Showing papers on "Natural frequency published in 1971"
TL;DR: In this article, a single acoustic resonance, excited by vortex shedding from the trailing edge of a flat plate, has been studied in detail, where the mode was traversed at resonance and the modal shape and natural frequency were found to agree well with computations.
105 citations
TL;DR: In this paper, the dynamic characteristics of two suspension bridges were estimated from experimentally measured ambient motion time histories using random vibration theory and the power spectral densities of ambient time histories.
Abstract: The dynamic characteristics (i.e., normal mode natural frequencies, damping, and shapes) of two suspension bridges are estimated from experimentally measured ambient motion time histories. These characteristics were estimated using random vibration theory and the power spectral densities of ambient time histories. Twenty normal modes of vibration were observed in the 0 cycle per min-60 cycle per min frequency range for the Newport Bridge in Rhode Island. These modes include nine vertical, six lateral, and two torsional deck modes, plus three longitudinal tower modes. For each mode, estimates are obtained of natural frequency of vibration, damping, and shape. For the other suspension bridge, the William Preston Lane Memorial Bridge, 13 normal modes of vibration were observed. These modes are six vertical, six lateral, and one torsional deck mode. No tower modes were observed in the 0 cycle per min-60 cycle per min frequency range.
68 citations
TL;DR: In this article, a model of a linear oscillator with a slowly varying frequency which at some time coincides with the constant frequency of the forcing function is presented, and the solution can be constructed by matching the two asymptotic expansions which one obtains for oscillations near and away from resonance.
Abstract: This paper concerns a model problem illustrating the techniques needed to handle passage through resonance for oscillatory systems with slowly varying frequencies. The model consists of a linear oscillator with a slowly varying frequency which at some time coincides with the constant frequency of the forcing function. It is shown that the solution can be constructed by matching the two asymptotic expansions which one obtains for oscillations near and away from resonance. As each of these asymptotic expansions depends simultaneously on two time scales, this example combines use of the two principal techniques of singular perturbations. The results show that the amplitude increases, then decreases as the natural frequency passes through the resonant value. Extension of the techniques to systems of differential equations is also indicated.
55 citations
Patent•
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24 May 1971
TL;DR: In this article, a floating power plant is built in a double-walled shell and its contents form part of a compound pendulum whose center of mass is located below the metacenter of the sphere and which has a natural frequency substantially below that of the prevailing wave frequency of the water.
Abstract: A floating power plant is housed in a generally spherical double-walled shell. The shell and its contents form part of a compound pendulum whose center of mass is located below the metacenter of the sphere and which has a natural frequency substantially below that of the prevailing wave frequency of the water. Consequently, the power plant is supported upright in the water and does not rock in response to the wave motion of the water.
36 citations
TL;DR: In this article, a modified finite difference technique is used to determine the natural frequencies and mode shapes of hyperbolic cooling tower shells, and the influence of the meridional curvature and the boundary conditions on the vibration characteristics of the tower is investigated.
Abstract: A modified finite difference technique is used to determine the natural frequencies and mode shapes of hyperbolic cooling tower shells. The influence of the meridional curvature and the boundary conditions on the vibration characteristics of the tower is investigated. In all cases, changes in frequency are found to be essentially due to changes in membrane energy. It is shown that, for a fixed-free shell, the increased meridional curvature leads to an increase in the natural frequency. The lack of axial restraint results in a large reduction in the membrane energy and consequently the natural frequency. For simply-supported shells, a critical meridional curvature at which the membrane energy effectively vanishes is shown to exist.
30 citations
01 Feb 1971
TL;DR: In this article, an experimental and theoretical study of rotor oscillations in reluctance machines, with particular reference to variable-frequency systems, is described, and measured performance characteristics, both steady-state and transient, are used to indicate the basic features of the oscillation and to confirm the validity of theoretically derived results.
