scholarly journals Longitudinal Strain Pulse Propagation in Wide Rectangular Bars: Part 1—Theoretical Considerations

1963 ◽  
Vol 30 (1) ◽  
pp. 51-60 ◽  
Author(s):  
O. E. Jones ◽  
A. T. Ellis
Keyword(s):  
Elastic Strain ◽  
Longitudinal Strain ◽  
Pulse Propagation ◽  
Equations Of Motion ◽  
Step Function ◽  
Infinite Strip ◽  
Asymptotic Expressions ◽  
Theoretical Considerations ◽  
Strain Pulse ◽  
Function Time

The propagation of a longitudinal elastic strain pulse in a wide rectangular bar is considered on the basis of approximate plane-stress equations of motion. Asymptotic expressions are obtained which, for large distances of travel, describe the pulse propagation in a semi-infinite strip with stress-free lateral edges, subject to the conditions that a uniform normal stress with a step-function time dependence is applied to the end and that the end is laterally constrained. Particular emphasis is given to describing the warping of plane sections during passage of the strain pulse.

scholarly journals Longitudinal Strain Pulse Propagation in Wide Rectangular Bars: Part 2—Experimental Observations and Comparisons With Theory

1963 ◽  
Vol 30 (1) ◽  
pp. 61-69 ◽  
Author(s):  
O. E. Jones ◽  
A. T. Ellis
Keyword(s):  
Plane Stress ◽  
Pulse Propagation ◽  
Step Function ◽  
Pressure Loading ◽  
Stress Theory ◽  
Second Mode ◽  
Fringe Patterns ◽  
Strain Pulse ◽  
Thickness Mode ◽  
Theory And Experiment

The plane-stress theory presented in Part 1 is shown to predict qualitatively the warping of plane sections observed in transient fringe patterns obtained using birefringent coatings and in dynamic photoelastic pictures obtained in other investigations. Measurements using conventional techniques are described in which wide rectangular bars were subjected to a longitudinal step-function pressure loading produced by a shock tube. Comparisons show that the gross features of the experimental records for the head of the pulse are qualitatively predicted by the theory. Both theory and experiment show that short-wavelength, second-mode disturbances arrive very early. Experimentally it is observed that these disturbances are accomplished by thickness-mode activity which cannot be accounted for by the plane-stress theory.

Strain pulse propagation in composite elastic rods

Composites ◽  
1970 ◽  
Vol 1 (3) ◽  
pp. 190
Author(s):  
V.K Varatharajulu ◽  
I Kayek Sabih
Keyword(s):  
Pulse Propagation ◽  
Elastic Rods ◽  
Strain Pulse

Diffraction of a pulse by a resistive half-plane. I. Normal incidence

1960 ◽  
Vol 255 (1283) ◽  
pp. 538-549 ◽  
Keyword(s):  
Time Dependence ◽  
Half Plane ◽  
Wave Diffraction ◽  
Diffraction Problem ◽  
Normal Incidence ◽  
Step Function ◽  
Two Dimensional ◽  
Dynamic Similarity ◽  
Function Time ◽  
Dimensional Wave

The two-dimensional wave diffraction problem, acoustic or electromagnetic, in which a pulse of step-function time dependence is diffracted by a resistive half-plane is solved by assuming dynamic similarity in the solution.

Coherent manipulations of atoms using laser light

2008 ◽  
Vol 58 (3) ◽  
Author(s):  
Bruce Shore
Keyword(s):  
Hilbert Space ◽  
Pulse Propagation ◽  
Laser Light ◽  
Equations Of Motion ◽  
Pulse Sequences ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
Quantum States ◽  
Excitation Energies ◽  
Mathematical Concepts

Coherent manipulations of atoms using laser lightThe internal structure of a particle - an atom or other quantum system in which the excitation energies are discrete - undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes - the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laser-pulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a three-dimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping "dark" states.

