Showing papers on "Rotary inertia published in 1985"

Random Vibration of a Structure via Classical and Nonclassical Theories

Abstract: Random vibration of Bresse-Timoshenko beams, with shear deformation and rotary inertia taken into account, is studied. Two types of excitation are considered — distributed loading represented by spacewise white noise, and concentrated point loading. Timewise, both excitations are given by band-limited white noise with lower and upper cutoff frequencies. When the lower cutoff frequency vanishes, the lower modes of vibration play a decisive role, and classical and nonclassical theories yield coincident or close results; if the lower cutoff frequency is such that mostly higher modes are excited, the difference between predictions by these theories, may reach 50%.

Ritz finite element approach to nonlinear vibrations of a Timoshenko beam

Abstract: The Ritz finite element approach is used to study the nonlinear free vibrations of a beam considering shear deformation and rotary inertia effects. The governing nonlinear equations are derived using Lagrange equations at the point of reversal of motion. The nonlinear strain-displacement relations include the curvature terms based on three-dimensional incremental deformations, as used in Trefftz theory. A simple and efficient beam element, with three independent degrees-of-freedom at each node, and with linear polynomial distributions within the element, is made use of. The reduced integration technique is adopted on the shear related matrix to eliminate spurious constraints occurring when exact integration is used for the same in the case of slender beams. The governing equations are solved using a direct iteration scheme. Numerical results are presented in the form of tables for hinged-hinged immovable beam. When the present results are compared with the available ones wherever possible, good agreement is in general, found.

Device for compensating for rotary shocks

Abstract: In the case of a device for compensating for rotary shocks and having at least two inertia masses which are arranged coaxially with respect to one another and can be rotated in a limited manner with respect to one another against the influence of a damping device, in order to improve the matching of the damping capacity of the device to the respective application and hence in order to optimise the damping characteristic of the device and to expand the possible field of use, an additional friction-damping provision, which does not start to operate until there is a specific rotation angle between the inertia masses, is provided between the two inertia masses.

Effects of Fluid Inertia Forces on the Performance of a Plane Inclined Sector Pad for an Annular Thrust Bearing Under Laminar Condition

Abstract: The hydrodynamic wedge of a plane inclined sector pad is analyzed in relation to the lubricant inertia forces under incompressible laminar conditions. Based on the usual assumptions of thin film lubrication theory without the thermal effects, modified Reynolds equations are derived by averaging out all the inertia terms of the Navier-Stokes equations across the film thickness. The equations are linearized with respect to the inertia parameter, and solved numerically for a plane inclined, sectorial configuration. The boundary value of the film pressure at the leading edge is set at the ambient pressure, under the assumption of a negligibly small rampressure thereat. The inertial effects on the static and dynamic performance such as the load carrying capacity, flow rate, frictional torque, position of pressure center, film stiffness, and damping coefficient are discussed, in which the effects of the centrifugal force and those of the other convective inertia forces are compared with each other.

Nonlinear axisymmetric static and transient analysis of orthotropic thick annular plates

Abstract: This paper deals with the geometrically nonlinear axisymmetric static and transient response of moderately thick cylindrically orthotropic circular plates subjected to uniformly distributed and ring loads. Immovable clamped and simply supported annular plates with and without a rigid plug subjected to static and step function loads have been considered. Shear deformation and rotary inertia have been included. Orthogonal point collocation method and Newmark-β scheme have been employed to solve the differential equations expressed in terms of transverse displacement ω, shear rotation φ and stress function ψ. The effect of transverse shear has been investigated for isotropic and orthotropic plates. A simple approximate method has also been used to predict the maximum dynamic response to step loads from the results for static loads.

Inertia tension compensative takeup/payoff device

Abstract: PURPOSE:To provide constant tension in a windup/payoff device for a band- or wire-shaped work to be processed, by increasing or decreasing the load energy quantity of the payoff device simultaneously in correspondence to the tension change of web caused by the inertia acting force to be generated during acceleration and deceleration. CONSTITUTION:Operation of a coiled web 1 on a takeup drum 8 is so controlled as to have a smoothly continued acceleration curve by a speed command operational part 16, and entry is made into a differentiating device 20 in the payoff side control system, and the polarity of the acceleration output shall be inverted by a polarity inverter 21, which is to be entered into an inertia calculating part 22. Here the initial-set inertia moments of the payoff side drive system and a payoff drum 2 and the initial inertia moment and outside dia. of the web 1 wound on the drum 2 are given by setting devices 18, 19, and the error in tension amount corresponding to the inertia tension caused by acceleration of the web 1 in the starting action is calculated to decrease the torque control quantity for a clutch 4 with magnetic powder through an amplifier 23. Thus the tension of web during acceleration or deceleration can be held constant.