Abstract: An experimental and theoretical study of rotor oscillations in reluctance machines, with particular reference to variable-frequency systems, is described. Measured performance characteristics, both steady-state and transient, are used to indicate the basic features of the oscillation and to confirm the validity of theoretically derived results. Machine sine-wave and invertor quasisquare voltage supplies are considered. Theoretical results are presented which bring out all the significant influences on the stability performance of reluctance machines. These lead to a much improved understanding of observed behaviour of actual machines, and indicate those directions in which improved performance may be achieved. The direct-axis-rotor-resistance/quadrature-axis-rotor-resistance ratio is shown to be particularly important in this respect. The theoretical results are obtained from the characteristic equation of the machine using the method of D decomposition, previously developed in a powerful form for the treatment of multiparameter systems, and permitting the derivation of the natural frequency and damping factor. The frequency of rotor oscillation increases progressively with supply frequency, but, in most practical circumstances, lies somewhere in the range 0.03?0.15 p.u., the supply frequency then being in the range 0.1?0.4 p.u. Brief consideration of the relationship between the reluctance-machine instability and that occurring in induction machines is included.
25 citations
TL;DR: In this paper, the mean and variance of n th natural frequency of a beam-column are obtained by a perturbation method when the material and geometric properties, the axial load, and the boundary conditions are probabilistic.
Abstract: The mean and variance of n th natural frequency of a beam-column are obtained by a perturbation method when the material and geometric properties, the axial load, and the boundary conditions are probabilistic. The realtive effects of uncertainty in input parameters such as axial load and structural properties with uncertainty in output parameters of natural frequency are studied. It is found that the deviation of the output is great for the small deviation of inputs.
22 citations
01 Jan 1971
TL;DR: In this article, the root-mean-square (rms) displacement of a flexible rod or tube in axial flow is calculated in terms of beam natural frequency, damping factor, and intensity of the mean square spectral density of the pressure field in the low-frequency range.
Abstract: Many reactor and plant equipment components, such as fuel pins, control rods, and heat exchanger tubes, are long, slender, beam-like members which are exposed to nominally axial coolant flow. The flowing coolant represents a source of energy which can induce vibratory motion of these components. This design guide presents a relationship for calculating the root-mean-square (rms) displacement of a flexible rod or tube in axial flow. The relationship is based on the results of a parameter study and is valid for components that can be approximated as beams with either simply-supported or fixed-fixed ends. It is given in terms of beam natural frequency, damping factor, and intensity of the mean-square spectral density of the pressure field in the low-frequency range; all three are functions of mean axial flow velocity. Empirical expressions are developed for damping factor and intensity of the mean-square pressure spectrum. With these, an empirical equation for rms displacement is written which is in terms of known quantities and, therefore, provides a tool which can be used by designers. Since the equation is based on experiments involving a smooth rod in flow with minimal entrance effects, the predicted displacements should be interpreted and used with care. They are not conservative and, at best, will represent the minimum response to be expected. (auth)
20 citations
Patent•
21 May 1971
TL;DR: In this paper, the thickness free resonance is defined as the natural frequency of vibration of a plate or sheet in the thickness mode when the same is not influenced by contact probes or the like and is not subject to the application of external energy.
Abstract: The ultrasonic frequency of the thickness mode free resonance of plates or sheets is measured to precisely determine their thickness. The thickness free resonance is the natural frequency of vibration of the plate or sheet in the thickness mode when the same is not influenced by contact probes or the like and is not subject to the application of external energy. The free resonance is induced by first subjecting the portion of the article to be measured to a noise source for a first time interval; thereafter picking up the free resonance ultra sound produced by the article; storing the decaying sound; and, after the article has ceased resonating, feeding back the decaying sound to the sheet to induce high amplitude resonant vibrations therein; stopping the feed-back after a short interval; allowing the resonance to decay in its natural mode; again picking up and storing the decaying resonant frequency sound produced by the article; after resonance has ceased, again feeding back the decaying resonant frequency sound to the sheet; and so forth repetitively. Sound frequency meters are employed for measuring the frequency of the sound produced by the article when it is not being excited, i.e., when the resonance is decaying in its natural mode. Apparatus provided by the invention comprises a liquid coupling medium in which the sheet or plate is immersed; an ultrasonic transducer for radiating ultrasound to the article; a second ultrasound transducer for picking up the resonant sound produced by the article; appropriate amplifiers; and a delay line in the form of a rotating magnetic recording apparatus for recording the decaying resonant frequency and, after the resonance has died out, feeding the same back through the irradiating transducer. Alternative apparatus locates the transducer ten centimeters away from an article to provide inherent delay in the transmission path to and from the article and comprises an electronic switch connecting the two ultrasonic transducers, and amplifiers in a feed-back loop with the article, the excitation being applied only at intervals greater than the decay period of the article''s resonance. Also disclosed is an auxiliary ultrasonic pulse echo system for measuring transmission distance from the transmitting transducer to the article plate and for controlling the electronic switch accordingly.
