Nonlinear Oscillation of a Cylinder Containing a Flowing Fluid

1969 ◽  
Vol 91 (4) ◽  
pp. 1147-1155 ◽  
Author(s):  
A. L. Thurman ◽  
C. D. Mote
Keyword(s):  
Approximate Solution ◽  
Fluid Transport ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Practical Interest ◽  
Longitudinal Motion ◽  
Flowing Fluid ◽  
Weakly Nonlinear ◽  
Efficient Calculation

The fundamental and second periods of transverse oscillation of a cylinder containing a flowing fluid are theoretically determined for the approximate solution of two, coupled, nonlinear partial differential equations describing the transverse and longitudinal motion. The calculations indicate that the existence of the fluid transport velocity reduces all cylinder natural periods of oscillation and increases the relative importance of non-linear terms in the equations of motion. Accordingly, in many cases of practical interest the linear analysis is shown to be severely limited in its applicability. Curves are presented that will assist one to estimate both the accuracy of the linear period and the approximate nonlinear period in selected examples. A new approximate solution method is utilized that permits accurate and efficient calculation of the nonlinear period. This method can be applied to the period determination of additional cylindrical models not examined herein; the method appears to be semi-generally applicable to the periodic solution of weakly nonlinear systems.

Free, Periodic, Nonlinear Oscillation of an Axially Moving Strip

1969 ◽  
Vol 36 (1) ◽  
pp. 83-91 ◽  
Author(s):  
A. L. Thurman ◽  
C. D. Mote
Keyword(s):  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Practical Interest ◽  
Limited Range ◽  
Fundamental Period ◽  
Transverse Motion ◽  
Longitudinal Motion ◽  
Moving Strip ◽  
Axially Moving ◽  
Linear Period

The free, nonlinear, fundamental period of transverse oscillation of axially moving strips (e.g., tapes, fibers, belts, and band saws) is determined by the approximate solution of two, coupled, nonlinear, partial differential equations. One equation describes longitudinal motion and the other transverse motion. A solution method is developed that permits accurate and efficient period calculations. The results indicate that the existence of the axial transport velocity reduces the fundamental period of oscillation and increases the relative importance of the nonlinear terms in the equations of motion. In many cases of practical interest the linear analysis is shown to be seriously in error and one may be led to erroneous conclusions because of its limited range of applicability. Curves are presented that assist one to estimate the accuracy of the linear period calculation.

A Perturbation Approach for Analyzing Dispersion and Group Velocities in Two-Dimensional Nonlinear Periodic Lattices

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
R. K. Narisetti ◽  
M. Ruzzene ◽  
M. J. Leamy
Keyword(s):  
Perturbation Technique ◽  
Equations Of Motion ◽  
Wave Dispersion ◽  
Perturbation Approach ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Nonlinear Lattices ◽  
Directivity Patterns ◽  
Group Velocities

The paper investigates wave dispersion in two-dimensional, weakly nonlinear periodic lattices. A perturbation approach, originally developed for one-dimensional systems and extended herein, allows for closed-form determination of the effects nonlinearities have on dispersion and group velocity. These expressions are used to identify amplitude-dependent bandgaps, and wave directivity in the anisotropic setting. The predictions from the perturbation technique are verified by numerically integrating the lattice equations of motion. For small amplitude waves, excellent agreement is documented for dispersion relationships and directivity patterns. Further, numerical simulations demonstrate that the response in anisotropic nonlinear lattices is characterized by amplitude-dependent “dead zones.”

scholarly journals Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

2020 ◽  
Vol 9 (1) ◽  
pp. 370-381
Author(s):  
Dinkar Sharma ◽  
Gurpinder Singh Samra ◽  
Prince Singh
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Present Scheme ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

scholarly journals IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion

1895 ◽  
Vol 186 ◽  
pp. 123-164 ◽  
Keyword(s):  
Singular Solution ◽  
Physical State ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Viscous Fluids ◽  
Linear Functions ◽  
Incompressible Viscous Fluids ◽  
Theoretical Results

1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.

