Showing papers on "Inertia published in 1981"

Energy flow in the cochlea

Abstract: With moderate acoustic stimuli, measurements of basilar-membrane vibration (especially, those using a Mossbauer source attached to the membrane) demonstrate: a high degree of asymmetry, in that the response to a pure tone falls extremely sharply above the characteristic frequency, although much more gradually below it;a substantial phase-lag in that response, and one which increases monotonically up to the characteristic frequency;a response to a ‘click’ in the form of a delayed ‘ringing’ oscillation at the characteristic frequency, which persists for around 20 cycles. This paper uses energy-flow considerations to identify which features in a mathematical model of cochlear mechanics are necessary if it is to reproduce these experimental findings.The response (iii) demands a travelling-wave model which incorporates an only lightly damped resonance. Admittedly, waveguide systems including resonance are described in classical applied physics. However, a classical waveguide resonance reflects a travelling wave, thus converting it into a standing wave devoid of the substantial phase-lag (ii); and produces a low-frequency cutoff instead of the high-frequency cutoff (i).By contrast, another general type of travelling-wave system with resonance has become known more recently; initially, in a quite different context (physics of the atmosphere). This is described as critical-layer resonance, or else (because the resonance absorbs energy) critical-layer absorption. It yields a high-frequency cutoff; but, above all, it is characterized by the properties of the energy flow velocity. This falls to zero very steeply as the point of resonance is approached; so that wave energy flow is retarded drastically, giving any light damping which is present an unlimited time in which to dissipate that energy.Existing mathematical models of cochlear mechanics, whether using one-, two- or three-dimensional representations of cochlear geometry, are analysed from this standpoint. All are found to have been successful (if only light damping is incorporated, as (iii) requires) when and only when they incorporate critical-layer absorption. This resolves the paradox of why certain grossly unrealistic one-dimensional models can give a good prediction of cochlear response; it is because they incorporate the one essential feature of critical-layer absorption.At any point in a physical system, the high-frequency limit of energy flow velocity is the slope of the graph of frequency against wavenumberIn any travelling wave, the wavenumber is the rate of change of phase with distance; for example, it is 2π/λ in a sine wave of length λ. at that point. In the cochlea, this is a good approximation at frequencies above about 1 kHz; and, even at much lower frequencies, remains good for wavenumbers above about 0·2 mm−1 (which excludes only a relatively unimportant region near the base).Frequency of vibration at any point can vary with wavenumber either because stiffness or inertia varies with wavenumber. However, we find that models incorporating a wavenumber-dependent membrane stiffness must be abandoned because they fail to give critical-layer absorption; this is why their predictions (when realistically light damping is used) have been unsuccessful. Similarly, models neglecting the inertia of the cochlear partition must be rejected.One-dimensional modelling becomes physically unrealistic for wavenumbers above about 0.7 mni-1, and the error increases with wavenumber. The main trouble is that a one-dimensional theory makes the effective inertia ‘flatten out’ to its limiting value (inertia of the cochlear partition alone) too rapidly as wavenumber increases. Fortunately, a two-dimensional, or even a three-dimensional, model can readily be used to calculate a more realistic, and significantly more gradual, ‘flattening out’ of this inertia. All of the models give a fair representation of the experimental data, because they all predict critical-layer absorption. However, the more realistic two- or three-dimensional models must be preferred. These retard the wave energy flow still more, thus facilitating its absorption by even a very modest level of damping. The paper indicates many other features of these models.The analysis described above is preceded by a discussion of waves generated a t the oval window. They necessarily include: the already-mentioned travelling wave, or ‘slow wave’, in which the speed of energy flow falls from around 100 m s−l at the base to zero at the position of resonance;a pure sound wave, or ‘fast wave’, travelling a t 1400 m s-1, with reflection at the apex which makes i t into a standing wave. Half of the rate of working of the stapes footplate against the oval window is communicated as an energy flow a t this much higher speed down the scala vestibuli, across the cochlear partition and back up the scala tympani to the round window, whence it becomes part of the slow general apical progress of the travelling wave; a progress which, as described above, comes to a halt altogether just in front of the position of resonance.Mathematical detail is avoided in the discussion of cochlear energy flow in the main part of the paper (§ 1–10), but a variety of relevant mathematical analysis is given in appendices A–E. These include, also, new comments about the functions of the tunnel of Corti (appendix A) and the helicotrema (appendix C).

