Showing papers on "Rotary inertia published in 1978"

The Parametric Response of a Horizontal Beam Carrying a Concentrated Mass Under Gravity

Abstract: This investigation treats the steady-state response of parametric vibration of a simply supported horizontal beam, carrying a concentrated mass under the influence of gravity. Nonlinear terms arising from moderately large curvatures, longitudinal inertia of the beam and concentrated mass, and rotatory inertia of the concentrated mass are included in the equation of motion. By using the one mode approximation and applying Galerkin’s method, the governing equation of motion is reduced to a nonlinear ordinary differential equation with periodic coefficient. The harmonic balance method is applied to solve the equation and the dynamic response is derived. The effects of the weight, the rotatory inertia, the location, and the vibratory amplitude of the concentrated mass on the natural frequency are also discussed.

Out-of-plane vibrations of a beam including non-linear inertia and non-linear curvature effects

Abstract: The harmonic, non-linear response and its stability, for a clamped-clamped/sliding beam subject to a planar excitation is investigated by a perturbation method taking into account the non-linear inertia and the non-linear curvature terms in the differential equations of motion. The influence of excitation and beam parameters in the planar and in the non-planar response of the beam is determined in detail and illustrated by several ‘response charts’.

Rotary impact mechanism having a spring accelerated inertia member

Abstract: The rotary impact mechanism has a plurality of helical springs disposed adjacent to the outer peripheral surface of a rotary inertia member which springs are anchored at one end to the inertia member and at the opposite end to a rotary driving input member so that upon relative rotative movement between the input and inertia members the springs are loaded and thereafter function to rotatively drive the inertia member. The inertia member carries at least one pawl which is capable of engagement and disengagement from a driven, toothed, output member, the pawl impacting against a tooth of the output member to drive the latter when the inertia member is rotatively driven by the springs.

The Cranking Moment of Inertia in a Static Potential

Abstract: Taking into account the self-consistency condition for the deformation, we estimate the cranking moment of inertia in the absence of pair-correlations for the Woods-Saxon potential and various versions of the modified oscillator potential. We investigate the expectation that in a static potential the moment of inertia is almost equal to the rigid-body moment of inertia at the self-consistent deformation. We examine especially the consequence of the presence of the l2 term in the conventional modified oscillator potential.

Non-linear vibrations of transversely isotropic rectangular' plates

Abstract: The large amplitude free flexural vibration of transversely isotropic rectangular plate, incorporating the effects of transverse shear and rotatory inertia, is studied using the von Karman field equations. A mode shape, consisting of three generalised-coordinates together with the Galerkin technique, results in a system of three non-linear simultaneous ordinary differential equations which govern the motion of the plate. These equations are integrated using a fourth-order Runge-Kutta method to obtain the period for each amplitude of vibration. The non-linear period vs amplitude behaviour is of the hardening type and it is also found that transverse shear and rotary inertia effects increase the period and that this increase is quite significant even for thin transversely isotropic plates. The results are compared with earlier results which were based on a one-term or one generalised coordinate solution and using the Berger approximation or the von Karman field equations.

Toggle controlled servo system

Abstract: Digital control signals can be accepted and translated directly into low inertia, high torque intermittent rotary motion by this fast time response apparatus which comprises a low mass, rotatably mounted driving member, a source of driving torque such as a torque motor, a low rotary inertia torsion member which interconnects the driving member with the torque member to thereby apply torque to rotate the driving member, reciprocatably operated escapement means for controlling the rotation of the driving member, and a two-ended toggle linkage connected at one end in an operating relationship with the escapement means, and at the other end to a mechanism which supplies a reciprocating driving force. The toggle linkage has a normally flexible knee joint which can be selectively locked by electromechanical means to which the digital signals are supplied. When locked, the toggle linkage transmits a reciprocating driving force from one end, thereby triggering the escapement means so that the driving member is selectively, incrementally rotated under power from the torque motor through the torsion member.

