Showing papers on "Rotary inertia published in 1975"

Dynamic Response of Laminated Composite Plates

Abstract: HE classical method of separation of variables combined with the Mindlin-Goodman procedure1 is employed to analyze the dynamic response of an infinitely long simplysupported composite plate under a uniform dynamic pressure, P0, on the upper surface of the plate. Two cases of dynamic pressures are considered; 1) the magnitude of the uniform pressure remains unchanged, and 2) the magnitude of the uniform pressure increases linearly as a function of time and then remains constant. Numerical results for eight layer granite/epoxy and glass/expoxy composites with (0/0/0/ — 0) s and (#/ — 0/0/0)5 stacking sequences are evaluated. Dynamic response characterized in terms of normal displacement, bending stress, interlaminar shear stress, and interlaminar normal stress are evaluated and compared with the corresponding quantities obtained statically (i.e., a dynamic load factor is established). It is observed that the dynamic values are consistently twice the corresponding static values for Case 1, and varies from one to two times the corresponding static values for Case 2. Contents The equations of motion, including transverse shear deformation and rotary inertia, for an infinitely long laminated composite plate under cylindrical bending are given in Ref. 2. The solution to the governing equations in terms of separation of variables in conjunction with the Mindlin-Goodman procedure] is also presented in Ref. 2. In the present paper the interlaminar shear stress TXZ is determined by integrating the equation of motion (1) with respect to z using the condition Txz(±h/2,t) = 0 and the condition of continuity at the interfaces. Once rxz(k) is determined the interlaminar normal stress ozz (k) can also be determined by integrating the equations of motion

Effect of shear deformations and rotary inertia on optimum beam frequencies

Abstract: Accounting for shear deformations and rotary inertia effects, necessary condition for optimum fundamental frequency of a vibrating beam of constant volume and with a given distribution of non-structural mass, is obtained through the calculus of variations. Minimum cross-section of the beam is controlled by the introduction of an inequality constraint. A finite element displacement formulation is then used in an iterativve manner to arrive at the optimum fundamental frequency and the corresponding material distribution for the discretized beam models with various boundary conditions. A comparison is then made with the corresponding results of an Euler beam.

Inertia power system

Abstract: An inertia power system in which the rotational energy stored in a rotating inertia wheel is translated into useful work. The system includes an inertia wheel which is electrically driven. A magnetic clutch is provided for engaging and disengaging the rotating inertia wheel into and out of driving relationships with a transmission assembly through which the rotation of energy of the inertia wheel is translated into useful work, e.g.; to drive a vehicle.

Elastomer and liquid torsional vibration damper

Abstract: A torsional vibration damper having two inertia members. A first inertia member is coupled to a hub by elastomer. A second inertia member is positioned within an annular cavity and is surrounded by a liquid of high viscosity. Under the influence of torsional vibrations relative movement arises between the hub and first inertia member, the hub and the second inertia member, and the first and second inertia members. The latter relative motion inhibits the attainment of resonance by either of the two inertia members.

Natural frequencies of elastically supported orthotropic reactangular plates

Abstract: An expression is derived from which the natural frequencies of a rectangular orthotropic plate, under any combination of simply supported, elastically supported, or clamped boundary conditions, can be obtained. The Mindlin–Timoshenko theory, which includes the effects of transverse shear and rotary inertia, is used to describe the plate motion. The solution is obtained with a previously developed extension of the Galerkin technique. Comparison of results with the limited results of previous investigations is very good. New results are presented for the fundamental frequencies of rectangular and square plates for boundary conditions on all four edges that vary continuously from simply supported to clamped, and for various combinations of length‐to‐thickness ratios and material constants. Additional results are presented for orthotropic plates simply supported and clamped on all four edges.

On local inertia in Cosserat continua

Abstract: A new equation governing local rotational inertia is obtained here for all theories employing the Cosserat continuum with deformable director triad. This equation represents a condition necessary to insure the invariance of the rotational kinetic energy under superposed rigid body motions.

Influence of rotary inertia and shear deformation on acoustic transmission through a plate

Abstract: The reflection and transmission of a harmonic acoustic plane wave from a fluid‐loaded plate is investigated using the Timoshenko–Mindlin plate equation. In contrast to the classical plate theory, the effects of rotary inertia and shear deformation are included in the Timoshenko–Mindlin theory. The usual acoustic coincidence frequency and angle based on the classical theory are shown to depart from the present results based on the Timoshenko–Mindlin theory as the frequency–plate thickness product increases. Furthermore, an additional acoustic coincidence frequency and angle are also noted in the present analysis for large frequency‐plate thickness products. Several numerical results are presented to illustrate the effects of the incident angle, frequency, plate thickness, and damping on the transmission of an incident acoustic plane wave through a steel plate in water.Subject Classification: 20.60; 40.24; 20.30.