Effects of inertia in forced corner flows

Abstract: When viscous fluid is contained in the corner between two planes intersecting at an 0 angle a, a flow may be ‘forced’ either by relative motion of the two planes keeping a constant (the ‘paint-scraper ’ problem- Taylor 1960) or by relative rotation of the planes about their line of intersection (the hinged-plate problem -Moffatt 1964). In either case, a similarity solution is available describing the flow sufficiently near the corner, where inertia forces are negligible. In this paper, we investigate the effects of inertia forces, by constructing regular perturbation series for the stream function, of which the leading term is the known similarity solution. The first-order inertial effect is obtained analytically, and, for the Taylor problem with a = Qn, 25 terms of the perturbation series for the wall stress are generated numerically. Analysis of the coefficients suggests that the radius of convergence of the series is given by r 1 U( /v z 9.1, where r is distance from the corner, U is the relative speed of the planes, and v is the kinematic viscosity of the fluid. For the hinged-plate problem, discussed in 5 5, the unsteadiness of the flow contributes to an inertial effect which is explicitly incorporated in the analysis. For both problems, streamline plots are presented which indicate the first influence of inertia forces at distances from the corner at which these become significant.

Natural Frequencies of Curved Girders

Abstract: A general finite element displacement formulation is presented to determine the natural frequencies of spatial thin-walled curved girders including the warping contribution. Also included are the rotatory inertia effects with respect to flexure and torsion, and the effects of antisymmetry of cross section (found to be significant). The stiffness and inertia properties of the finite element are obtained using the solutions of homogeneous differential equations governing the static problem as deformation modes. The obtained element relationships were programmed for use in digital computers, and a few example problems were analyzed. Some charts are given to expedite the determination of natural frequencies of horizontally curved girders.

Dynamic Tracking of Angular Misalignment in Liquid-Lubricated End-Face Seals

Abstract: End-face seals sometimes fail because the flexibly mounted face is unable to track the inevitable angular misalignment (relative to the shaft axis) of the fixed face, resulting in rubbing contact. It is important, then, that the critical amount of misalignment just to cause contact in a fully liquid-lubricated seal should be known so allowances can be made in the manufacturing and assembly tolerances. An analysis of dynamic tracking is presented for both common end-face seal arrangements. Expressions for critical misalignment are derived in terms of inertia, elastomer stiffness and damping, and fluid-film hydrostatic and hydrodynamic moment effects in the diametral tilt mode. Fluid-film effects are found to promote tracking, elastomer effects to resist. Tilt inertia resists tracking only for the flexibly mounted stator arrangement. However, as the inertia term is generally insignificant, this arrangement is preferred because, in practice, it is much easier to achieve good alignment of a rotating face fixe...

On the dynamic behavior of the wobblestone

Abstract: The wobblestone is a generalized form of a top with distinct inertias and a nonspherical surface at the point of contact to the horizontal plane on which it moves. Some wobble-stones exhibit a curious property of allowing steady rotation about the vertical principal inertia axis only when rotated in one direction, while other wobblestones exhibit repeated reversals of the direction of rotation after being spun. Here, nonlinear equations governing the motion of a wobblestone are derived assuming no slippage at the point of contact to the supporting rigid plane, which corresponds to a conservative model. The equations are formulated in a manner suitable for numerical integration. The major observed properties of the motion of these asymmetrical tops are demonstrated in numerical simulations. The results lead to a better understanding of their complex and fundamentally nonlinear motion.

Nonlocal Continuum Theory of Liquid Crystals

Abstract: A nonlocal continuum theory of liquid crystals is constructed to explain and predict the physical behavior of liquid crystals under long range intermolecular forces Balance laws consist of conservation of mass and mocroinertia, balance of momenta and energy. Constitutive equations are given for the equibilibirium and non-equilibirium parts of the stress, couple strees, free energy, entropy an nonlocal body force and couple. Thermodynamic restrinctions and material frame-indifference are studied. The theory is valid for liquid crystals having arbitrary shapes (inertia), Passage is made to the thread-like molecuels and to local theory. Applications are considered to two-dimensional problmes, steady, plane shear flows and disperison of twist waves.

Stabilization due to gyroscopic coupling in dual-spin satellites subject to gravitational torques

Abstract: The stability of attitude equilibria relative to gravitational torques for a rigid satellite in a circular orbit has been divided into three inertia regions, the Lagrange region of assured Liapunov stability, the Beletskii-Delp region which is often described as stabilized due to gyroscopic coupling, and an assured instability region. The generalization of these regions to the case of dual-spin or gyrostat satellites whose internal spin momentum is along a principal axis is treated here. The stability boundaries are obtained for all possible equilibrium orientations for such vehicles, and the variations of these boundaries corresponding to changes in the internal momentum magnitude, or to aligning the momentum with a different principal axis, are determined.

