scholarly journals Development of a Combined-Ritz Method for Modeling 3D Acoustics in Candu Fuel Sub-Channels

2021 ◽  
Author(s):  
David Villero
Keyword(s):  
Equations Of Motion ◽  
Ritz Method ◽  
Axial Direction ◽  
Acoustic System ◽  
Lagrange Equations ◽  
Acoustic Wave Propagation ◽  
Absorbing Material ◽  
Acoustic Pressure Wave ◽  
System Equations ◽  
Triangular Elements

A combined finite element-Ritz method is developed to effectively model the 3D lowfrequency acoustics in CANDU fuel sub-channels. The complex acoustic behavior of CANDU fuel sub-channels in the cross section is captured using the six-node isoparametric triangular elements; and the acoustic wave propagation in the axial direction is modeled using the polynomials of order n. The Lagrange equations are utilized to formulate the system equations of motion. The acoustic system considered in this study consists of pipe-like medium (water) with rigid and smooth walls. At the inlet of the fuel channel acoustic system, an acoustic pressure wave is prescribed to simulate the pulsation induced by the main feeder pumps. At the outlet, the acoustic system is assumed to interact with a reacting and absorbing material with prescribed acoustic impedance. The method was tested for several scenarios of interest. Numerical results obtained are in excellent agreement with the analytical and ANSYS solutions.

scholarly journals Development of a Combined-Ritz Method for Modeling 3D Acoustics in Candu Fuel Sub-Channels

2021 ◽  
Author(s):  
David Villero
Keyword(s):  
Equations Of Motion ◽  
Ritz Method ◽  
Axial Direction ◽  
Acoustic System ◽  
Lagrange Equations ◽  
Acoustic Wave Propagation ◽  
Absorbing Material ◽  
Acoustic Pressure Wave ◽  
System Equations ◽  
Triangular Elements

A combined finite element-Ritz method is developed to effectively model the 3D lowfrequency acoustics in CANDU fuel sub-channels. The complex acoustic behavior of CANDU fuel sub-channels in the cross section is captured using the six-node isoparametric triangular elements; and the acoustic wave propagation in the axial direction is modeled using the polynomials of order n. The Lagrange equations are utilized to formulate the system equations of motion. The acoustic system considered in this study consists of pipe-like medium (water) with rigid and smooth walls. At the inlet of the fuel channel acoustic system, an acoustic pressure wave is prescribed to simulate the pulsation induced by the main feeder pumps. At the outlet, the acoustic system is assumed to interact with a reacting and absorbing material with prescribed acoustic impedance. The method was tested for several scenarios of interest. Numerical results obtained are in excellent agreement with the analytical and ANSYS solutions.

scholarly journals Asymmetric Vibrations and Chaos in Spherical Caps under Uniform Time-varying Pressure Fields

2021 ◽  
Author(s):  
Giovanni Iarriccio ◽  
Antonio Zippo ◽  
Francesco Pellicano
Keyword(s):  
Equations Of Motion ◽  
Ritz Method ◽  
Excitation Frequency ◽  
Lagrange Equations ◽  
Reduced Order ◽  
Pressure Fields ◽  
Time Histories ◽  
Implicit Solver ◽  
Spherical Caps ◽  
External Excitation Frequency

Abstract This paper presents a study on nonlinear asymmetric vibrations in shallow spherical caps under pressure loading. The Novozhilov’s nonlinear shell theory is used for modelling the structural strains. A reduced-order model is developed through the Rayleigh-Ritz method and Lagrange equations. The equations of motion are numerically integrated using an implicit solver. The bifurcation scenario is addressed by varying the external excitation frequency. The occurrence of asymmetric vibrations related to quasi-periodic and chaotic motion is shown through the analysis of time histories, spectra, Poincaré maps, and phase planes.

Elastodynamic Analysis of a Completely Elastic System

1977 ◽  
Vol 99 (3) ◽  
pp. 604-609 ◽  
Author(s):  
D. Kohli ◽  
D. Hunter ◽  
G. N. Sandor
Keyword(s):  
Vibration Analysis ◽  
Elastic System ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Lagrange Equations ◽  
Elastic Supports ◽  
Linear Ordinary Differential Equations ◽  
Elastic Links ◽  
Inertia Forces ◽  
Crank Mechanism

