Identification for gain scheduling control

2001

In this paper the use of discrete-time Linear Parameter Varying (LPV) models for the gain scheduling control and identification methods for non-linear or time-varying system is considered. We report an overview on the existing literature on LPV systems for gain scheduling control and identification. Moreover, assuming that inputs, outputs and the scheduling parameters are measured, and a form of the functional dependence of the coefficients on the parameters is known, we show how the identification problem can be reduced to a linear regression so that a Least Mean Square and Recursive Least Square identification algorithm can be reformulated. Our methodology is applied for the identificatio…

Incremental dynamic based fragility assessment of reinforced concrete structures: Stationary vs. non-stationary artificial ground motions

2017

Abstract Artificial and natural records are commonly employed by researches and practitioners to perform refined seismic assessments of structures. The techniques for the generation of artificial records and their effectiveness in producing signals which are significantly representative of real earthquakes are still debated as well as results of the consequent seismic assessment to expect from their application. The paper presents an in-depth comparative study highlighting the effect of employing different typologies of artificial ground motion records on seismic assessment results, especially addressing seismic fragility curves. Three sets of 50 stationary, nonstationary evenly modulated a…

Journeys from quantum optics to quantum technology

2017

Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student and look at how the time with him has influenced our research.

Stability analysis of rotor whirl under nonlinear internal friction by a general averaging approach

2016

The two main sources of internal friction in a rotor-shaft system are the shaft structural hysteresis and the possible shrink-fit release of the assembly. The internal friction tends to destabilize the over-critical rotor running, but a remedy against this effect may be provided by a proper combination of some external damping in the supports and an anisotropic arrangement of the support stiffness, or at most by the support damping alone, depending on the system geometry. The present analysis reported here considers a general asymmetric rotor-shaft system, where the rotor is perfectly rigid and is constrained by viscous–flexible supports having different stiffnesses on two orthogonal plane…

Desychronization of one-parameter families of stable vector fields

2005

Given a one-parameter family of vector fields on , Fλ(x), , such that for each λ, Fλ has a global asymptotically stable equilibrium point xλ, we construct a vector field on of the form G(λ, x) = (g(λ, x), Fλ(x)) which exhibits chaotic behaviour. This result is an incursion in the inverse problem of master–slave synchronization.This paper discusses self-disorganization of parameter dependent stable vector fields. Motivations are found in applications to drug design: one way to lead an unfriendly organism to death is to destabilize its metabolism. In this paper we envisage the mathematical aspect of the question. We show that for a very stable system (one globally attracting equilibrium state…

Effect of uncertain damping coefficient on the response of a SDOF system

2022

In this paper, a full probabilistic description of the response of a randomized SDOF system in both the time and the frequency domain is done. Considering that the damping of the structure does not simply relate to any single physical phenomenon, the sensitivity of the response to the randomness of the damping parameter is investigated. The stochastic analysis is conducted via the Probability Transformation Method therefore the first probability density function of the response is evaluated. The effect of the uncertain damping coefficient on the response of the SDOF system has been investigated through several numerical examples. From the response probability density function as well as fro…

Probabilistic solution of a homogeneous linear second-order differential equation with randomized complex coefficients

2022

In this paper, an exact expression for the first probability density function of the solution stochastic process to a randomized homogeneous linear second-order complex differential equation is determined. To complete the probabilistic analysis, the first probability density functions of the real and complex contributions of the solution stochastic process are also calculated. To compute the densities, the random variable transformation method is applied under general hypothesis, all coefficients and initial conditions are absolutely continuous complex random variables. The capability of the theoretical results established is demonstrated by several numerical examples. Finally, we show the …

A Computational Two-Scale Approach to Nonlinear Analysis of Etherogeneous Composite Structures

2010

An application of the arithmetic euler function to the construction of nonclassical states of a quantum harmonic oscillator

2001

Abstract All quantum superpositions of two equal intensity coherent states exhibiting infinitely many zeros in their Fock distributions are explicitly constructed and studied. Our approach is based on results from number theory and, in particular, on the properties of arithmetic Euler function. The nonclassical nature of these states is briefly pointed out. Some interesting properties are brought to light.

Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral

2014

A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…