Composite inertia latch for vehicle seat back

Abstract: A passenger car seat back inertia latch providing gravity actuated latch release and deceleration responsive inertia latch retention characterized by a compound resolution of predominant opposing gravity and deceleration forces to provide more sensitive and dependable latch retention at a predetermined minimum emergency vehicle deceleration as well as minimum weight to unlock the latch when the vehicle is stationary over a wider range of seat back adjustment and vehicle inclination than is possible with the conventional simple one-piece inertia latch wherein horizontal and vertical coordinates of the center of gravity relative to a latch pivot are solely depended upon to produce respective opposite gravity actuated release and inertia actuated locking moments on the latch element.

Linearized Solution to Inlet Equation with Inertia

Abstract: The present note describes a solution technique using a linearization technique of equation friction-work over the tidal cycle in a nonlinear approach to form of bay tide.

Non-isothermal developing flow of a generalised power-law fluid in a tapered tube

Abstract: A numerical solution of developing non-isothermal flow of a generalised power-law fluid in a slightly converging circular tube is given. Results are presented in graphical from. They indicate that, inertia forces and kinetic energy, which increase along the cone, are factors which markedly affect the development of velocity and stress distribution and demonstrate the effect of the parameters on the process.

On the efficiency of thermal engines with power output: Consideration of inertial effects

Abstract: We consider an idealized heat engine with nonzero power output, which receives heat from and rejects heat to reservoirs by linear heat conduction and produces work in the surroundings by providing kinetic and potential energy to a mass in the gravitational field. The working fluid of the engine is in internal equilibrium. For this engine we write the equations of motion including inertial effects, i.e., we include Newton’s equation for conservation of momentum. We define variables, controls, parameters, and boundary conditions in these equations in connection with the optimization of some performance (cost) functional. The conceptual neglect of inertial effects, as has been done previously, is shown to change the set of variables and controls, thus changing the optimization problem. Furthermore, the neglect of these terms leads to requirements of energy balance which must be incorporated as boundary conditions. We do not solve any optimization problem explicitely but show that appropriate inclusion of inertial effects in such engines precludes in the optimal cycle the existence of isothermal branches which are not preceded and followed by acceleration and deceleration branches.

Finite Element Analysis of Dynamic Crack Propagation

Abstract: : A finite element analysis of stationary and propagating cracks in the presence of inertia forces is presented. An extension of the J-integral approach is employed. To model a propagating crack, a conceptually simple yet effective technique has been developed. The new crack propagation scheme eliminates the difficulties associated with the use of moving singular elements. (Author)

On the efficiency of thermal engines with power output: Harmonically driven engines

Abstract: In a previous article we defined and studied a model of a heat engine with the purpose of emphasizing the role of inertial effects, particularly their importance in relation to optimization problems. Here we pursue our argument on this issue by comparing the performance of models of heat engines harmonically driven around a state of equilibrium. For the first model, with inertia, we define the model, calculate its nonlinear response with emphasis on the linear approximation, and discuss the issues related to the coupling of the thermal and mechanical driving forces. We study the influence of increasing values of the mechanical friction coefficient, and show that when this coefficient is small the work output displays subharmonic resonances that disappear when the friction coefficient increases. In the second model, without inertial effects, no such resonances appear as expected, since these are due only to the inertial terms.

Device for balancing rotation bodies

Abstract: A device for balancing rotating bodies comprising two inertia masses, which are disposed in a cylindrical housing which can be connected to the body to be balanced such as a grinding disc, and which are mutually connected by means of a self-locking worm gear. The inertia masses may be displaced by means of one single switch shaft having four positions in which the two inertia masses can be displaced either countercurrently in both directions or concurrently. When braking is effected by means of a brake knob disposed on the switch shaft, displacement occurs until the indicated imbalance lies within the low, desirable range. The worm shaft and the worm wheel contained in the inertia masses are in engagement with the worm gear of the switch shaft and the housing. An arrangement of this type permits, on the one hand, a simple mechanical construction and operation, and, on the other hand, a large inertia mass, relative to the volume available, with a wide range of adjustment.

Locking device reacting to inertia forces for retractors

Abstract: A locking mechanism for seat belt retractors responding to movement or accelerations of a vehicle, including a freely movable inertia body (2, 24, 25) and a pivotable pawl (3), in which a mechanism (31-35) on the pawl (3) can engage the inertia body and movement of the inertia body is limited by a means (1, 12, 13) arranged next to the inertia body.

