Effect of Forcing Terms and General Characteristics of Torsional Vibrations of Marine Engine Systems with Variable Inertia

1974 ◽  
Vol 18 (02) ◽  
pp. 131-138
Author(s):  
W. D. Carnegie ◽  
M. S. Pasricha
Keyword(s):  
Equations Of Motion ◽  
Mean Value ◽  
Wave Form ◽  
Actual System ◽  
Computer Methods ◽  
Reciprocating Engine ◽  
Complex Wave ◽  
Wave Forms ◽  
Crankshaft Rotation ◽  
Engine Systems

The torsional vibration phenomenon in the running gear of reciprocating engine systems is usually dealt with by considering a series of constant inertias connected by sections of massless shafting. Such a simplified model does not reproduce the exact dynamic characteristics of the actual system. In recent years several cases of marine crankshaft failures have been attributed to the phenomenon of secondary resonance, which is explained by the fact that the effective inertia of each slider crankmechanism varies about a mean value in relation to the position of the crank. When the variableinertia effect is allowed for, the equations of motion taking into account the effect are nonlinear. Assuming small displacements, the equations can be linearized to predict important characteristics of the motion. The motions in the form of complex wave forms are studied at different speeds of engine rotation and some of the wave form solutions are analyzed in the range of present investigations. Computer methods making use of numerical analysis processes, namely, the modifiedEuler's equations and the Runge-Kutta constants, have been applied in the investigations. A study of the effect on the motion of the system due to variation of inertia ratio is carried out at a particular speed of the crankshaft rotation; also investigated are the variations in the motions due to the action of external excitations with respect to changes in phase angle and inertia ratio. General comments on Draminsky's work in the light of the present investigations are included.

scholarly journals The foreshock activity of the 1971 San Fernando earthquake, California

1978 ◽  
Vol 68 (5) ◽  
pp. 1265-1279
Author(s):  
Mizuho Ishida ◽  
Hiroo Kanamori
Keyword(s):  
Small Area ◽  
Main Shock ◽  
Source Region ◽  
Structural Heterogeneity ◽  
Propagation Path ◽  
Wave Form ◽  
Epicentral Area ◽  
Complex Wave ◽  
Wave Forms ◽  
San Fernando

abstract All of the earthquakes which occurred in the epicentral area of the 1971 San Fernando earthquake during the period from 1960 to 1970 were relocated by using the master-event method. Five events from 1969 to 1970 are located within a small area around the main shock epicenter. This cluster of activity is clearly separated spatially from the activity in the surrounding area, so these five events are considered foreshocks. The wave forms of these foreshocks recorded at Pasadena are, without exception, very complex, yet they are remarkably similar from event to event. The events which occurred in the same area prior to 1969 have less complex wave forms with a greater variation among them. The complexity is most likely the effect of the propagation path. A well located aftershock which occurred in the immediate vicinity of the main shock of the San Fernando earthquake has a wave form similar to that of the foreshocks, which suggests that the foreshocks are also located very close to the main shock. This complexity is probably caused by a structural heterogeneity in the fault zone near the hypocenter. The seismic rays from the foreshocks in the inferred heterogeneous zone are interpreted as multiple-reflected near the source region which yielded the complex wave form. The mechanisms of the five foreshocks are similar to each other but different from either the main shock or the aftershocks, suggesting that the foreshocks originated from a small area of stress concentration where the stress field is locally distorted from the regional field. The number of small events with S-P times between 3.8 to 6 sec recorded at Mt. Wilson each month suggests only a slight increase in activity of small earthquakes near the epicentral area during the 2-month period immediately before the main shock. However, because of our inability to locate these events, the evidence is not definitive. Since the change in the wave forms is definite the present result suggests that detailed analyses of wave forms, spectra, and mechanism can provide a powerful diagnostic method for identifying a foreshock sequence.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

Elastic displacements in the near-field of a propagating fault

1969 ◽  
Vol 59 (2) ◽  
pp. 865-908
Author(s):  
N. A. Haskell
Keyword(s):  
Fault Plane ◽  
Near Field ◽  
Strong Motion ◽  
Dislocation Motion ◽  
Displacement Discontinuity ◽  
Wave Form ◽  
Strong Motion Station ◽  
Ramp Function ◽  
Wave Forms ◽  
Parkfield Earthquake

abstract Displacement, particle velocity, and acceleration wave forms in the near field of a propagating fault have been computed by numerical integration of the Green's function integrals for an infinite medium. The displacement discontinuity (dislocation) on the fault plane is assumed to have the form of a unilaterally propagating finite ramp function in time. The calculated wave forms in the vicinity of the fault plane are quite similar to those observed at the strong motion station nearest the fault plane at the Parkfield earthquake. The comparison suggests that the propagating ramp time function is roughly representative of the main features of the dislocation motion on the fault plane, but that the actual motion has somewhat more high frequency complexity. Calculated amplitudes indicate that the average final dislocation on the fault at the Parkfield earthquake was more than an order of magnitude greater than the offsets observed on the visible surface trace. Computer generated wave form plots are presented for a variety of locations with respect to the fault plane and for two different assumptions on the relation between fault length and ramp function duration.

Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2020 ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa Maria Berruti
Keyword(s):  
Parametric Excitation ◽  
Rotational Speed ◽  
Input Parameter ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Mean Value ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Jeffcott Rotor

Abstract Rolling bearings are still widely used in aeroengines. Whenever rotors are modeled, rolling bearing components are typically modeled using springs. In simpler models, this spring is considered to have a constant mean value. However, the rolling bearing stiffness changes with time due to the positions of the balls with respect to the load on the bearing, thus giving rise to an internal excitation known as Parametric Excitation. Due to this parametric excitation, the rotor-bearings system may become unstable for specific combinations of boundary conditions (e.g. rotational speed) and system characteristics (rotor flexibility etc.). Being able to identify these instability regions at a glance is an important tool for the designer, as it allows to discard since the early design stages those configurations which may lead to catastrophic failures. In this paper, a Jeffcott rotor supported and excited by such rolling bearings is used as a demonstrator. In the first step, the expression for the time–varying stiffness of the bearings is analytically derived by applying the Hertzian Contact Theory. Then, the equations of motion of the complete system are provided. In this study, the Harmonic Balance Method (HBM) is used to as an approximate procedure to draw a stability map, thus dividing the input parameter space, i.e. rotational speed and rotor physical characteristics, into stable and unstable regions.

Some numerical solutions for Lamb's problem

1974 ◽  
Vol 64 (2) ◽  
pp. 473-491
Author(s):  
Harold M. Mooney
Keyword(s):  
Rayleigh Wave ◽  
Poisson’S Ratio ◽  
Pulse Width ◽  
Numerical Solutions ◽  
Pulse Height ◽  
P Wave ◽  
Poisson's Ratio ◽  
Wave Form ◽  
Lamb’S Problem ◽  
Wave Forms

abstract We consider a version of Lamb's Problem in which a vertical time-dependent point force acts on the surface of a uniform half-space. The resulting surface disturbance is computed as vertical and horizontal components of displacement, particle velocity, acceleration, and strain. The goal is to provide numerical solutions appropriate to a comparison with observed wave forms produced by impacts onto granite and onto soil. Solutions for step- and delta-function sources are not physically realistic but represent limiting cases. They show a clear P arrival (larger on horizontal than vertical components) and an obscure S arrival. The Rayleigh pulse includes a singularity at the theoretical arrival time. All of the energy buildup appears on the vertical components and all of the energy decay, on the horizontal components. The effects of Poisson's ratio upon vertical displacements for a step-function source are shown. For fixed shear velocity, an increase of Poisson's ratio produces a P pulse which is larger, faster, and more gradually emergent, an S pulse with more clear-cut beginning, and a much narrower Rayleigh pulse. For a source-time function given by cos2(πt/T), −T/2 ≦ T/2, a × 10 reduction in pulse width at fixed pulse height yields an increase in P and Rayleigh-wave amplitudes by factors of 1, 10, and 100 for displacement, velocity and strain, and acceleration, respectively. The observed wave forms appear somewhat oscillatory, with widths proportional to the source pulse width. The Rayleigh pulse appears as emergent positive on vertical components and as sharp negative on horizontal components. We show a theoretical seismic profile for granite, with source pulse width of 10 µsec and detectors at 10, 20, 30, 40, and 50 cm. Pulse amplitude decays as r−1 for P wave and r−12 for Rayleigh wave. Pulse width broadens slightly with distance but the wave form character remains essentially unchanged.

STUDIES OF DISTAL COLONIC MOTILITY IN CHILDREN

PEDIATRICS ◽  
1956 ◽  
Vol 17 (6) ◽  
pp. 820-833
Author(s):  
Murray Davidson ◽  
Marvin H. Sleisenger ◽  
Thomas P. Almy ◽  
Samuel Z. Levine
Keyword(s):  
Ulcerative Colitis ◽  
Bowel Movement ◽  
Colonic Motility ◽  
Distal Colon ◽  
Wave Form ◽  
Spontaneous Bowel Movement ◽  
Normal Individuals ◽  
Iced Water ◽  
Wave Forms

A characteristic propulsive wave, previously reported in adults with ulcerative colitis, has been found in infants with acute diarrhea but not in children with ulcerative colitis. The reasons for this are discussed. The induction of propulsive wave forms in normal individuals by administration of magnesium sulfate orally is described and attention is called to its application to therapeutic studies. The relation of this wave form to propulsion of fecal contents and defecation and its role in the production of abdominal discomfort are considered. Observed variations in the responses of individual children to subcutaneous injection of Mecholyl®, to oral administration of iced water, and to rectal distention may explain innate differences in susceptibility to the development of colonic symptoms in different children. A classification of wave forms from the distal colon based on current concepts of their probable physiologic significance is offered. A tracing from the distal colon in a child having a spontaneous bowel movement is presented and commented on.