The approximation of pressure waveforms of impact sound radiation from clamped circular plates of various thicknesses

Abstract: The purpose of this paper is to investigate the mechanism of impact noise generation, in order to reduce noise at its source. A fundamental model, the case of a ball striking a clamped circular plate, was studied. In the experiments, the effects of plate thickness and observation distance on sound pressure were observed. In the theoretical analysis, the rotary inertia of the plate, shear deformation, and the air reaction of the radiated sound were considered. The impact force history was assumed to be a triangular pulse, since it was determined by three parameters: the maximum impact force, the impact duration, and the rise time. The time when the maximum sound pressure occurred, the influence of the rise time on the sound pressure level, and the vibrational modes which contributed to the sound were obtained using this approximation.

擬塑性流体を用いたスクイズフィルム軸受における流体慣性力の影響 : 第1報,平行円板形スクイズフィルム軸受

Abstract: In this research work, the effects of fluid inertia forces in parallel circular squeeze film bearings lubricated with pseudo-plastic fluids are examined theoretically. In the analysis, the cubic equation obtained from the empirical flow curves for pseudo-plastic fluids is used as the relation between shear stress and rate of shear and the inertia term in the momentum equation is approximated by the mean value averaged across the film thickness. The effects of inertia forces on the pressure distribution of the circular bearings are discussed for various nonlinear factors of pseudo-plastic fluids.

Vibration isolating supporter

Abstract: PURPOSE:To simplify the structure by providing a rotary inertia ring while screwing over a ball threaded shaft in a casing and providing a balance spring between said ring and casing then integrating the ball threaded section and brake mechanism. CONSTITUTION:Upon application of slow force onto the joint section 1, said force is transmitted to a ball threaded shaft 2 and through a ball 8 in ball thread mechanism to a rotary inertia ring 7. Said ring 7 is regulated with same setting force through a sleeve 12 of bearing 11 and balance spring 10 and made rotatable through clearances (da), (db). Consequently, the ring 7 will rotate together with the ball 8 to allow the axial displacement of ball threaded shaft 2. While upon application of relatively abrupt external force onto the joint section 1, rotation of ring 7 will not increase as the resistance increases thus to contact the side face section of ring 7 against the convex face section of cover 4. Consequently, rotation of ring 7 is blocked to provide vibration isolating function.

Static and dynamic analysis of beams with a single discontinuity in section

Abstract: Many methods exist for the analysis of the static and dynamic transverse behaviour of uniform beams. However, each method involves certain assumptions that may not be satisfied when two (or more) beams are joined together. This is particularly true when there is a discontinuity at the junction of two beams. The accuracy of the predictions of natural frequencies of such stepped beams using both a finite element and a receptance approach is compared with experimental results for beams with a range of step size. Both methods were investigated using elements based on simple beam theory, ie, without shear and rotary inertia, and also including these effects. It was found for the beams under consideration that for the first four natural frequencies the errors did not exceed 10 per cent when shear and rotary inertia were included (a).

Eigenvalues and stability problems of rotors

Abstract: The essential theoretical results of the application of a developed transfer matrix method to the free transverse vibration of a rotor are shown. Gyroscopic and shear effects, rotary inertia, and external and internal damping as well as the influence of sleeve bearings and rotor supports are taken into consideration. The eigenvalues of the motion equations of the rotor are searched by using a modified determinant method.

Dynamic analyses of frames with semi rigid joints

Abstract: A method is presented for analyses of frames with semi rigid joints. The dynamic deformation method used for analysis is suitable for free or forced vibrations. The method incorporates all influences such as semi rigidity, axial force, rotary inertia and shear force into one expression with improved numerical stability desirable for computer modelling (a).

