Showing papers on "Natural frequency published in 1987"

The detuning of relativistic Langmuir waves in the beat-wave accelerator

Abstract: In the beat‐wave accelerator, a large‐amplitude Langmuir wave is produced by the beating of two laser beams whose frequencies differ by approximately the plasma frequency. The growth of this Langmuir wave saturates because of a nonlinear shift in its natural frequency. At present, there are three different formulas for the nonlinear frequency shift in the literature. By taking all relevant nonlinearities into account, the original result of Akhiezer and Polovin [Dokl. Akad. Nauk SSSR 102, 919 (1955)] is shown to be correct. The maximum amplitude of the Langmuir wave depends on the incident laser intensity and the frequency mismatch, which is the difference between the beat frequency of the incident waves and the plasma frequency. Two different studies have produced contradictory conclusions on the ‘‘optimum’’ frequency mismatch. The reasons for this contradiction are discussed and the result of Tang, Sprangle, and Sudan [Phys. Fluids 28, 1974 (1985)] is shown to be essentially correct. However, the requir...

Asymptotic expansions in nonlinear rotordynamics

Abstract: This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.

Determination of natural frequencies of a thick spinning annular disk using a numerical Rayleigh–Ritz’s trial function

Abstract: Consideration is given in this paper to the problem of a thick, spinning, annular disk constrained at its inner radius. Mindlin’s transverse shear deformation and rotary inertia terms are included in the eigenvalue formulation. In the modified Rayleigh–Ritz method used here, the ‘‘admissible’’ or ‘‘trial functions’’ are developed numerically by an iterative scheme so that all the forced, as well as natural, boundary conditions are fully satisfied. The natural frequencies for different mode shapes of the disk have been computed and are presented in a nondimensional form as a function of rotating speed.

Analytical and experimental investigation on vibrating circular plates with stepped thickness over a concentric circular region

Abstract: Transverse vibrations of the structural elements described in the title are studied for the case where the edges are elastically restrained against translation and rotation. Since finding an exact solution is a difficult task, it was considered convenient to approximate the response of the plate in the case of free, axisymmetric vibrations by means of a summation of simple polynomial coordinate functions that satisfy the governing boundary conditions. The Ritz method is used in order to generate the frequency equation. The natural frequency coefficients are optimized by minimizing each eigenvalue with respect to an undetermined exponential parameter included in each coordinate function.

Method of Estimating Equivalent Mass of Multi-Degree-of-Freedom System

Abstract: To attain the optimum design of vibration controllers to suppress the many resonance peaks of machine structures, it is necessary to know the equivalent mass at the location at which the controller is mounted. This paper shows two ways of estimating equivalent mass, one is a modal analysis method, and the other is called the mass response method which utilizes the change in natural frequency of a structure when an additional mass is attached. The first method is useful for identifying a modal mass having a physical meaning, while the other method is more suitable for application to experimental analysis. The accuracy of these methods are compared by applying them to three kinds of mechanical structure.

Seismic response analysis of a multi-walled coaxial cylindrical tank.

Abstract: The large-sized, multi-walled coaxial cylindrical tank has been studied in recent years because various kinds of oil can be stored in one tank It is important to design such tanks considering seismic response. This paper describes theoretical studies of the coupled vibration of the contained liquid and the shell plate of the cylindrical tank in response to lateral earthquake excitation, by the finite element method. In this paper, the bulging motion which occurs in the relatively high frequency region due to the flexibility of the shell is analyzed. The natural frequency the time history of the displacement response of the shell and the dynamic pressure response of the liquid of the actual tank are derived by the modal analysis approach.

Multi-Mode Response of a Square Membrane : Vibration, Control Engineering, Engineering for Industry

Abstract: The problem of the nonlinear forced oscillations of a square membrane is considered. For a theoretical analysis, modal equations are first derived from the governing nonlinear partial differential equations. Then, based on these modal equations, the characteristics of oscillations induced by harmonic excitation near a primary resonance point are discussed. A numerical calculation is conducted for a typical case in which the excitation frequency comes near to the resonance point of the mode with one nodal line. It is shown that near this resonance point, two modes which exist with the same natural frequency and with the same modal shape are excited simultaneously due to nonlinear coupling, and thus two-mode oscillations can occur. It is also shown that two kinds of two-mode oscillations are possible, one in which the two modes are excited with a time lag of nearly π/2, and the other without a time lag. The former implies the occurrence of oscillations of the rotary-type, and the latter the occurrence of oscillations whose nodal line is shifted from that of the linear harmonic oscillation. An experimental analysis is also conducted, which confirms the validity of the theoretical analysis.