Rotational Motion of a Free Body Induced by Mass Redistribution

Abstract: The effects of mass redistribution on the rotational motion of a free body, initially rotating uniformly about its axis of maximum moment of inertia, are studied using a simple three-body model composed of two "control" points masses and a triaxial rigid body. An exact analytical solution for the motion of the original spin axis after redistribution of the masses is developed from the classical solution for the rotational motion of a free triaxial rigid body. Yhis motion in interpreted geometrically using the reciprocal inertia ellipsoid of the redistributed system and the angular momentum integral. Application of simple mass redistribution to the problem of spacecraft attitude control is discussed and results for a particular system are presented. T is a well-known fact1 that for a free, triaxial, rigid body, the condition of uniform rotation about its axis of in- termediate, principal moment of inertia is unstable. This in- stability manifests itself when small disturbances in the angular velocity components about the other principal axes occur; for then, the once-stationary axis of intermediate moment of inertia performs large-angle motions with respect to a nonrotating reference frame. Recently, Beachley and Dicker2 and Beachley,3 have suggested that this characteristic of rigid body rotational motion might be used to advantage to "control" a spinning spacecraft in the sense that predictable large-angle motions of an axis fixed in the spacecraft might be induced by changing the mass distribution of the spacecraft.% A control system based on this idea might be more economical than a mass expulsion system which would rotate the angular momentum vector of the spacecraft. Changes in the mass distribution of the spacecraft may be accomplished by internal motion of control masses. The ef- fects of such internal mass motion on the rotational motion of a free system of bodies have been studied by several authors and a review of some of the work in this area is given by Lorell and Lange,5 who propose an automatic mass-trim system for spinning spacecraft which utilizes movable control masses. The primary purpose of this paper is not to study the effects of internal mass motion on the rotational motion of a free system of bodies, although these effects cannot be ignored en- tirely and will be considered. Our main goal is to obtain an analytical description of the spacecraft's rotational motion af- ter a redistribution of mass has occurred. Such a description has previously been obtained only in a limited way by numerical integration.3 We shall also provide geometrical in- terpretation of the analytical results and consider the use of simple mass redistribution as a means for spacecraft attitude control. In this paper we shall consider a system similar to those discussed in Ref. 3 and employ some results from the classical theory for the rotational motion of a free, triaxial, rigid body.

On non-symmetric vibration of deep spherical sandwich shells

Abstract: This paper deals with the free non-symmetric vibration of deep spherical sandwich shells. The sandwich shell considered herein consists of three layers. A variational technique is utilized to obtain the equations of motion as well as the appropriate boundary conditions. The effects of transverse shear deformation and rotary inertia have been included in this analysis.

On the inertia defect, l-doubling constant and force constant solutions

Abstract: The utility of data on the inertia defect (Δ) in determining the unique and exact solutions of the force constants for planar molecules is discussed. The nature of the force field corresponding to the extremal values of Δvib (0), the accuracy of the force constants obtained from inertia defect and use of approximation methods in deriving reliable values of Δvib (0) for XY2 (C2v ) type molecules have been studied in detail. The calculation of the l-doubling constants using approximation methods and their sensitivity to the force field for XYZ(C∞v ) type molecules are also discussed in addition.

Elastic deformation of the gyro rotor in the relativity gyro experiment

Abstract: The elastic deformation of a spinning sphere is calculated from first principles. Numerical results are quoted for a quartz sphere spinning at 200 Hz, the most likely configuration for the relativity gyro experiment. The difference in principal moments of inertia is also calculated for the spinning gyro.

Acoustical radiation from periodically stiffened membrane excited by turbulent boundary layer

Abstract: : Characteristics of periodically stiffened membrane are studied by using a string model loaded with equally-spaced mass and rotary inertia. The acoustical radiation by periodically stiffened membrane excited by a turbulent boundary layer is estimated using a modal analysis on an individual bay of membrane between stiffeners. Two theoretical predictions of radiated sound power are made using statistical energy methods. One is based upon measured wall pressure data, the other upon measured vibratory response of the membrane. Both agree well with direct measurements of radiated sound power.