From kinematical geodesy to inertial positioning

Abstract: WhenH. Moritz (1967, 1971) studied “kinematical geodesy” for the purpose of separation of gravitation and inertia, especially within combined accelerometer-gradiometer systems, it was hard to believe that within five years time inertial survey systems would be available, exactly operating according to his theoretical design. Here, we attempt to give a geodetic introduction into the fundamental equation of inertial positioning materialized by inertial survey systems with emphasis on a careful error model, including 36 parameters of type time interval, initial positions, initial gravity, varying acceleration, varying gravity gradients, accelerometer bias, accelerometer random uncertainty, accelerometer non-orthogonality, initial misalignment angles, accelerometer scale factor uncertainty. The notion of “multipoint” boundary value problem and initial value problem of inertial positioning is reviwed. So-called “post-mission” adjustment techniques for inertial surveys are discussed.

Vehicle braking indicator operated independently of brake pedal - using inertia mass to operate warning switches for rear lights etc.

Abstract: The braking indicator uses an inertia switch comprising an inertia mass (3) movable along a guide path (13) parallel to the direction of movement of the vehicle against a return spring (5). At least one warning switch (6) is positioned along the guide path, for actuation by the inertia mass to operate different signalling devices, e.g. the vehicle rear brake lights. Pref. the guide path is defined by a central rod along which the inertia mass slides, or by a hollow cylinder (13), with the inertia mass (3) in the form of a piston within the cylinder (13). The latter may be of insulating material with contact rail sections (6) for the warning switches embedded in its internal surface.

Friction welder of inertia system

Abstract: PURPOSE:To weld the welded member at desired position, by providing pressing mechanism between the eccentric shaft and inertia body, in the inertia type friction welder. CONSTITUTION:In conventional inertia system friction welding, when the eccentric shaft is moved to the center shaft, the eccentric shaft once moved to the center position is shifted from the position and the welded member can not be welded at the desired correct position relation. To prevent this, the pressing mechanism is provided between the eccentric shaft 5 and the inertia body. The pressing mechanism consists of the slide plate 15a, pressing body 15 and compression spring 15b. The ring shape slide plate 15a is in contact with the flat slide plate 15d formed under the eccentric shaft 5 and fixed to the pressing body 15. The pressing body 15 has some rod shape projections under it and is protruded toward the main shaft 4, and coupled to the hole of inertia body 14. The compression spring 15b surrounds the said projections and is located between the pressing body and the inertia body 14. Thus, relative rotation is produced between the eccentric shaft 5 and inertia body 14, enabling to deliver the specified torque.

Effects of viscosity on water waves

Abstract: The paper deals with the behaviour of a viscous liquid whose flow preserves the structure of the material columns. A balance law for energy is established which accounts for Navier-Stokes dissipation; on appealing to the invariance of such a low under rigid motions, balance equations for mass and linear momentum are derived. It is an outstanding consequence of the theory that the simultaneous occurence of viscosity and inertia terms makes long gravity waves be governed by the combined Korteweg-de Vries and Burgers equation.

Method of making rubber/viscous torsional vibration dampers

Abstract: In tuned rubber/viscous torsional vibration damper assemblies of the kind having supporting rotor disk means mounting an inertia mass coupled to the disk means by viscous damping medium and elastic tuning spring, spacing and sealing rubber rings are produced by providing a low melting point metal barrier in the assembly between rubber ring accommodating grooves and the viscous damping medium working chamber defined within the inertia mass, the rubber rings molded and vulcanized in situ in said grooves and to the rotor disk and the inertia mass, whereafter the barrier is melted out and the damper completed. The dampers may be provided with rubber spacer and bumper fingers extending from the rubber rings into the working chamber of the damper. The rubber rings may also be keyed to the inertia mass by means of integral lugs extending into socket apertures in the inertia mass. The dampers may be coated with a rubber skin on outside areas, the skin being connected to exposed areas of the rubber rings.

The Problem of Inertia

Abstract: Many modern commentators on inertial phenomena hold (or just assume) that there is no "problem of inertia", on the grounds that either (a) no explanation is needed for such phenomena or (b) the explanation is already at hand. My purpose here is to comment on both views, defending the thesis that the problem is real and still unsolved.

On the motion of a flexible shallow spherical shell in orbit

Abstract: A mathematical model for the motion of a large, flexible shallow spherical shell in a circular orbit is presented. For small elastic displacements and attitude angles the linearized equations for the roll and yaw (out-of-plane) motions completely separate from the pitch (in-plane) and elastic motions. However, the pitch and only the axisymmetric elastic modes are seen to be coupled in the linear range. With the shell's symmetry axis following the local vertical, the structure undergoes a static deformation under the influence of gravity and inertia. Further, the pitch and roll motions are unstable due to the unfavorable moment of inertia distribution. A rigid lightweight dumbbell with heavy tip masses and connected to the shell at its apex by a spring loaded double gimbal joint is proposed to gravitationally stabilize the structure. It is noted that the dumbbell motion can excite only those elastic modes having one nodal diameter. A sensitivity study of the system response characteristics to the key system parameters is carried out.