Showing papers on "Natural frequency published in 1975"

Simulation of low frequency undamped oscillations in large power systems

Abstract: New techniques were applied to the analysis of spontaneous power oscillations that occur in the Mid-Continent Area Power Pool (MAPP). System natural frequencies below one hertz were calculated along with the relative velocity deviations of major generating units at each frequency. Operating data was used to determine which of these low natural frequencies correspond to system oscillations. Simulation of the spontaneous oscillation was obtained using a dynamic stability program by giving each generator an initial velocity deviation proportional to the previously calculated relative velocity deviations for that frequency. The oscillation was also obtained by suddenly dropping load in one area of the dynamic model and picking it up in another area. A number of simulations were carried out to about twenty seconds or approximately three cycles of the natural frequency to investigate dynamic stability limits under various conditions. Quantitative calculations of synchronizing power flow capability between areas were used to evaluate the effects of operating and design changes.

Natural vibrations of suspension cables

Abstract: Natural frequencies and modes of vibration for suspension cables are determined using a discretized system composed of a linkage of straight bars connected by frictionless pins with concentrated masses at the connection points. The governing equations are linearized which limits the applicability to small oscillations. The frequencies are determined by a generalized Holzer method coupled with the solution of the associated boundary value problem as a set of initial-value problems. The method is applied to sample numerical problems and the results are compared with the results obtained by alternate approaches. The sensitivity of the results to the nature of the discretization is studied. Also, several parameter studies are conducted to determine how the natural vibrations are altered in response to dimensional variations in the suspension cable. The results of the parameter studies are summarized in a nondimensional form.

Extensional vibration of thin plates of various shapes

Abstract: The problem of free extensional (in plane) vibration of thin plates of Hookean material of various shapes was studied. Solutions for dilatational and rotational vibrations were obtained separately. The boundary conditions were satisfied in a least‐square sense. Numerical computations were performed for circular, elliptical, triangular, square, and hexagonal plates. The nodal pattern corresponding to each natural frequency for different modes was obtained. The frequency parameters computed for the circular plate are found to be within 0.05% of published results. For plates where known results were not available, the accuracy was checked by taking additional terms in the series solution and by dividing the boundary perimeter into finer intervals. It was found that the circular plate had the lowest fundamental frequency (k1) at 2.049. The value increases as the shape is changed from a circle, with the triangular plate having the highest value at 6.733 in dilatational vibration while the frequencies in rotati...

Dynamic Response of Cantilevers with Attached Masses

Abstract: Using generalized functions, the frequency equation for free vibrations of a cantilever beam-column having rotational and translational springs at its support, and carrying concentrated masses, is established in matrix form and is evaluated numerically. The effect of rotatory inertia of the concentrated masses is also included. Moreover, a procedure for establishing the mode shapes is presented. Finally, the differential equation for the modal amplitudes of forced motion is established.

Magnetoelastic Buckling and Vibration of a Rod Carrying Electric Current

Abstract: The effect of high electric currents on the stability and dynamics of a circular rod is investigated. A uniform current distribution in the undeformed rod is assumed. The perturbed magnetic field due to bending deformation is shown to set up a system of destabilizing forces. For long wavelength vibrations, a frequency-current dispersion relation is obtained which shows a continuous decrease in the natural frequency of the rod as the current in the rod is increased. At a critical value of current the natural frequency of the rod goes to zero and the rod buckles, which is the solid analog to the “kink instability” in plasma physics. The critical current criteria is applied to find the minimum support distance for a superconducting coil for magnetic levitation of trains. Experiments were conducted on a copper rod to observe the destabilizing effect of the electric currents of up to 400 A. Dynamic tests show that the natural frequencies decrease as the current in the rod increased. The frequency-current dispersion and the estimated critical current agree reasonably with the corresponding theoretical values.

Oscillating reed electric motors

Abstract: An electric motor of the kind in which an oscillating element carries a magnet which is coupled magnetically to a rotor to transmit drive thereto. The electrical driving signals for the oscillating element, derived for example from a divided-down quartz crystal oscillator, have a frequency f which is f/2Q less than the natural resonant frequency of the oscillating element, where Q is the Q factor of the element, to maintain drive of the latter for all variations in natural frequency due to ambient changes.