Towards a Technique for Nonlinear Modal Analysis

2012 ◽  
Author(s):  
Simon A. Neild ◽  
Andrea Cammarano ◽  
David J. Wagg
Keyword(s):  
Normal Form ◽  
Modal Analysis ◽  
Equations Of Motion ◽  
Transformation Process ◽  
Second Order ◽  
Identity Transformation ◽  
Modal Testing ◽  
System Response ◽  
Weakly Nonlinear ◽  
Nonlinear Modal Analysis

In this paper we discuss a theoretical technique for decomposing multi-degree-of-freedom weakly nonlinear systems into a simpler form — an approach which has parallels with the well know method for linear modal analysis. The key outcome is that the system resonances, both linear and nonlinear are revealed by the transformation process. For each resonance, parameters can be obtained which characterise the backbone curves, and higher harmonic components of the response. The underlying mathematical technique is based on a near identity normal form transformation. This is an established technique for analysing weakly nonlinear vibrating systems, but in this approach we use a variation of the method for systems of equations written in second-order form. This is a much more natural approach for structural dynamics where the governing equations of motion are written in this form as standard practice. In fact the first step in the method is to carry out a linear modal transformation using linear modes as would typically done for a linear system. The near identity transform is then applied as a second step in the process and one which identifies the nonlinear resonances in the system being considered. For an example system with cubic nonlinearities, we show how the resulting transformed equations can be used to obtain a time independent representation of the system response. We will discuss how the analysis can be carried out with applied forcing, and how the approximations about response frequencies, made during the near-identity transformation, affect the accuracy of the technique. In fact we show that the second-order normal form approach can actually improve the predictions of sub- and super-harmonic responses. Finally we comment on how this theoretical technique could be used as part of a modal testing approach in future work.

Investigation of Train Dynamics in Passing Through Curves Using a Full Model

Joint Rail ◽  
2004 ◽  
Author(s):  
Mohammad Durali ◽  
Mohammad Mehdi Jalili Bahabadi
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Full Model ◽  
Bogie Frame ◽  
Nonlinear Characteristics ◽  
Train Derailment ◽  
Train Dynamics

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible train derailment.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Determination of Instability Boundaries for a Highly Flexible Prismatic-Jointed Robot Performing Repetitive Maneuvers

1991 ◽  
Author(s):  
Keith W. Buffinton
Keyword(s):  
Floquet Theory ◽  
Equations Of Motion ◽  
Perturbation Techniques ◽  
Axial Motion ◽  
The Third ◽  
Straightforward Application ◽  
Method Yield ◽  
Robotic Devices ◽  
Axially Moving

Abstract Presented in this work are the equations of motion governing the behavior of a simple, highly flexible, prismatic-jointed robotic manipulator performing repetitive maneuvers. The robot is modeled as a uniform cantilever beam that is subject to harmonic axial motions over a single bilateral support. To conveniently and accurately predict motions that lead to unstable behavior, three methods are investigated for determining the boundaries of unstable regions in the parameter space defined by the amplitude and frequency of axial motion. The first method is based on a straightforward application of Floquet theory; the second makes use of the results of a perturbation analysis; and the third employs Bolotin’s infinite determinate method. Results indicate that both perturbation techniques and Bolotin’s method yield acceptably accurate results for only very small amplitudes of axial motion and that a direct application of Floquet theory, while computational expensive, is the most reliable way to ensure that all instability boundaries are correctly represented. These results are particularly relevant to the study of prismatic-jointed robotic devices that experience amplitudes of periodic motion that are a significant percentage of the length of the axially moving member.