Waterhammer in Non-Rigid Pipes: Precursor Waves and Mechanical Damping

1977 ◽  
Vol 19 (6) ◽  
pp. 237-242 ◽  
Author(s):  
D. J. Williams
Keyword(s):  
Elastic Strain ◽  
Longitudinal Strain ◽  
Viscous Damping ◽  
Flexural Waves ◽  
Strain Waves ◽  
Fluid Theory ◽  
Mechanical Damping ◽  
Theory And Experiment

When a pipe can move, waterhammer effects are altered by the existence of precursor waves, i.e. longitudinal elastic strain waves in the pipe walls, modified by the presence of the fluid. Theory and experiment show that precursor waves cannot be ignored, if the effect of longitudinal strain is to be considered; conventional waterhammer theory is thus unsatisfactory. Flexural waves may also occur. It was found experimentally that pipe motion caused mechanical damping of the waterhammer–greater than the viscous damping. Viscoelastic piping also gave rise to strong mechanical damping, even without pipe motion.

scholarly journals An Asymptotic Approach for the Elastodynamic Problem of a Plate under Impact Loading

2010 ◽  
Vol 2010 ◽  
pp. 1-10
Author(s):  
Penelope Michalopoulou ◽  
George A. Papadopoulos
Keyword(s):  
Laplace Transform ◽  
Impact Loading ◽  
Step Function ◽  
Infinite Strip ◽  
Asymptotic Approach ◽  
Heaviside Step Function ◽  
Inertia Effects ◽  
Elastodynamic Problem ◽  
Line Force ◽  
The One

An approach is presented for analyzing the transient elastodynamic problem of a plate under an impact loading. The plate is considered to be in the form of a long strip under plane strain conditions. The loading is taken as a concentrated line force applied normal to the plate surface. It is assumed that this line force is suddenly applied and maintained thereafter (i.e., it is a Heaviside step function of time). Inertia effects are taken into consideration and the problem is treated exactly within the framework of elastodynamic theory. The approach is based on multiple Laplace transforms and on certain asymptotic arguments. In particular, the one-sided Laplace transform is applied to suppress time dependence and the two-sided Laplace transform to suppress the dependence upon a spatial variable (along the extent of the infinite strip). Exact inversions are then followed by invoking the asymptotic Tauber theorem and the Cagniard-deHoop technique. Various extensions of this basic analysis are also discussed.

Experiments on Dispersive Pulse Propagation in Laminated Composites and Comparison With Theory

1969 ◽  
Vol 36 (3) ◽  
pp. 485-490 ◽  
Author(s):  
J. S. Whittier ◽  
J. C. Peck
Keyword(s):  
Pulse Propagation ◽  
Laminated Composites ◽  
Rear Surface ◽  
Step Function ◽  
Surface Velocity ◽  
Flat Plates ◽  
Theoretical Predictions ◽  
Long Time ◽  
Capacitance Gauge ◽  
High Degree

Transient stress-wave experiments on laminated composites are described, and the results are compared with theoretical predictions. The composites are laminated from alternating layers of high and low-modulus material, which cause a high degree of geometric dispersion of waves propagating in the composite. Experiments were conducted in which waves propagated parallel to the laminations. Flat plates were subjected on one face to a uniform pressure with step-function time dependence induced by a gas-dynamic shock wave. Under this loading, the central portion of the specimen initially responds as if it were laterally unbounded. The average velocity over a 3/8-in-dia area of the backface of the plate was measured with a capacitance gauge. The results are in good agreement with theoretical predictions made with a long-time asymptotic approximation called the head-of-the-pulse approximation. The theory isolates the dominant character of the response and predicts timing and amplitude of oscillations in normalized rear surface velocity within a few percent.

On use of equations of motion for two-rotor airship

2011 ◽  
Vol 226 (8) ◽  
pp. 2093-2103
Author(s):  
Wojciech Adamski ◽  
Przemysław Herman
Keyword(s):  
Simulation Model ◽  
Equations Of Motion ◽  
Control Scheme ◽  
Applied Forces ◽  
Theoretical Considerations ◽  
Trajectory Generator ◽  
Derivative Control

In this article, equations of motion for a two-rotor airship are derived. Moreover, the problem of engine applied forces and torques is analysed, and a trajectory generator is described and implemented into a proportional–derivative control scheme. The theoretical considerations are validated by a set of simulation tests. The simulation model takes into account the structure of the drives, namely the two engines placed symmetrically on both sides of the object. The conducted simulations validate the robustness of the controller in the case of unexpected disturbance occurrence.

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