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Linear Dynamic Systems (linear + dynamic_system)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Linear random vibration by stochastic reduced-order models

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010
Mircea Grigoriu
Abstract A practical method is developed for calculating statistics of the states of linear dynamic systems with deterministic properties subjected to non-Gaussian noise and systems with uncertain properties subjected to Gaussian and non-Gaussian noise. These classes of problems are relevant as most systems have uncertain properties, physical noise is rarely Gaussian, and the classical theory of linear random vibration applies to deterministic systems and can only deliver the first two moments of a system state if the noise is non-Gaussian. The method (1) is based on approximate representations of all or some of the random elements in the definition of linear random vibration problems by stochastic reduced-order models (SROMs), that is, simple random elements having a finite number of outcomes of unequal probabilities, (2) can be used to calculate statistics of a system state beyond its first two moments, and (3) establishes bounds on the discrepancy between exact and SROM-based solutions of linear random vibration problems. The implementation of the method has required to integrate existing and new numerical algorithms. Examples are presented to illustrate the application of the proposed method and assess its accuracy. Copyright © 2009 John Wiley & Sons, Ltd. [source]

State-space time integration with energy control and fourth-order accuracy for linear dynamic systems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006
Steen Krenk
Abstract A fourth-order accurate time integration algorithm with exact energy conservation for linear structural dynamics is presented. It is derived by integrating the phase-space representation and evaluating the resulting displacement and velocity integrals via integration by parts, substituting the time derivatives from the original differential equations. The resulting algorithm has an exact energy equation, in which the change of energy is equal to the work of the external forces minus a quadratic form of the damping matrix. This implies unconditional stability of the algorithm, and the relative phase error is of fourth-order. An optional high-frequency algorithmic damping is constructed by optimal combination of three different damping matrices, each proportional to either the mass or the stiffness matrix. This leads to a modified form of the undamped algorithm with scalar weights on some of the matrices introducing damping of fourth-order in the frequency. Thus, the low-frequency response is virtually undamped, and the algorithm remains third-order accurate even when algorithmic damping is included. The accuracy of the algorithm is illustrated by an application to pulse propagation in an elastic medium, where the algorithmic damping is used to reduce dispersion due to the spatial discretization, leading to a smooth solution with a clearly defined wave front. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A new framework for data reconciliation and measurement bias identification in generalized linear dynamic systems

AICHE JOURNAL, Issue 7 2010
Hua Xu
Abstract This article describes a new framework for data reconciliation in generalized linear dynamic systems, in which the well-known Kalman filter (KF) is inadequate for filtering. In contrast to the classical formulation, the proposed framework is in a more concise form but still remains the same filtering accuracy. This comes from the properties of linear dynamic systems and the features of the linear equality constrained least squares solution. Meanwhile, the statistical properties of the framework offer new potentials for dynamic measurement bias detection and identification techniques. On the basis of this new framework, a filtering formula is rederived directly and the generalized likelihood ratio method is modified for generalized linear dynamic systems. Simulation studies of a material network present the effects of both the techniques and emphatically demonstrate the characteristics of the identification approach. Moreover, the new framework provides some insights about the connections between linear dynamic data reconciliation, linear steady state data reconciliation, and KF. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source]

The piecewise full decoupling method for dynamic problems

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Dr.-Ing., Nenad Kranj
The piecewise full decoupling method is a new developed numerical procedure of explicit integration based on piecing together local linear solutions. The method is applied for solving piecewise linear dynamic systems under periodic excitations. Close agreement is found between obtained results and published findings of a harmonic balance method and a finite element method in time domain. [source]