Optimization of Ring Stiffened Cylindrical Shells

Abstract: This paper deals with the optimum structural design of circular cylindrical shells reinforced with identical uniformly spaced T-ring stiffeners, and subjected to external pressure loading. The optimization problems considered are of three types: 1) minimum-weigh t design, 2) design for maximum separation of the lowest two natural frequencies, and 3) design for maximum separation of the lowest two natural frequencies which have primarily axial content. Gross buckling is precluded by specifying a minimum natural frequency, and additional behavioral constraints preclude yielding or buckling of panels, T-ring stiffeners, and web and flange instabilities within each T-ring. The analysis is based on use of an equivalent orthotropic shell model, and optimization is accomplished through use of a sequential unconstrained minimization technique. Examples indicate that moderate increases in weight above optimum (minimum) values can result in more than a doubling of the frequency separations, and that maximum frequency separations are obtained when second and third lowest frequencies approach each other. (A], df

Distribution of natural frequencies in certain structural elements

Abstract: The paper deals with the natural frequency distribution in beams, plates, and shallow spherical shells. Expressions are found for the distribution functions (number of modes not exceeding a given cutoff level), for these integral approximations, and for the frequency derivatives of the latter—the so−called smeared modal densities. Special attention is paid to the singularities in these densities (present in certain elements), which were noted by Bolotin and are referred to in literature as ’’condensation points.’’ It is shown that omission of the concept of lowest natural frequency leads to a physical paradox, and that the findings of most studies of modal densities should be revised. The method of integral approximations is applied to the problem of random vibrations of a shallow spherical viscoelastic panel. It is shown that the integral approximation of the averaged spectral density in the high−frequency range is equivalent to an infinite−system model, and, moreover that the physically inconsistent res...

Compliant wall-turbulent skin-friction reduction research

Abstract: Previous compliant-wall experiments successful in reducing skin-friction drag probably have had a (unplanned) membrane resonance at a favorable frequency, amplitude, wave shape, length, and speed. The most probable drag reduction mechanism involves a direct coupling between the fluid and the moving wall when the wall natural resonance frequencies are near the fundamental turbulent burst frequency. Local skin-friction reductions of 61% were measured with mylar/PVC plastisol compliant surfaces. These reductions were observed only at certain flow conditions, indicating that changing tunnel total temperature may have altered the substrate dynamic modulus, damping, and coupled mylar tension. Apparently, the coupled membrane/substrate must be excited in compatible narrow-band natural frequency modes. An accelerated effort is required to develop practical durable compliant surfaces optimized for maximum drag reduction. Application of compliant walls to other transportation modes appears feasible with liquid flows offering the greatest skin-friction drag reduction potential.

Drive line vibration absorber

Abstract: A drive line vibration absorber, for a mass elastic system having an engine operatively connected to a gear train through an elongated drive shaft, includes an inertia mass disposed in parallel relation to such mass elastic system and a resilient ring secured to the mass elastic system in axially driving cooperation with the inertia mass and permitting limited torsional movement thereof for effectively reducing the amplitude of the relatively low natural frequency torsional vibrations of the mass elastic system.

Optimal design in axial motion for several frequency constraints

Abstract: Governing equations for the optimal design of a rod with tip mass subject to several constraints on natural frequency are developed. The relation of this mass distribution to the globally optimum design for lowest frequency is discussed. A numerical example for two frequencies is presented. Some continuity results concerning the optimal mass distribution are presented.

Study on the Damping Capacity of Bolted Joints : Effects of the Joint Surfaces Condition

Abstract: As a serial study on the damping capacity of a bolted joint, in here effects of the machining method and roughness of joint surfaces, joint materials and also interfacial layers, on the damping have been investigated. By measuring the logarithmic damping decrement and the natural frequency of bolted cantibeams, how the damping and its amplitude dependence, and also the optimum preload, change themselves with different conditions of joint surfaces, has been also discussed. From the results it is known that the contact condition of joint surfaces has large effects on the damping capacity, but a little effect on the natural frequency. In the metal contact condition, the micro-slip on joint surface caused by the plastic deformation or the tearing of seizured points, is of importance to know the behaviour of damping. In the oiled joint, the increase of damping can not be always expected even if high viscosity oil is applied to joint surfaces.

Device for damping the tipping and yawing oscillations of the guidance system of a flying vehicle

Abstract: The guidance system for a flying vehicle having at least one guidance channel for converting an error signal to a command signal for a control surface servo of the vehicle includes means for damping oscillations at the natural frequency of the vehicle. A damping means includes a notch filter in the guidance channel which serves to damp oscillations at the notch frequency. The notch frequency is controlled and conformed to the natural frequency of the vehicle, as the natural frequency of the vehicle varies with vehicle speed, by providing the notch filter with a signal related to vehicle speed. The notch filter is arranged to vary the notch frequency in accordance with the signal provided thereto.

Adjusting method of frequency temperature characteristics of gt-cut cr ystal resonator

Abstract: PURPOSE:To adjust the natural frequency of the crystal resonator at the final natural frequency adjustment without fitting the resonator by changing the ratio of its side lengths.