Large-Deformation Response of Deep Circular Arches to Radial Magnetomotive Forces

Abstract: Circular-arch specimens were produced from aluminium rings By using suitable rigid inserts in a ring, only a small portion of it was allowed to deform freely The rings were subjected to uniformly-distributed, radially-inward-directed impulsive forces The forces were generated by a high-energy electrical discharge through a single-turn coil which surrounded the ring The induced currents in the ring were high enough to engender large, transient, radially-directed magnetomotive forces which caused gross plastic deformation The elastic–plastic response of the arches was predicted by using a finite-difference numerical technique to solve the equations of motion The analysis allows for circumferential and shear forces, as well as large changes in geometry It also incorporates strain-hardening, but it ignores the influence of rotary inertia High-speed photographs were used to record the transient shape of the collapsing arches These were found to be in good agreement with the predicted profiles

Free Vibration of Neutrally Buoyant Inflatable Cantilevers in the Ocean Environment

Abstract: Free vibration analysis of the neutrally buoyant inflated cantilevers, made of plastic sandwiched films, is presented, accounting for the added inertia and nonlinear hydrodynamic drag. The significant feature of the analysis is the reduction of the shell equations (the membrane, Fliigge's, and Herrmann-Armenakas') into a single equation which is similar in form to that for a vibrating beam with rotary inertia effects. The natural frequencies obtained are compared with the experimental results and those predicted by the Rayleigh-Ritz method in conjunction with the Washizu and membrane shell theories. The analyses show, and the experimental program confirms, that Fltigge's shell equation in reduced form is capable of predicting free vibration behavior quite accurately. However, the reduction technique should be applied with care, since in several cases it leads to misleading results, e.g., in the case of the Herrmann-Armenakas theory, generally accepted to be one of the most elaborate.

Rotary inertia body

Abstract: PURPOSE:To comparatively easy obtain even a rotary inertia body in large scale and for high speed revolution, by winding a band steel, which one end portion is fixed to an outer circumferential surface of a shaft, in multilayer shape by providing the band steel with strong tension with advance to the outer circumferential side from the inner circumferential side.

A Microscopic Description of Nuclear Rotational Motion. I

Abstract: A previous work in which we have attempted to construct a microscopic theory of the rotational problem is developed further. For the purpose of improving our method the structure of the intrinsic state is rcinvestigatcd in connection with the equation of motion and the properties of the operator R'M which generates rotational states. On the assumption that R\"'r is a one-body operator, it is found that each intrinsic state can be described by a single Slater determinant of individual particle states. On the basis of this result our previous method is reformulated into the form of the IIF approximation for the intrinsic I-Iamiltonim> II,n =H(l/2J) J'. In contrast with the usual IIF approximation method effects of the residual interaction can be reduced by an appropriate choice of the moment of inertia g_ Single-j shell system is analyzed according to this prescription and tl1e moment of inertia obtainecl agrees >Yith that in a previous paper. A comment on the interrelation between rotations and independent particle motions is also given.

Vibrations of rings with circular cross section

Abstract: 1. Rotary inertia and shear have a substantial effect on the vibrations of a ring, both in the plane of its curvature and outside it. This effect is particularly great at the higher harmonics. 2. The effect of tensile strain on the pure bending vibrations is slight and is notic eable only with the lower harmonics. In the higher harmonics, tension does not affect the pure bending vibrations of the ring, and bending does not affect the pure radial vibrations. 3. For a ring of circular cross section the low frequencies (light dots in Fig. 1) practically coincide, both in the plane of the ring and outside it. In calculations of these frequencies the torsional strain may be disregarded.

Dynamic coefficient of an elastically supported, pre-stressed beam

Abstract: An analysis is made of the problem of vibrations of a beam with an axial force resting on eltstic foundation, when the beam is uniform and of finite length and is subjected to an impulsive load. The solution is presented within the framework of a beam theory which includes the effects of shear deformation and rotary inertia. An example is provided where the dynamic coefficient for the bending moment is calculated. From the results of theoretical analysis, it becomes evident that the axial force in the beam and the stiffness of the foundation have considerable effect upon the dynamical behaviour of the system.

Gaussian step-pressure loading of rigid viscoplastic plates

Abstract: The response of a thin, rigid viscoplastic plate subjected to a spatially axisymmetric Gaussian step pressure impulse loading was studied analytically. A Gaussian pressure distribution in excess of the collapse load was applied to the plate, held constant for a length of time, and then suddenly removed. The plate deforms with monotonically increasing deflections until the dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid viscoplastic materials. For the small deflection bending response of the plate, the governing system of equations is essentially nonlinear. Transverse shear stress is neglected in the yield condition and rotary inertia in the equations of dynamic equilibrium. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and to obtain the analytical solutions in the form of eigenvalue expansions. The effects of load concentration, of an order of magnitude change in the viscosity of the plate material, and of load duration were examined while holding the total impulse constant.