Resonant Oscillations: A Regular Perturbation Approach

1971 ◽  
Vol 12 (7) ◽  
pp. 1069-1075 ◽  
Author(s):  
Michael P. Mortell
Keyword(s):  
Perturbation Approach ◽  
Regular Perturbation

scholarly journals Perturbation Approach in the Dynamic Buckling of a Model Structure with a Cubic-quintic Nonlinearity Subjected to an Explicitly Time Dependent Slowly Varying Load

2019 ◽  
pp. 1-19
Author(s):  
A. M. Ette ◽  
I. U. Udo-Akpan ◽  
J. U. Chukwuchekwa ◽  
A. C. Osuji ◽  
M. F. Noah
Keyword(s):  
Perturbation Technique ◽  
Dynamic Buckling ◽  
Buckling Load ◽  
Time Dependent ◽  
Initial Time ◽  
Perturbation Approach ◽  
Elastic Model ◽  
Model Structure ◽  
Regular Perturbation ◽  
Long Run

This investigation is concerned with analytically determining the dynamic buckling load of an imperfect cubic-quintic nonlinear elastic model structure struck by an explicitly time-dependent but slowly varying load that is continuously decreasing in magnitude. A multi-timing regular perturbation technique in asymptotic procedures is utilized to analyze the problem. The result shows that the dynamic buckling load depends, among other things, on the first derivative of the load function evaluated at the initial time. In the long run, the dynamic buckling load is related to its static equivalent, and that relationship is independent of the imperfection parameter. Thus, once any of the two buckling loads is known, then the other can easily be evaluated using this relationship.

scholarly journals A regular perturbation approach to surface tension driven flows

1982 ◽  
Vol 9 (4) ◽  
pp. 217-224 ◽  
Author(s):  
Ignacio Da-Riva ◽  
Emilio Alvarez Pereira
Keyword(s):  
Surface Tension ◽  
Perturbation Approach ◽  
Regular Perturbation

Moment Lyapunov Exponents and Stochastic Stability of a Three-Dimensional System on Elastic Foundation Using a Perturbation Approach

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Vladimir Stojanović ◽  
Marko Petković
Keyword(s):  
Lyapunov Exponents ◽  
Elastic Foundation ◽  
Stochastic Stability ◽  
Coupled Oscillators ◽  
Complex Structure ◽  
Perturbation Approach ◽  
Dimensional System ◽  
Regular Perturbation ◽  
Moment Stability ◽  
Moment Lyapunov Exponents

In this paper, the stochastic stability of the three elastically connected Euler beams on elastic foundation is studied. The model is given as three coupled oscillators. Stochastic stability conditions are expressed by the Lyapunov exponent and moment Lyapunov exponents. It is determined that the new set of transformation for getting Ito∧ differential equations can be applied for any system of three coupled oscillators. The method of regular perturbation is used to determine the asymptotic expressions for these exponents in the presence of small intensity noises. Analytical results are presented for the almost sure and moment stability of a stochastic dynamical system. The results are applied to study the moment stability of the complex structure with influence of the white noise excitation due to the axial compressive stochastic load.

Perturbation Approach to Hydrodynamic Lubrication Theory

1994 ◽  
Vol 116 (1) ◽  
pp. 110-118 ◽  
Author(s):  
C. M. Myllerup ◽  
B. J. Hamrock
Keyword(s):  
Journal Bearing ◽  
Iterative Scheme ◽  
Hydrodynamic Lubrication ◽  
Perturbation Approach ◽  
Perturbation Scheme ◽  
Regular Perturbation ◽  
Corner Flow ◽  
Higher Order Terms ◽  
Hydrodynamic Lubrication Theory ◽  
Coordinate Perturbation

Three perturbation approaches that apply for regular hydrodynamic lubrication problems are discussed: a cross-film coordinate perturbation, an iterative scheme, and a regular perturbation in terms of the film aspect ratio. The methods are used to derive higher order terms for a driven corner flow with a Newtonian lubricant of constant properties. Reasons for preferring the regular perturbation scheme are presented, and this method is used to obtain the correct curvature correction in an infinitely long journal bearing. Criteria for identifying singular geometries in hydrodynamic lubrication are set fourth.

scholarly journals Forward Roll Coating of a Williamson’s Material onto a Moving Web: A Theoretical Study

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. Zahid ◽  
I. Siddique ◽  
S. Saleem ◽  
A. Al-Zubaidi ◽  
M. A. Rana ◽  
...  
Keyword(s):  
Coating Thickness ◽  
Gradient Flow ◽  
Separation Point ◽  
Maximum Pressure ◽  
Perturbation Approach ◽  
Regular Perturbation ◽  
Roll Coating ◽  
Flow Equations ◽  
Operating Variables ◽  
Roll Separating Force

This paper presents a mathematical model for the thin film roll coating process of an incompressible Williamson material, passing through a closed passage between a rotating roll and a web. In light of lubrication approximation theory, the flow equations are nondimensionalized. The regular perturbation approach is used to provide solutions for the velocity profile, pressure gradient, flow rate per unit width, and shear stress at the roll surface. Important engineering quantities such as coating thickness, maximum pressure, separation point, roll/sheet separating force, and roll-transmitted power to the fluid are also obtained. The effects of several factors are graphically projected. The study shows that the material factors that are involved determine the operating variables. Coating thickness and separation point are controlled by Weissenberg’s number, therefore acting as a controlling parameter for the rate of flow, thickness in coating, power contribution, pressure, roll separating force, and separation point. In comparison to the existing results in the literature, the current results are broader and zero-order results are more accurate.

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