Spatial vibrations of eflical heal-exchange pipes excited by internal flow of a heat carrier

Abstract: The principal result of the present work is that on the basis of the variational principle of Hamilton-Ostrogradskii we obtained a complete system of differential equations of the vibrations of helical heat exchange pipes excited by internal flow of the heat carrier, and the analytical formulation of the set of all permissible boundary conditions is provided. It was shown that from the presented system there follow as special cases many results obtained earlier in connection with curved and straight pipes and spatial rods. It was established that depending on the conditions of constraint of the ends of a heat exchange pipe, the system may be conservative or nonconservative. In the former case, loss of stability may be in flexural form when the critical flow rate is exceeded, in the latter case it is the flutter form. We examined actual examples of conservative and nonconservative systems, and we formulated boundary-value problems for them. The suggested equations and dependences may be the basis for further improvement of the theory of vibrations of spatial heat exchange pipes excited by a flow of heat carrier, by taking additionally into account the viscosity of the liquid, the nonsteady state of the flow, the initial stresses in the pipe, the rotary inertia of its sections, damping, and other factors in dependence on the problem under examination and the accuracy required for the actual applications. On the other hand, being very general, the equations and dependences may find applications of their own in practical engineering calculations.

Coupled vibration of multi shaft-disc systems.

Abstract: This thesis presents the dynamic behaviour of a rotor consisting of multidiscs on a solid or hollow shaft, of the type used in gas or steam turbines. The effect of shaft flexibility on the dynamic characteristics of discs and the coupling effects between the discs and shaft modes are investigated. The influence of the disc flexibility on the hehaviour of single span and multispan shaft system is also investigated. A new, thick, three-dimensinnal, Isoparametric, cylindrical element is developed to determine the axial, bending and torsional modes and their coupling effects on the vibrating shaft-discs systems. The element is chosen to have eight nodes at its corners with twelve degrees of freedom at each node giving ninety-six degrees of freedom for a complete element. The triple integration over the element of stiffness and mass matrices are evaluated algebraically and numerically by Gaussian Quadrature using a 4 x 4 x 4 mesh. The main objective of the research reported in this thesis is to fulfil the requirement for a theoretical solution capable of accurate analysis, and the development of finite element program using a double precision arithmetic to obtain the dynamic characteristics of a multirotor system. The effect of disc flexibility on the dynamic characteristics of a system where the discs are carried in the interior of thin-walled cylindrical hollow shafts or "drums" are also studied. This type of disc-drum assemblies are used in aeroengines. Advantage of the rotational periodicity and linear periodicity of the wave propagation technique is fully utilised in the analysis. A new technique of combination of the two methodsis developed to investigate the dynamic behaviour of multidiscs - multi span systems. The present investigation is divided in two parts. The first part deals with several applications of the study of vibration characteristics of circular and annular discs, sector plates, cylindrical shells, hollow cylinders and shafts for various boundary conditions. The results for such applications are obtained separately by using the thick , three-dimensional element, and are compared with those of existing results given by classical plate and shell theory,by exact and other numerical methods of analysis. They also show very good agreement with the experimental results. The objective of this part is to present the accuracy of the thick, three-dimensional element solution including the effects of rotary inertia and shear deformation on the vibration characteristics in the case of axisymmetric and non-symmetric modes of vibration. The effect of the radii ratio b/a and thickness variation of uniform and variable thickness disc on the frequencies of vibration is discussed. The effect of sectorial angle 0 of the sector plate, the ratio of L/R[m], R[1]./R[o] and R[m]/t of the shaft on the dynamic behaviour are also studied. A thin, two-dimensional annular sector element with twelve degrees of freedom is also developed to find the mass and stiffness matrices and to obtain the frequencies of a uniform and variable thickness disc. A comparison between the results of vibrating disc obtained by the thick three-dimensional element and by this element is made to show the superiority of the thick, three-dimensional element to the thin, two-dimensional element for the dynamic analysis and also to find the influence of shear deformation and rotary inertia on the dynamic behaviour which is not allowed for in the thin plate theory. The large size of the stiffness and mass matrices obtained in the case of a three-dimensional cylindrical element analysis are reduced by using the eigenvalue economizer technique. The second part of this investigation is to present the coupling influence and interaction between the discs and the shaft by using the thick, three-dimensional element. Results presented for various cases with differing flexibility and geometry show clearly the coupling effects in a multi disc-shaft system. An inference diagram is developed from which the dynamic behaviour of a system can be predicted for differing flexibility relationships between the solid or hollow shafts and the discs. The effect of various fixing conditions and boundary conditions on the coupling characteristics are also presented. The effectiveness, simplicitiy of use and significance of the element applied and its superiority over other elements in the dynamic analysis is studied. The theoretical results show very close agreement with the experimental results.