15 citations
TL;DR: In this article, an approximation to the lowest natural frequency of vibrating beams is obtained analytically by applying eigenvalue, eigenfunction theory to the defining integral equation, which produces successively closer values for both upper and lower bounds to the fundamental frequency.
11 citations
TL;DR: In this paper, a variable parameter nutation damper for a dual-spin satellite is presented, which includes the capability of command changing the pendulum resonant frequency and damping constant in order to obtain optimum spin axis stabilization for both a dual and single-spin spacecraft dynamical condition.
Abstract: This paper presents design objectives, functional description and in-flight performance of a variable parameter nutation damper for a dual-spin satellite. The damper consists of a torsion wire mounted pendulum which includes the capability of command changing the pendulum resonant frequency and damping constant in order to obtain optimum spin axis stabilization for both a dual-spin and single-spin spacecraft dynamical condition. State-of-theart features of this damper include: 1) taut-band suspension, for a pendulous mass, which has no mechanical friction of hysteresis, 2) magnetic circuit for changing the torque constant of the taut-band thereby changing the damper natural frequency, 3) chargeable magnet system for varying the damping coefficient, and 4) 7-bit optical readout for telemetering the damper motion. The damper weights 2.7 Ib and draws 20 mw power when functioning for dual-spin conditions. The minimum nutation damping time constant in this mode is 12 min with a predicted spin axis pointing accuracy of 1 min of arc. Stabilization to better than 2 min of arc has been achieved in orbit.
TL;DR: In this paper, the response of two weakly coupled oscillators, one of which is subjected to an initial impulse, is examined by a simple perturbation analysis, and an expression for the time-dependent energy flow is derived.
TL;DR: In this article, the inverse problem of nonlinear vibration is often encountered and the most comprehensive and straightforward analysis is possible with systems having a nonlinear restoring force and a linear damping.
Abstract: In experimental research, the inverse problem of nonlinear vibration is often encountered. The most comprehensive and straightforward analysis is possible with systems having a nonlinear restoring force and a linear damping. With such systems the derivation of the restoring force can be separated from the determination of the damping and mass. This is possible by construction of the curve of natural frequencies pertinent to a given response curve. The shape of the curve of natural frequencies directly indicates the nature of the restoring force. All systems having the same linear damping and various nonlinear or linear restoring forces are related in a simple manner. The resonant amplitudes of all such systems are determined by a straight line passing through the origin. Also, two fairly general cases of nonlinear damping are considered (in addition to the nonlinear restoring force) in both one and many degrees-of-freedom.
TL;DR: In this paper, the authors considered the problem of designing a trashrack with the natural frequency of the bars sufficiently higher than the forcing frequency to prevent a resonant condition from developing.
Abstract: Trashracks subjected to high velocity flow should be designed to avoid operating under resonant conditions. This requires that design consideration be given to the natural frequency of the trashrack bars and the forcing frequency due to the velocity of the fluid through the trashrack. The natural frequency of a trashrack bar is primarily dependent upon the material, cross sectional configuration, unrestrained length and the end fixity. The forcing frequency, due to flow considerations, is primarily dependent upon the velocity of the fluid and the cross sectional configuration of the bar. The fundamental consideration is to design a trashrack with the natural frequency of the bars sufficiently higher than the forcing frequency to prevent a resonant condition from developing.