Digital computer program DF1758 fully coupled natural frequencies and mode shapes of a helicopter rotor blade

Abstract: The analytical techniques and computer program developed in the fully-coupled rotor vibration study are described. The rotor blade natural frequency and mode shape analysis was implemented in a digital computer program designated DF1758. The program computes collective, cyclic, and scissor modes for a single blade within a specified range of frequency for specified values of rotor RPM and collective angle. The analysis includes effects of blade twist, cg offset from reference axis, and shear center offset from reference axis. Coupled inplane, out-of-plane, and torsional vibrations are considered. Normalized displacements, shear forces and moments may be printed out and Calcomp plots of natural frequencies as a function of rotor RPM may be produced.

Method for improvement of loudspeaker properties - applies to natural and lower frequency ranges

Abstract: The response characteristic of a loudspeaker is improved if it has a rapid acceleration. Improvement is achieved by movement negative feed back, and frequency correction is realised by positive feed back. A signal proportional to the coil current is positively fed back through a low pass filter, whose cut-off frequency lies in the oscillator natural frequency range ((+-) 1 octave). The lower cut off frequency of the power amplifier ensures a high-pass filter characteristic with a steep flank, suppressing very low frequencies outside the required range. The system also minimises parasitic oscillations.

Simplified Analysis of Dynamic Structure–Ground Interaction

Abstract: A simplified method of analysis is presented for the determination of dynamic properties of single-story structures founded on flexible foundations. The general equations for natural frequency, mode shapes, and modal damping are applied to structures founded on an elastic half-space and on piles. The results of parameter studies, including the effects of hysteretic soil material damping, are presented for these two cases.

Optimal design of elastic structures under dynamic loads

Abstract: : In this report, optimal design of elastic structures under dynamic loads is considered. A general objective functional for the problem is defined, and a functional treatment of the transient dynamic response constraints (stress and displacement constraints) is presented. Constraints on the natural frequency of the structure and the design variables are also included. The general method developed for this class of problems is then applied to truss-frame structures.

Seakeeping Characteristics of the XR-5, a High Length-Beam Ratio Manned Surface Effect Testcraft: 1. XR-5 Model Response in Regular Head Waves,

Abstract: Motion response data for regular waves in head seas is presented for a model of a high length-beam ratio surface effect ship (SES). Data is presented in normalized form for pitch, heave, relative bow velocity, relative bow motion stern seal motion, bow acceleration and heave acceleration. The pitch motion data exhibits a resonant or underdamped behavior governed by a constant natural frequency throughout the speed range investigated. The wave pumping effect was observed in the supercritical frequency range, and was particularly evident in the normalized acceleration data. The relative bow motion exhibits a pronounced peak at a frequency slightly above the pitching natural frequency.

Cleaning ferromagnetic metal parts - using electromagnet to oscillate the part during spray washing

Abstract: Cleaning bodies made at least partly of ferromagnetic matl. in which each body is brought separately and at least partially into an oscillating magnetic field with a frequency greater than the mains frequency and a cleaning liq. is simultaneously poured over the body. The frequency of the magnetic field is pref. the natural frequency of the system comprising the body and the components used to generate the field. The pref. device consists of at least two and esp. three coils arranged as an equilateral triangle and connected in a circuit supplying AC or a three phase supply and contg. two semiconductor diodes. Only a low amt. of energy is required to vibrate the metal part at its natural frequency or at a harmonic of this frequency.

Shake test of rotor test apparatus in the 40- by 80-foot wind tunnel

Abstract: A shake test was conducted to determine the dynamic characteristics of a rotor test apparatus on strut systems. The rotor-off hub transfer function (acceleration per unit force as a function of frequency) was measured in the longitudinal and lateral directions, using a combination of broadband and discrete frequency excitation techniques. The dynamic data is summarized for the configurations tested, giving the following properties for each mode identified: the natural frequency, the hub response at resonance, and the fixed system damping. The complete transfer functions are presented, and the detailed test results are included as an appendix. Data analysis techniques developed to obtain on-line measurements of the system modal properties, including the damping coefficient and the damping ratio are discussed.

Device providing a coupling between an electric driving motor and a driven element

Abstract: In a device which provides a coupling between an electric motor and an element which is driven in rotation at very high speed and suspended from a connecting-rod which works in traction, the diameter and length of the connecting-rod are determined in respect of a given weight of the driven element and a given torque so that the ratio of the length to the diameter of the connecting-rod is higher than 50 and preferably between 90 and 200. The result thereby achieved is a minimum value of the natural frequency of the connecting-rod and maximum transverse stability.

A Study of Wave-Induced Vibrations (2nd report)

Abstract: Wave-induced vibrations (springing) have been studied both theoretically and experimentally The model experiments have been carried out using a tanker model of 7 meter length Higher harmonic excitation in regular waves (which means the exciting force with the frequency multiple of the frequency of encounter) and the response to it have been confirmed both in theory and experiment Also it has been shown that the natural frequency of the 2-noded hull vibration and the ship speed play an important role in the response of springing The necessity of the future work is emphasized especially in the field of estimation of hydrodynamic exciting force in the region of short wave length, in order to refine the numerical accuracy