Bioelectric Regulation of Tentacle Movement in a Dinoflagellate

1967 ◽  
Vol 47 (3) ◽  
pp. 433-446
Author(s):  
ROGER ECKERT ◽  
TAKAO SIBAOKA
Keyword(s):  
Temporal Relationship ◽  
Sea Water ◽  
Outward Current ◽  
Wave Form ◽  
Applied Current ◽  
Inward Current ◽  
Wave Forms ◽  
Noctiluca Miliaris ◽  
Spike Wave ◽  
Peripheral Cytoplasm

1. Recurring extensions and flexions of the food-gathering tentacle of Noctiluca miliaris occur spontaneously. Identical movements can be evoked by appropriate electrical stimulation. 2. Spontaneous recurring potential wave forms (TRPs) were recorded from the vacuole of the luminescent form of Noctiluca during movements of the tentacle. The basic TRP wave form consists of a characteristic negative-going spike which arises at -20 to -30 mV. from the slowly redeveloping negativity of a pre-spike depolarization, and is followed by a quasi-stable post-spike d.c. level of relative vacuolar negativity (-45 to -60 mV.). 3. The TRP complex, similar in shape to that which occurs spontaneously, follows an intracellularly applied current pulse of either polarity if the vacuolar potential is at the post-spike level. The duration of the evoked pre-spike wave is related to the current intensity and duration. During the pre-spike state outward current is ineffective, although a TR spike occurs in response to inward current. 4. The TRP is distinct in its behaviour and wave form from the flash-triggering potential, which can be evoked in the same cell, even though both exhibit all-or-none spikes. 5. Simultaneous recordings of intracellular potentials and movements of the tentacle showed a consistent temporal relationship between potential changes and subsequent movement. Extension of the tentacle begins 1-2 sec. after the spike and flexion begins within 1 sec. after beginning of the pre-spike wave. 6. Tentacle movement ceased in Ca-free sea water even though the cyclic potential changes continued normally. 7. Electron micrographs of the tentacle showed longitudinal aggregations of microtubules near the outer surface of the peripheral cytoplasm. It is proposed that contraction of these microtubules is the immediate cause of tentacle movements.

Uterine work in parturition

1976 ◽  
Vol 41 (3) ◽  
pp. 316-322 ◽  
Author(s):  
T. J. Kriewall
Keyword(s):  
Viscoelastic Model ◽  
Geometrical Model ◽  
Clinical Findings ◽  
Cervical Dilatation ◽  
Wave Form ◽  
Intrauterine Pressure ◽  
Wave Forms ◽  
Internal Volume ◽  
Synergistic Relationship ◽  
Incremental Volume

This paper presents a theoretical analysis relating work expended by the uterus to the synergistic relationship between intrauterine pressure (IUP) and cervical dilatation (CD). By utilizing a geometrical model for the fetal presenting part which is assumed to be in contact with the cervix, the changes in internal volume of the uterus with each contraction can be shown to be functionally related to cervical dilatation. Thus work, expressed in terms of foot-pounds, can be calculated using the integral of pressure times incremental volume. By simulating intrauterine pressure and cervical dilatation with continuous analytical wave forms, the alterations required in uterine work to dilate the cervix are calculated for various wave-form aberrations which are seen in clinical situations. The wave-form aberrations are applied to an elastic cervical model as well as a viscoelastic model. Using the principles of thermodynamics the areas of the fetouterine complex which absorb the work generated by the contractions are defined. It is shown that the efficiency of the contractions to dilate the cervix can be calculated by evaluating the work expended in these various areas of energy absorption. The purpose of this paper is to present the theory upon which clinical findings in obstetrics can be based so that conclusions drawn will be technically sound.

scholarly journals Quaternionic wave function

2019 ◽  
Vol 34 (02) ◽  
pp. 1950001 ◽  
Author(s):  
Pavel A. Bolokhov
Keyword(s):  
Wave Function ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Variational Calculus ◽  
Nonrelativistic Limit ◽  
Natural Choice ◽  
Complex Wave ◽  
Spinor Formalism ◽  
Function Language

We argue that quaternions form a natural language for the description of quantum-mechanical wave functions with spin. We use the quaternionic spinor formalism which is in one-to-one correspondence with the usual spinor language. No unphysical degrees of freedom are admitted, in contrast to the majority of literature on quaternions. In this paper, we first build a Dirac Lagrangian in the quaternionic form, derive the Dirac equation and take the nonrelativistic limit to find the Schrödinger’s equation. We show that the quaternionic formalism is a natural choice to start with, while in the transition to the noninteracting nonrelativistic limit, the quaternionic description effectively reduces to the regular complex wave function language. We provide an easy-to-use grammar for switching between the ordinary spinor language and the description in terms of quaternions. As an illustration of the broader range of the formalism, we also derive the Maxwell’s equation from the quaternionic Lagrangian of Quantum Electrodynamics. In order to derive the equations of motion, we develop the variational calculus appropriate for this formalism.

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