Patent•
27 Sep 1971TL;DR: In this paper, a method of controlling a motor in which an elastic element is coupled in a sub-critically damped manner to the load and the natural frequency of the system which comprises the elasticity of the element and the mass of the driven part is utilized to cause the speed of the load to increase and to decrease as quickly as possible.
Abstract: A method of controlling a motor in which an elastic element is coupled in a sub-critically damped manner to the load and the natural frequency of the system which comprises the elasticity of the element and the mass of the driven part is utilized to cause the speed of the load to increase and to decrease as quickly as possible.
TL;DR: In this article, the natural frequency of roof-shaped panels is evaluated on the basis of Reissner's simplified equations for thin shallow shells, which are approximately solved with the aid of Galerkin's method.
TL;DR: In this article, the eigenvalues of the potential energy matrix of an elastic body with respect to the combined kinetic energy of the body and fluid are derived to obtain a quadratic form for the fluid energy.
Abstract: A previously developed procedure, in which the natural frequencies of a body vibrating in a fluid are given by the eigenvalues of the potential energy matrix of an elastic body with respect to the combined kinetic energy matrix of the body and fluid, is applied to a body of revolution. Integral relations between the velocity potential on the body and the vibration velocity and the expression for the kinetic energy of the fluid as a surface integral are discretized to obtain a quadratic form for the fluid energy. Integrals for the kinetic and potential energies of the elastic body, taking both bending and shear into account, are also discretized. The method is illustrated by application to a form with assumed inertial and elastic characteristics.
Patent•
21 Dec 1971
TL;DR: In this paper, an electronic circuit allowing sustaining oscillation of a resonator by a reference frequency substantially exceeding the natural frequency of the resonator is presented, where pulses at the reference frequency and natural frequency are applied to the inputs of an AND-gate and the resonance is coupled to the output of the AND gate for sustaining its oscillation by the output pulses.
Abstract: An electronic circuit allowing sustaining oscillation of a resonator by a reference frequency substantially exceeding the natural frequency of the resonator, wherein pulses at reference frequency and natural frequency are applied to the inputs of an AND-gate and the resonator is coupled to the output of the AND-gate for sustaining its oscillation by the output pulses of the AND-gate.
TL;DR: In this article, the problem of a spherical shell containing a through crack of length 2c and subjected to periodic transverse vibrations of frequency ω was solved for the in-plane and Kirchhoff bending stresses.
Abstract: Using an integral formulation, the problem of a spherical shell containing a through crack of length 2c and subjected to periodic transverse vibrations of frequency ω is solved for the in-plane and Kirchhoff bending stresses. The usual inverse square root singular behavior characteristic to crack problems is recovered. Furthermore, it is found that the transverse vibrations reduce the stresses in the vicinity of the crack tip, except when the forcing frequency ω reaches the natural frequency of the uncracked shell in which case they become infinite.
Journal Article•
TL;DR: In this paper, the authors deal with a method of determination of virtual mass for partially and fully submerged structures surrounded by water, where the virtual mass depends on the geometry of the structure and its dynamic properties in air.
Abstract: This paper deals with a method of determination of virtual mass for partially and fully submerged structures surrounded by water. The experimental technique is simple and can be used for determination of virtual mass m case of structures like intake towers, bridge piers and similar structures. The virtual mass depends on the geometry of the structure and its dynamic properties in air. Due to the surrounding water, the natural frequency of vibration of a structure decreases but the damping increases. Due to the added mass of the surrounding water, the stresses and strains in the structure under dynamic conditions will be increased but some relief will be provided by increased damping.
TL;DR: In this article, an iterative technique is presented by which the properties of natural frequency, stiffness and viscous damping for two simple resonators may be derived from an experimentally determined response curve so that the combined responses of the resonators to a sinusoidal excitation is identical to that of the recorded response.
TL;DR: In this article, an empirical quasi-static analysis of elastic string and rigid rod oscillations in a fluid undergoing uniform shearing motion is presented. But it is shown that the oscillations can become unbounded, in the sense of the linearized analysis, when a parameter designated as the shear frequency exceeds the unaffected natural frequency.
TL;DR: In this paper, it is shown that the discrepancy between calculated and measured values of the natural frequency ωn of hydraulic actuators is due to three factors: 1. The effective mass of the pipe oil volume, the pipe cross section can be optimized.
