Dynamical Behaviour of a Materially Damped Flexible Towed Cable

1972 ◽  
Vol 23 (2) ◽  
pp. 109-120 ◽  
Author(s):  
T C Cannon ◽  
J Genin
Keyword(s):  
Closed Form ◽  
Natural Frequencies ◽  
Equilibrium Shape ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dynamical Behaviour ◽  
Aerodynamic Loading ◽  
Towed Cable ◽  
Closed Form Approximation ◽  
Good Agreement

SummaryThe three-dimensional equations of motion of a flexible towed cable are developed. A closed-form approximation for the equilibrium shape of a cable subjected to arbitrary aerodynamic loading is developed and used in the study of a heavy, vibrating tow cable. Natural frequencies of vibration and cable shapes are computed for typical cables and are shown to be in good agreement with exact, numerically obtained values.

Three-Dimensional Dynamical Behaviour of a Flexible Towed Cable

1972 ◽  
Vol 23 (3) ◽  
pp. 201-210 ◽  
Author(s):  
T C Cannon ◽  
J Genin
Keyword(s):  
Approximate Solution ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Three Dimensional ◽  
Dynamical Behaviour ◽  
Flexible Cable ◽  
Linear Equations Of Motion ◽  
Towed Cable ◽  
Non Linear Equations

SummaryThe three-dimensional motion of a body towed by a flexible cable is studied. An approximate solution is developed for the non-linear equations of motion of the system to determine cable shapes. This solution is then used to compute natural frequencies and damping rates for longitudinal and lateral motions of the system. Conditions necessary for the uncoupling of the lateral and longitudinal motions are defined.

Vibration Characteristics of Straight Blades of Asymmetrical Aerofoil Cross-Section

1969 ◽  
Vol 20 (2) ◽  
pp. 178-190 ◽  
Author(s):  
W. Carnegie ◽  
B. Dawson
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Limited Range ◽  
First Order ◽  
Special Cases ◽  
Theoretical Results ◽  
Theoretical Procedure ◽  
Good Agreement

SummaryTheoretical and experimental natural frequencies and modal shapes up to the fifth mode of vibration are given for a straight blade of asymmetrical aerofoil cross-section. The theoretical procedure consists essentially of transforming the differential equations of motion into a set of simultaneous first-order equations and solving them by a step-by-step finite difference procedure. The natural frequency values are compared with results obtained by an analytical solution and with standard solutions for certain special cases. Good agreement is shown to exist between the theoretical results for the various methods presented. The equations of motion are dependent upon the coordinates of the axis of the centre of flexure of the beam relative to the centroidal axis. The effect of variations of the centre of flexure coordinates upon the frequencies and modal shapes is shown for a limited range of coordinate values. Comparison is made between the theoretical natural frequencies and modal shapes and corresponding results obtained by experiment.

scholarly journals The Variational Reduction for Low-Dimensional Fermi Gases and Bose–Fermi Mixtures: A Brief Review

2019 ◽  
Vol 4 (1) ◽  
pp. 22
Author(s):  
Pablo Díaz ◽  
David Laroze ◽  
Boris Malomed
Keyword(s):  
Equations Of Motion ◽  
Mean Field ◽  
Three Dimensional ◽  
Field Approximation ◽  
Matter Wave ◽  
Mean Field Approximation ◽  
Degenerate Gases ◽  
Dynamical Regimes ◽  
Low Dimensional ◽  
Good Agreement

We present a summary of some recent theoretical results for matter-wave patterns in Fermi and Bose–Fermi degenerate gases, obtained in the framework of the quasi-mean-field approximation. We perform a dimensional reduction from the three-dimensional (3D) equations of motion to 2D and 1D effective equations. In both cases, comparison of the low-dimensional reductions to the full model is performed, showing very good agreement for ground-state solutions. Some complex dynamical regimes are reported too for the corresponding 1D systems.

Vibration of a Rotating Asymmetric Shaft Supported in Asymmetric Bearings

1968 ◽  
Vol 10 (3) ◽  
pp. 252-261 ◽  
Author(s):  
H. F. Black ◽  
A. J. McTernan
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Forced Vibrations ◽  
Variation Method ◽  
Approximate Theory ◽  
Cross Sectional ◽  
Mass Unbalance ◽  
The Mean ◽  
Theoretical Results ◽  
Good Agreement

The parametrically excited vibrations of this system with assumed small asymmetry of the shaft cross-section are discussed in terms of the motion of a symmetric shaft having the mean cross-sectional flexibility, and the equations of motion are solved by the approximate perturbation-variation method of Hsu. Both features yield a more lucid appreciation of the motions expected than previous treatments: in particular, simpler explicit expressions for unstable bounds are given and forced vibrations due to mass unbalance are discussed with greater facility. The practically important case of nearly coincident natural frequencies is examined. The theoretical results are compared with analogue computation: good agreement with the approximate theory is found even for quite large shaft asymmetry.

Dynamic Analysis of the Ultrasonic Machining Process

1996 ◽  
Vol 118 (3) ◽  
pp. 376-381 ◽  
Author(s):  
Z. Y. Wang ◽  
K. P. Rajurkar
Keyword(s):  
Dynamic Analysis ◽  
Material Removal ◽  
Removal Rate ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dynamic Contact ◽  
Machining Process ◽  
Ultrasonic Machining ◽  
Factors Affecting ◽  
Good Agreement

This paper presents a dynamic analysis of the ultrasonic machining process based on impact mechanics. Equations representing the dynamic contact force and stresses caused by the impinging of abrasive grits on the work, are obtained by solving the three-dimensional equations of motion. The factors affecting the material removal rate have been studied. It is found that the theoretical estimates obtained from the dynamic model are in good agreement with the experimental results.