The completely elastic system considered for this vibration analysis consists of an offset slider-crank mechanism having (a) elastic supports and mountings of the mechanism permitting translational vibrations of the shafts and supports, (b) elastic shafts permitting torsional vibrations, (c) elastic links of the mechanism which deform due to external or internal body forces and allow flexural and axial vibrations. Both the effect of the deformations caused by the inertia forces in the mechanism links, shafts, and supports and the effect of change in the inertia forces due to these deformations are taken into account in constructing a general mathematical model for conducting elastodynamic analysis. The rigid displacements (finite and infinitesimal) of the mechanism links due to deformations in the support are evaluated using a truncated Taylor series approximation. Deformation in the links caused by the inertia forces is approximated by a finite number of terms in a Fourier series using the Raleigh-Ritz method. The Lagrange equations of motion are used to obtain coupled time varying linear ordinary differential equations of motion for the vibration analysis of the slider-crank mechanism. The method in general may be applied to any planar or spatial system consisting of elastic links, elastic shafts, and elastic supports. Numerical examples are presented for illustration.

Dynamic Behavior and Stability of a Rotor Under Base Excitation

2006 ◽  
Vol 128 (5) ◽  
pp. 576-585 ◽  
Author(s):  
M. Duchemin ◽  
A. Berlioz ◽  
G. Ferraris
Keyword(s):  
Dynamic Behavior ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Base Excitation ◽  
Flexible Rotor ◽  
Lagrange Equations ◽  
Rotor Systems ◽  
Simple Systems ◽  
Flexible Rotor Systems

The dynamic behavior of flexible rotor systems subjected to base excitation (support movements) is investigated theoretically and experimentally. The study focuses on behavior in bending near the critical speeds of rotation. A mathematical model is developed to calculate the kinetic energy and the strain energy. The equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. Also, the method of multiple scales is applied to study stability when the system mounting is subjected to a sinusoidal rotation. An experimental setup is used to validate the presented results.

Nonlinear Planar Dynamics of Fluid-Conveying Cantilevered Extensible Pipes

2013 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Michael P. Païdoussis ◽  
Marco Amabili
Keyword(s):  
Flow Velocity ◽  
Trivial Solution ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Time Integration ◽  
Axial Direction ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Critical Flow Velocity ◽  
The Stability

This paper for the first time investigates the nonlinear planar dynamics of a cantilevered extensible pipe conveying fluid; the centreline of the pipe is considered to be extensible resulting in coupled longitudinal and transverse equations of motion; specifically, the kinetic and potential energies are obtained in terms of longitudinal and transverse displacements and then the extended version of the Lagrange equations for systems containing non-material volumes is employed to derive the equations of motion. Direct time integration along with the pseudo-arclength continuation method are employed to solve the discretized equations of motion. Bifurcation diagrams of the system are constructed as the flow velocity is increased as the bifurcation parameter. As opposed to the case of an inextensible pipe, an extensible pipe elongates in the axial direction as the flow velocity is increased from zero. At the critical flow velocity, the stability of the system is lost via a supercritical Hopf bifurcation, emerging from the trivial solution for the transverse displacement and non-trivial solution for the longitudinal displacement and leading to a flutter.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

Time Integration Incorporated Sensitivity Analysis With Generalized-α Method for Multibody Dynamics Systems

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Dynamic Loading ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Time Integration ◽  
Optimization Method ◽  
Sensitivity Analysis Method ◽  
System Equations ◽  
Consecutive Time

The topology optimization method is extended for the optimization of geometrically nonlinear, time-dependent multibody dynamics systems undergoing nonlinear responses. In particular, this paper focuses on sensitivity analysis methods for topology optimization of general multibody dynamics systems, which include large displacements and rotations and dynamic loading. The generalized-α method is employed to solve the multibody dynamics system equations of motion. The developed time integration incorporated sensitivity analysis method is based on a linear approximation of two consecutive time steps, such that the generalized-α method is only applied once in the time integration of the equations of motion. This approach significantly reduces the computational costs associated with sensitivity analysis. To show the effectiveness of the developed procedures, topology optimization of a ground structure embedded in a planar multibody dynamics system under dynamic loading is presented.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

Concise Equations for Rotor Dynamics Analysis

1995 ◽  
Author(s):  
W. J. Chen
Keyword(s):  
Equations Of Motion ◽  
Rotor Dynamics ◽  
Memory Storage ◽  
The Other ◽  
Dynamics Analysis ◽  
Real Domain ◽  
The Matrix ◽  
System Equations ◽  
Ordering Algorithms ◽  
Matrix Bandwidth

Abstract Concise equations for rotor dynamics analysis are presented. Two coordinate ordering methods are introduced in the element equations of motion. One is in the real domain and the other is in the complex domain. The two proposed ordering algorithms lead to more compact element matrices. A station numbering technique is also proposed for the system equations during the assembly process. This numbering technique can minimize the matrix bandwidth, the memory storage and can increase the computational efficiency.

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