TL;DR: In this article, the lateral vibration of a rotating shaft system with a rotating anisotropic anisotropy is discussed. And it can be concluded that forced vibration with the frequency ω 0 or ω'0( = 2λω-ω0) arises when ω0≒p or ψ 0=p^-(2λω)-p).
Abstract: Lateral vibration of a rotating shaft system with a rotating anisotropy is discussed in the present paper. Let the rotating speed of the shaft, the angular velocity of the anisotropy, the natural frequency of the system and the frequency of an external periodic force acting on the system be ω, λω, p and ω0 respectively. A resonant phenomenon arises when ω0≒2λω-p as well as when ω0≒p in such a vibratory system. It can be concluded that forced vibration with the frequency ω0 or ω'0(=2λω-ω0) arises when ω0≒p or ω0=p^-(=2λω-p). Furthermore, a certain vibration the cause of which is relatively hard to under stand can be defined physically by referring to the above conclusion.
TL;DR: In this article, the free oscillations of diagrids and orthogonal grids with elastically supported innernodes were studied, where the stiffness of the elastic supports increases all the natural frequency values of the grids and in particular, that of the fundamental frequency significantly.
01 Jan 1971
TL;DR: In this paper, the problem of a spherical shell containing a through crack of length 2c and subjected to periodic transverse vibrations of frequency co is solved for the in-plane and Kirchhoff bending stresses.
Abstract: Usmg an integral formulation, the problem of a spherical shell contaimng a through crack of length 2c and subjected to periodic transverse vibrations of frequency co is solved for the in-plane and Kirchhoff bending stresses. The usual inverse square root singular behavior characteristic to crack problems is recovered. Furthermore, it is found that the transverse vibrations reduce the stresses in the vicinity of the crack tip, except when the forcing frequency co reaches the natural frequency of the uncracked shell in which case they become infinite.
TL;DR: In this article, the lateral vibration of a deep girder in water has been treated, where the fatigue due to vibration is supposed to be one of the principal causes of the fractures in the local structures in the cargo tanks.
Abstract: The lateral vibration of deep girder in water has been treated in this report since the fatigue due to vibration is supposed to be one of the principal causes of the fractures in the local structures in the cargo tanks. The inertia of surrounding water is calculated by two-dimensional FEM using distributed sources and sinks, and taking account of three-dimensional correction.The effect of both the structure and the hydrodynamic inertia on the lateral vibration is examined theoretically where the latter is expressed in term of kinetic energy for the linear combination of the elastic modes. The effect of the face plate upon the pressure distribution and upon the frequency is shown to be large in water.The model experiments have been carried out and the results fairly agreed with that of calculation.The calculated natural frequency agrees with that obtained on board a large tanker with about 10% of errors and it is shown that the present calculation method is applicable to the actual structures and that the frequencies of this type of structures immersed in water may be lowered enough to cause the resonance with the blade frequency component of the exciting forces.
TL;DR: In this article, five modes of vibration of a six-storey reinforced concrete building were excited by steady-state resonance testing, and a good correlation between predicted and measured frequencies was obtained.
Abstract: Five modes of vibration of a six-storey reinforced concrete building were excited by steady-state resonance testing. Good correlation between predicted and measured frequencies was obtained.
In the lateral translation tests, two translation modes and the vibration of the roof as a free-free beam were excited. Damping measured in the fundamental mode was 4.1% critical and the average contribution of foundation compliance to the top-storey deflection was 32%. Damping in the second translation mode was 6.6% and of the free-free beam vibration, 3.6%.
The first torsional mode of the building was excited, and for an eight-fold increase in excitation force, the natural frequency reduced by 1.2%, indicating a slight degree of non-linearity in the response. Damping in this mode was 6.9% , no change being noted for the eight-fold force increase.
In the longitudinal direction, two modes were excited, the first torsional mode and the first longitudinal translation mode. Properties of the former were similar to those determined from the torsional response test. Damping in the translation mode was 10.1% and the foundation compliance contributed 24% of the top-storey deflection.