Finite Element Modeling of Annular-Like Acoustic Cavities

1985 ◽  
Vol 107 (1) ◽  
pp. 81-85
Author(s):  
Chaw-Hua Kung ◽  
Rajendra Singh
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Pressure Oscillation ◽  
Transient Heat Conduction ◽  
Natural Frequencies And Modes ◽  
Acoustic Cavities ◽  
Eigen Solutions ◽  
Element Technique ◽  
Good Agreement

A finite element technique has been developed to find natural frequencies and modes of undamped three-dimensional acoustic cavities. This method utilizes the analogy between a special form of the discretized transient heat conduction equations and discretized equations of acoustic pressure oscillation. The proposed technique is verified by applying it to several cavities of known theoretical eigen-solutions. Computed results for an acoustic ring, an acoustic disk, and a pure annular cavity match extremely well with exact solutions. In addition, the condensation scheme is investigated and guidelines of selecting acoustic master nodes appropriately are also discussed in the paper. Using the validated finite element method along with suitable condensation, the eigenvalue problem of an annular-like cavity is solved. Since the exact solution for this case is not possible, finite element computations for natural frequencies and modes are compared with the measured results obtained using an acoustic modal analysis experimental technique; again very good agreement has been found.

Closed-Form Primitives for Generating Volume Preserving Deformations

1993 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Closed Form ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Physical Systems ◽  
Mechanics Of Materials ◽  
Time Simulation ◽  
Infinite Variety ◽  
Volume Preserving ◽  
Three Dimensional Space

Abstract In this paper, methods for generating closed-form expressions for locally volume preserving deformations of general volumes in three dimensional space are introduced. These methods potentially have applications to computer aided geometric design, the mechanics of materials, and realistic real-time simulation and animation of physical processes. In mechanics, volume preserving deformations are intimately related to the conservation of mass. The importance of this fact manifests itself in design, and in the realistic simulation of many physical systems. Whereas volume preservation is generally written as a constraint on equations of motion in continuum mechanics, this paper develops a set of physically meaningful basic deformations which are intrinsically volume preserving. By repeated application of these primitives, an infinite variety of deformations can be written in closed form.

Modal Analysis of Ballooning Strings With Small Sag

1999 ◽  
Author(s):  
Rongjun Fan ◽  
Sushil K. Singh ◽  
Christopher D. Rahn
Keyword(s):  
Steady State ◽  
High Speed ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Theoretical Predictions ◽  
Nonlinear Equations Of Motion

Abstract During the manufacture and transport of textile products, yarns are rotated at high speed and form balloons. The dynamic response of the balloon to varying rotation speed, boundary excitation, and disturbance forces governs the quality of the associated process. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three dimensional nonlinear equations of motion are simplified via small steady state displacement (sag) and vibration assumptions. Axial vibration is assumed to propagate instantaneously or in a quasistatic manner. Galerkin’s method is used to calculate the mode shapes and natural frequencies of the linearized equations. Experimental measurements of the steady state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

scholarly journals Vibration Analysis of a Tire in Ground Contact under Varied Conditions

2017 ◽  
Vol 47 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Murat Karakus ◽  
Aydin Cavus ◽  
Mehmet Colakoglu
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Concrete Block ◽  
Ground Contact ◽  
Tire Model ◽  
Inflation Pressure ◽  
Monitoring Method ◽  
The Impact ◽  
Good Agreement

Abstract The effect of three different factors, which are inflation pressure, vertical load and coefficient of friction on the natural frequencies of a tire (175/70 R13) has been studied. A three dimensional tire model is constructed, using four different material properties and parts in the tire. Mechanical properties of the composite parts are evaluated. After investigating the free vibration, contact analysis is carried out. A concrete block and the tire are modelled together, using three different coefficients of friction. Experiments are run under certain conditions to check the accuracy of the numerical model. The natural frequencies are measured to describe free vibration and vibration of the tire contacted by ground, using a damping monitoring method. It is seen, that experimental and numerical results are in good agreement. On the other hand, investigating the impact of three different factors together is quite difficult on the natural frequencies. When some of these factors are assumed to be constant and the variables are taken one by one, it is easier to assess the effects.

Vibration Analysis of a Railway Carbody Model as a Non-Circular Cylindrical Shell

2007 ◽  
Author(s):  
Yukinori Kobayashi ◽  
Kotaro Ishiguri ◽  
Takahiro Tomioka ◽  
Yohei Hoshino
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Elastic Vibration ◽  
Mode Shapes ◽  
Simply Supported ◽  
Vibration Problems ◽  
Good Agreement

Railway carbody is modeled as a non-circular cylindrical shell with simply-supported ends in this paper. The shell model doesn’t have end plates of the carbody and other equipments attached to actual carbody are neglected. We have applied the transfer matrix method (TMM) to the analysis of three-dimensional elastic vibration problems on the carbody. We also made a 1/12 size carbody model for experimental studies to verify the validity of the numerical simulation. The model has end plates and was placed on soft sponge at both ends of the model to emulate the freely-support. The modal analysis was applied to the experimental model, and natural frequencies and mode shapes of vibration were measured. Comparing the results by TMM and the experiment, natural frequencies and mode shapes of vibration for lower modes show good agreement each other in spite of differences of boundary conditions.

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