Search results for "Random vibration"
showing 10 items of 27 documents
Non-linear systems under delta correlated processes handled by perturbation theory
1998
Statistical responses in terms of moment and correlation functions of non-linear systems driven by non-normal delta correlated external pulses are derived. The procedure takes full advantage of the perturbation theory approach. Then, by means of a proper coordinate transformation, the system is replaced by a quasi-linear system for which the statistical quantities can be exactly found.
Spectral Approach to Equivalent Statistical Quadratization and Cubicization Methods for Nonlinear Oscillators
2003
Random vibrations of nonlinear systems subjected to Gaussian input are investigated by a technique based on statistical quadratization, and cubicization. In this context, and depending on the nature of the given nonlinearity, statistics of the stationary response are obtained via an equivalent system with a polynomial nonlinearity of either quadratic or cubic order, which can be solved by the Volterra series method. The Volterra series response is expanded in a trigonometric Fourier series over an adequately long interval T, and exact expressions are derived for the Fourier coefficients of the second- and third-order response in terms of the Fourier coefficients of the first-order, Gaussian…
Stochastic dynamics of nonlinear systems driven by non-normal delta-correlated processes
1993
In this paper, nonlinear systems subjected to external and parametric non-normal delta-correlated stochastic excitations are treated. A new interpretation of the stochastic differential calculus allows first a full explanation of the presence of the Wong-Zakai or Stratonovich correction terms in the Itoˆ’s differential rule. Then this rule is extended to take into account the non-normality of the input. The validity of this formulation is confirmed by experimental results obtained by Monte Carlo simulations.
Higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses
1999
The higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses are evaluated by means of knowledge of the first order statistics and without any further integration. This is made possible by a coordinate transformation which replaces the original system by a quasi-linear one with parametric Poisson delta-correlated input; and, for these systems, a simple relationship between first order and higher order statistics is found in which the transition matrix of the dynamical new system, incremented by the correction terms necessary to apply the Ito calculus, appears.
Ideal and physical barrier problems for non-linear systems driven by normal and Poissonian white noise via path integral method
2016
Abstract In this paper, the probability density evolution of Markov processes is analyzed for a class of barrier problems specified in terms of certain boundary conditions. The standard case of computing the probability density of the response is associated with natural boundary conditions, and the first passage problem is associated with absorbing boundaries. In contrast, herein we consider the more general case of partially reflecting boundaries and the effect of these boundaries on the probability density of the response. In fact, both standard cases can be considered special cases of the general problem. We provide solutions by means of the path integral method for half- and single-degr…
Optimal tuning of tuned liquid column damper systems in random vibration by means of an approximate formulation
2014
Passive control devices are often added to slender and flexible systems in order to increase their structural safety. Several types of devices have been proposed in order to reduce the dynamic responses of different kind of structural systems. Among them, the tuned liquid column damper (TLCD) proved to be very effective in reducing vibration of various type of structures by means of a combined action which involves the motion of the liquid mass within the tube. The restoring force, in particular, is produced by the force of gravity acting on the liquid and the damping effect is generated by the hydrodynamic head losses that arise during the motion of the liquid inside the TLCD. Since the in…
Experimental Investigation of Random Vibration Control Through Dry Friction
1997
The purpose of this experimental investigation is to measure the response statistics in the presence of base friction and other friction sources. The experimental model emulates a one-floor building supported on four leaf springs, subjected to band limited random excitation. Two different types of model base are considered, a friction base and a frictionless base. In both cases friction can also be applied at two sides of the model’s main mass against the direction of its motion. Excitation and response transducer signals are processed to estimate excitation and response statistics in the presence and in the absence of top mass friction. Measured statistics include mean squares, autocorrela…
The Influence of Particular Modes of Vibration
1986
When vibration stress occurs at the place of work, 1, 2, or 3 directions of the coordinate system related to man, or vectors of these axes, can be involved (Fig. 1). In such multiaxial vibration, the stress may predominate in one direction or may have similar magnitudes in all directions. In addition, rotational vibration about these axes may also take place (see section “Rotational Vibration,” p. 125).
Dynamics analysis of distributed parameter system subjected to a moving oscillator with random mass, velocity and acceleration
2002
Abstract The problem of calculating the response of a distributed parameter system excited by a moving oscillator with random mass, velocity and acceleration is investigated. The system response is a stochastic process although its characteristics are assumed to be deterministic. In this paper, the distributed parameter system is assumed as a beam with Bernoulli–Euler type analytical behaviour. By adopting the Galerkin's method, a set of approximate governing equations of motion possessing time-dependent uncertain coefficients and forcing function is obtained. The statistical characteristics of the deflection of the beam are computed by using an improved perturbation approach with respect t…
A simplified analysis for the evaluation of stochastic response of elasto-plastic oscillators
1999
Abstract The paper deals with dynamic hysteretic oscillators without post-yielding hardening, called ideal elasto-plastic oscillators, subjected to white noise. They are characterized by the fact that they do not reach stationarity even though excited by stationary stochastic processes. A simplified solution procedure to capture this behaviour is presented in this paper. It is based on modelling the accumulated plastic deformations as a homogeneous compound Poisson process. In particular, two aspects are addressed in the paper: (1) evaluation of the probabilistic parameters of the accumulated plastic deformation process; and (2) evaluation of the second-order cumulants of the response by me…