A Unique Approach in Modelling Flow in Tight Oil Unconventional Reservoirs With Viscous, Inertial and Diffusion Forces Contributions

2021 ◽  
Author(s):  
Mohammed Aldhuhoori ◽  
Hadi Belhaj ◽  
Bisweswar Ghosh ◽  
Ryan Fernandes ◽  
Hamda Alkuwaiti ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Fluid Transport ◽  
Synthetic Data ◽  
Diffusion Term ◽  
Flowing Fluid ◽  
New Model ◽  
Forchheimer’S Equation ◽  
Low Viscosity ◽  
Flow Parameters ◽  
Unique Approach

Abstract A model for single-phase fluid flow in tight UCRs was previously produced by modifying the flow Forchheimer’s equation. The new modification addresses the fluid transport phenomena into three scales incorporating a diffusion term. In this study, a new liner model, numerically solved, has been developed and deployed for a gas huff and puff project. The new model has been numerically validated and verified using synthetic data and huff and puff case study. Ideally, the new model suits fluid flow in tight UCRs. The modified Forchheimer’s model presented is solved using the MATLAB numerical method for linear multiphase flow. For the huff & puff case, very simple profiles and flow dynamics of the main flow parameters have been established and a thorough parametric analysis and verifications were performed. It has been observed that the diffusion system becomes more prominent in regulating flow velocity with low permeability of the formation rock and low viscosity of the flowing fluid. The findings indicate a behavioral alignment with a previous hypothesis that matches actual reservoir behavior.

scholarly journals ANALYSIS OF RELATIONSHIPS BETWEEN THE CAPACITY OF CHEMICALS TO THE CUMULATION AND THE STRUCTURE OF THEIR MOLECULES

2019 ◽  
Vol 96 (10) ◽  
pp. 970-974
Author(s):  
Nina V. Kharchevnikova ◽  
Z. I. Zholdakova ◽  
V. I. Zhurko ◽  
D. Yu. Fedortsova ◽  
V. G. Blinova
Keyword(s):  
Lethal Dose ◽  
Practical Interest ◽  
Training Dataset ◽  
Jsm Method ◽  
Hazard Class ◽  
Structural Class ◽  
Chemical Hazard ◽  
Leave One Out ◽  
The Relationship

The relationships between the capacity of chemicals to cumulate a toxic effect (functional cumulation) and the structure of their molecules were investigated. In the process of substantiation of safe levels (MAC) of substances in water this capacity is characterized by the cumulation hazard class (later in the text - hazard class). This class is stated to be depend on the value of the relationship between the mean lethal dose of the acute experiment and the threshold dose of the chronic experiment. The experimental study of a huge amount of new chemicals in the chronic experiments is a very difficult task, thus the study of the possibility to predict the hazard class of a chemical is of great scientific and practical interest. By using a logical combinatorial method JSM, named in honor of an English logic J.S. Mill, the structural groups in molecules, determining the appurtenance of these chemicals to a hazard class were identified and the possibility of the prediction of the hazard class of a chemical belonging to a definite structural array, containing such structural group were investigated. The training dataset (583 compounds) was automatically derived from the database WATERTOX, containing the data on acute and chronic toxicity for about 2000 substances. The results suggest the JSM method to be limitedly applicable for the determination of a hazard class of an untested chemical using this heterogeneous training dataset because we were unable to unambiguously derive the list of chemicals belonging to the class of moderately hazard substances. The chemical in some cases was predicted to belong to one or other of the neighboring classes. However taking in mind this uncertainty, the accuracy of the method evaluated, when using the “leave-one-out” method was 78%. Nevertheless the JSM method enables us to find structural subgroups “responsible” for the functional cumulation. The relation of the hazard class of a chemical belonging to a definite structural class with its structure and the possibility of the prediction of an untested chemical hazard class are demonstrated. The prognosis of the hazard classes for chemicals belonging to several structural sets including the anthraquinone derivatives, phthalimides, perfluorated aliphatic compounds, chlorosubstituted phenols, phenylureas is performed.

Sign in / Sign up

Export Citation Format

Share Document