scholarly journals Multiple scales analysis of water hammer attenuation

2011 ◽  
Vol 69 (4) ◽  
pp. 677-690 ◽  
Author(s):  
S. Y. Han ◽  
D. Hansen ◽  
G. Kember
Keyword(s):  
Multiple Scales ◽  
Water Hammer ◽  
Multiple Scales Analysis

The Small Scale Effect on Linear Vibration of Beam-Like Nanostructures

2012 ◽  
Vol 446-449 ◽  
pp. 3432-3435
Author(s):  
Cheng Li ◽  
Lin Quan Yao
Keyword(s):  
Axial Load ◽  
Vibration Mode ◽  
Multiple Scales ◽  
Separation Of Variables ◽  
Classical Mechanics ◽  
Small Scale ◽  
Transverse Displacement ◽  
Linear Vibration ◽  
Small Scale Effect ◽  
Multiple Scales Analysis

Transverse free dynamics of a beam-like nanostructure with axial load is investigated. The effects of a small size at nano-scale unavailable in classical mechanics are presented. Explicit solutions for natural frequency, vibration mode and transverse displacement are obtained by separation of variables and multiple scales analysis. Results by two methods are in close agreement.

Nonlinear Stability of Thermoelastic Sliding Contact

2005 ◽  
Vol 74 (3) ◽  
pp. 595-598
Author(s):  
Jason D. Miller ◽  
D. Dane Quinn
Keyword(s):  
Multiple Scales ◽  
Dynamical Behavior ◽  
Stable State ◽  
Nonlinear Behavior ◽  
Sliding Contact ◽  
Stability Criteria ◽  
Multiple Scales Analysis ◽  
Two Equilibria

A model for sliding contact of a thermoelastic rod is considered and is subjected to a multiple scales analysis to uncover its nonlinear behavior near a neutrally stable state. The analysis reveals a combination of the contact resistance and frictional intensity that describes the generic unfolding of this critical state and its associated bifurcations. In particular, the system can describe how two equilibria coalesce in a saddle-node bifurcation and generalizes stability criteria that have been presented previously in the literature for this model. Moreover, this analysis describes the role of the initial deformation of the rod on its long-term dynamical behavior.

A Multiple-Scales Analysis of Nonlinear, Localized Modes in a Cyclic Periodic System

1993 ◽  
Vol 60 (2) ◽  
pp. 388-397 ◽  
Author(s):  
A. Vakakis ◽  
T. Nayfeh ◽  
M. King
Keyword(s):  
Vibration Isolation ◽  
Multiple Scales ◽  
Algebraic Equations ◽  
Localized Modes ◽  
Mode Localization ◽  
Nonlinear Mode ◽  
Weakly Coupled ◽  
Passive Vibration Isolation ◽  
Coupling Stiffness ◽  
Multiple Scales Analysis

In this work the nonlinear localized modes of an n-degree-of-freedom (DOF) nonlinear cyclic system are examined by the averaging method of multiple scales. The set of nonlinear algebraic equations describing the localized modes is derived and is subsequently solved for systems with various numbers of DOF. It is shown that nonlinear localized modes exist only for small values of the ratio (k/μ), where k is the linear coupling stiffness and μ is the coefficient of the grounding stiffness nonlinearity. As (k/μ) increases the branches of localized modes become nonlocalized and either bifurcate from “extended” antisymmetric modes in inverse, “multiple” Hamiltonian pitchfork bifurcations (for systems with even-DOF), or reach certain limiting values for large values of(k/μ) (for systems with odd-DOF). Motion confinement due to nonlinear mode localization is demonstrated by examining the responses of weakly coupled, perfectly periodic cyclic systems caused by external impulses. Finally, the implications of nonlinear mode localization on the active or passive vibration isolation of such structures are discussed.

Parametric Vibrations in Discs: Point-Wise and Distributed Loads, Including Rotating Friction

1995 ◽  
Author(s):  
H. Ouyang ◽  
S. N. Chan ◽  
J. E. Mottershead ◽  
M. I. Friswell ◽  
M. P. Cartmell
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Transverse Load ◽  
Transverse Mass ◽  
Follower Load ◽  
Parametric Resonances ◽  
Spring System ◽  
Multiple Scales Analysis ◽  
Mass Spring ◽  
Rotating Load

Abstract This paper is concerned with the parametric resonances in a stationary annular disc when excited by a rotating load system. Two forms of the load system are considered. In the first, the load consists of a discrete transverse mass-spring-damper system and a frictional follower load. Secondly, a distributed mass-spring system (without friction) is studied. In both cases the transverse load is rotated at a uniform speed around the disc. Equations of motion are developed for the two cases, and the results of a multiple scales analysis are presented. The disc is found to exhibit many parametric resonances at subcritical speeds when friction is present.

scholarly journals Multiple-scales analysis of photonic crystal waveguides

2003 ◽  
Vol 39 (6) ◽  
pp. 778-786 ◽  
Author(s):  
J. Poon ◽  
E. Istrate ◽  
M. Allard ◽  
E.H. Sargent
Keyword(s):  
Photonic Crystal ◽  
Multiple Scales ◽  
Photonic Crystal Waveguides ◽  
Multiple Scales Analysis

Second-Order Perturbation Analysis of Low-Amplitude Traveling Waves in a Periodic Nonlinear Chain

2013 ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Traveling Waves ◽  
Perturbation Analysis ◽  
Multiple Scales ◽  
Periodic Structures ◽  
Second Order ◽  
Quadratic Nonlinearity ◽  
Wave Number ◽  
Nonlinear Chain ◽  
Multiple Scales Analysis ◽  
Low Amplitude

Traveling waves in one-dimensional nonlinear periodic structures are investigated for low-amplitude oscillations using perturbation analysis. We use second-order multiple scales analysis to capture the effects of quadratic nonlinearity. Comparisons with the linear and cubical nonlinear cases are presented in the dispersion relationship, group velocity and phase velocity and their dependence on wave number and amplitude of oscillation. Quadratic nonlinearity is shown to have a significant effect on the behavior.

Spatial and Temporal Stabilities of Flow in a Natural Circulation Loop: Influences of Thermal Boundary Condition

2003 ◽  
Vol 125 (4) ◽  
pp. 612-623 ◽  
Author(s):  
Y. Y. Jiang ◽  
M. Shoji
Keyword(s):  
Boundary Condition ◽  
Multiple Scales ◽  
Natural Circulation ◽  
Three Dimensional ◽  
Thermal Boundary Condition ◽  
Circular Loop ◽  
Thermal Boundary Conditions ◽  
Natural Circulation Loop ◽  
Control Of Flow ◽  
Multiple Scales Analysis

In a natural circular loop, the thermal convection demonstrates various spatial patterns and temporal instabilities. Problem consists in determining them with respects to thermal boundary conditions. To this end a multiple scales analysis is applied which resembles the inherent characteristic of the pattern formation in the Rayleigh-Be´nard convection. A three-dimensional nonlinear model is proposed by incorporating the flow modes derived along the analysis. The differences of thermal boundary condition are reflected by a coefficient δ. For small δ, numerical solution to the model shows that only temporal instability exists and Lorenz chaos is possible, otherwise, for large values both spatial and temporal instabilities occur leading to cellular flow and intermittency chaos. The model predicted some additional phenomena opening for experimental observation. It seems significant that this study proposes an algorithm for the control of flow stability and distribution by varying the thermal boundary condition.

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