Fluid-Coupled Vibrations of Immersed Spent Nuclear Racks: A Nonlinear Model Accounting for Squeeze-Film and Dissipative Phenomena

2004 ◽  
Author(s):  
Miguel Moreira ◽  
Jose´ Antunes
Keyword(s):  
Dynamical Behavior ◽  
Coupled System ◽  
Differential Algebraic Equations ◽  
Nonlinear Flow ◽  
Squeeze Film ◽  
Algebraic Equations ◽  
Spent Fuel ◽  
Coupled Modes ◽  
Small Water ◽  
Flow Effects

Fluid-coupling effects lead to a complex dynamical behavior of immersed spent fuel assembly storage racks. Predicting their responses under strong earthquakes is of prime importance for the safety of nuclear plant facilities. In the near-past we introduced a simplified linearized model for the vibrations of such systems, in which gap-averaged velocity and pressure fields were described analytically in terms of a single space-coordinate for each fluid inter-rack channel. Using such approach it was possible to generate and assemble a complete set of differential-algebraic equations describing the multi-rack fluid coupled system dynamics. Because of the linearization assumptions, we achieved computation of the flow-structure coupled modes, but also time-domain simulations of the system responses. However, nonlinear squeeze-film and dissipative flow effects, connected with very large amplitude responses and/or relatively small water gaps, cannot be properly accounted unless the linearization assumption is relaxed. Such is the aim of the present paper. Here, using a similar approach, we generalize our theoretical model to deal with nonlinear flow effects. Besides that the proposed methodology can be automatically implemented in a symbolic computational environment, it is much less computer-intensive than finite element formulations. Using the proposed technique, computations of basic flow-coupled rack configurations subjected to impulse excitations are presented, in order to highlight the essential features of such systems as well as the relevance of squeeze-film and dissipative effects. Finally, more realistic simulations of complex system responses to strong seismic excitations are presented and discussed.

Use of the Non-Inertial Coordinates in the Analysis of Train Longitudinal Forces

2011 ◽  
Vol 7 (1) ◽  
Author(s):  
Ahmed A. Shabana ◽  
Ahmed K. Aboubakr ◽  
Lifen Ding
Keyword(s):  
Differential Equations ◽  
Virtual Work ◽  
Three Dimensional ◽  
Coupled System ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
State Equations ◽  
Car Body ◽  
Nonlinear Coupler ◽  
Inertia Forces

In this investigation, a new three-dimensional nonlinear train car coupler model that takes into account the geometric nonlinearity due to the coupler and car body displacements is developed. The proposed nonlinear coupler model allows for arbitrary three-dimensional motion of the car bodies and captures kinematic degrees of freedom that are not captured using existing simpler models. The coupler kinematic equations are expressed in terms of the car body coordinates, as well as the relative coordinates of the coupler with respect to the car body. The virtual work is used to obtain expressions for the generalized forces associated with the car body and coupler coordinates. By assuming the inertia of the coupler components negligible compared to the inertia of the car body, the system coordinates are partitioned into two distinct sets: inertial and noninertial coordinates. The inertial coordinates that describe the car motion have inertia forces associated with them. The noninertial coupler coordinates; on the other hand, describe the coupler kinematics and have no inertia forces associated with them. The use of the principle of virtual work leads to a coupled system of differential and algebraic equations expressed in terms of the inertial and noninertial coordinates. The differential equations, which depend on the coupler noninertial coordinates, govern the motion of the train cars; whereas the algebraic force equations are the result of the quasi-static equilibrium conditions of the massless coupler components. Given the inertial coordinates and velocities, the quasi-static coupler algebraic force equations are solved iteratively for the noninertial coordinates using a Newton–Raphson algorithm. This approach leads to significant reduction in the numbers of state equations, system inertial coordinates, and constraint equations; and allows avoiding a system of stiff differential equations that can arise because of the relatively small coupler mass. The use of the concept of the noninertial coordinates and the resulting differential/algebraic equations obtained in this study is demonstrated using the knuckle coupler, which is widely used in North America. Numerical results of simple train models are presented in order to demonstrate the use of the formulation developed in this paper.

Towards a Simulation Knowledge Network With Application to Coupled Physiological Systems

2000 ◽  
Author(s):  
Bei Gu ◽  
H. Harry Asada
Keyword(s):  
Coupled System ◽  
Differential Algebraic Equations ◽  
Knowledge Network ◽  
Distributed Model ◽  
Algebraic Equations ◽  
Simulation Environment ◽  
Multistage Processes ◽  
Algebraic Constraints ◽  
Model Database ◽  
Physiological Systems

Abstract A new approach is proposed for the simulation of interacting human physiological subsystems. The new simulation environment will allow users to build, analyze and solve coupled physiological system models based on available distributed subsystem models. The subsystem models as an abstract form of physiological knowledge are shared through the Internet. The simulation knowledge network includes a distributed model database, an information server, and an analysis and solution environment that can be downloaded from the server. To represent the coupled system, we use Differential Algebraic Equations (DAE) as the basic format. There are three common sources of algebraic constraints in models of physiological systems. They are causal conflict, simulation optimization, and multistage processes. The singularly perturbed sliding manifolds method is chosen for solving DAEs. Possible future improvements are discussed. Examples of simulation of coupled circulatory, thermoregulatory, and renal systems are presented to demonstrate the simulation environment.

Analysis of the Effect of Spatial Uncertainties on the Dynamic Behavior of Electrostatic Microactuators

2016 ◽  
Vol 20 (2) ◽  
pp. 279-300
Author(s):  
Aravind Alwan ◽  
Narayana R. Aluru
Keyword(s):  
Physical Model ◽  
Electrostatic Force ◽  
Damping Ratio ◽  
Full Range ◽  
Uncertainty Propagation ◽  
Dynamical Behavior ◽  
Electrostatic Actuation ◽  
Squeeze Film ◽  
Coupled Modes ◽  
Actuation Force

AbstractThis paper examines the effect of spatial roughness on the dynamical behaviour of electrostatic microactuators. We develop a comprehensive physical model that comprises a nonlinear electrostatic actuation force aswell as a squeeze-film damping term to accurately simulate the dynamical behavior of a cantilever beam actuator. Spatial roughness is modeled as a nonstationary stochastic process whose parameters can be estimated from profilometric measurements. We propagate the stochastic model through the physical system and examine the resulting uncertainty in the dynamical behavior that manifests as a variation in the quality factor of the device. We identify two distinct, yet coupled, modes of uncertainty propagation in the system, that result from the roughness causing variation in the electrostatic actuation force and the damping pressure, respectively. By artificially turning off each of these modes of propagation in sequence, we demonstrate that the variation in the damping pressure has a greater effect on the damping ratio than that arising from the electrostatic force. Comparison with similar simulations performed using a simplified mass-spring-damper model show that the coupling between these two mechanisms can be captured only when the physical model includes the primary nonlinear interactions along with a proper treatment of spatial variations. We also highlight the difference between nonstationary and stationary covariance formulations by showing that the stationary model is unable to properly capture the full range of variation as compared to its nonstationary counterpart.

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

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