The acoustic radiation damping of the modes of a rectangular panel

Abstract: The acoustic damping for single modes of a finite rectangular panel, simply supported in an infinite baffle, is theoretically determined from the ratio of the acoustic energy radiated per cycle to the vibratory energy of the panel Asymptotic solutions for the low‐frequency region are presented for a panel mode driven at an arbitrary frequency and for a panel mode vibrating at its natural frequency Curves of acoustic damping for a panel mode vibrating at resonance, as a function of the panel thickness‐to‐length ratio, are presented for various panel aspect ratios For panels vibrating below the critical frequency, the damping depends on the aspect ratio with square panels developing the smallest value For panels vibrating above the critical frequency, the damping is nearly independent of the aspect ratio

Nonlinear vibration of circular corrugated plates

Abstract: In this paper, first by using Hamilton principle, we derive the variational equation of circular corrugated plates. Taking the central maximum amplitude of circular corrugated plates as the perturbation parameter and adopting the perturbation variational method, in the first-order approximation, we obtain the natural frequency of linear vibration of circular corrugated plates and then the nonlinear natural frequency of the corrugated plates. By comparing with the linear results, the attempt of this paper is proved feasible.

Stability and Regulation of a Variable-Displacement Vane-Pump

Abstract: Pressure fluctuations may develop in the hydraulic system of automatic transmissions, even under steady-state conditions. To analyze this phenomenon, a dynamic model was developed for a system which consists of a variable-displacement vane-pump, a regulator, and a resistive load. The model was linearized and reduced to generate a stability criterion for the pressure-regulation circuit. This criterion determines a critical frequency that the natural frequency of the pressure-regulation valve must exceed to assure stability. This critical frequency depends primarily on the daming of the spool of the pressure-regulation valve and on its position; the latter is a function of the regulation-chamber leakage characteristics. The analysis shows that line pressure, flow and leakage, along with production tolerances and different operating conditions, have a significant effect on the stability of the hydraulic system. Test data supports the analysis.

Method for adjusting the damping force in motor vehicles in dependence on output signals of an acceleration transmitter

Abstract: A method for the damping force adjustment of motor vehicles in dependence on output signals of an acceleration transmitter connected with the vehicle body which are prepared and compared with a predetermined threshold value and which trigger a signal for changing the damping, respectively, spring force when exceeding, respectively, falling below the threshold value. An output signal of an acceleration transmitter rigidly connected with the vehicle body is slidingly determined over a first and a second measuring period, the difference of the two average values are subtracted from one another and are compared with the threshold value. The measuring periods are thereby larger, respectively, smaller than the natural period (reciprocal natural frequency) of the vehicle body.

Pile Fatigue Failures. III: Motions in Seas

Abstract: Motion response calculation procedures are described for a vertical, singly standing pile with no top restraint. Discussion is directed to: (1) Sea state energy distribution versus frequency; (2) hydrodynamic force formulation; and (3) synchronisation between pile natural frequency and vortex shedding frequency in wave flows. A nondimensional plot of in-line hydrodynamic force suggests that experimentally based force coefficient values used in the analysis provide a reasonable to conservative force estimate when vortices were formed but not shed during 90% of the construction period. Sensitivity studies with alternative lift force formulations suggest that significant motion response and substantial fatigue damage occurred due to vortex shedding synchronisation during the peak of the December 4-6, 1974 storm.

Vibration damping device

Abstract: PURPOSE:To suppress the vibration of a machine table on which a vibration generating source is mounted, by supporting a weight through a spring on the machine table, equalizing a natural frequency of the weight and the spring to a frequency of a vibratory force of the vibration generating source, and reversing a vibrating direction of the machine table relative to that of the weight and the spring CONSTITUTION:A base plate 1 is fixed to a floor surface in a factory, and a machine table 2 is fixedly supported through vibration isolating rubbers 3 onto the base plate 1 A vibration generating source, eg, a vertical air compressor 5 is mounted on the machine table 2 Further, a weight 8 is mounted through a coil spring 9 to the machine table 2 A weight of the weight 8 and a spring constant of the spring 9 are so set as to develop a natural frequency equal to that of the vibration generating source Further, the weight 8 and the vibration generating source are vibrated with a phase of 180 degC, and an inertial force of the weight 8 cancels a vibratory force

Free Vibrations of Imperfect Cantilever Bars under Self-Weight Loading

Abstract: This brief study examines the relationship between the natural frequency of small oscillations and the length of vertical cantilever struts in a gravitational field. The analysis uses a Rayleigh approach and includes post-buckled equilibrium states and emphasizes the influence of initial imperfections.

On the Vortex-Induced Oscillation of Long Structural Elements

Abstract: Previous solutions to the vortex-induced vibration of structures have been primarily based on modal analysis, using a one or two-mode approximation. Such an analysis is generally meaningful only when the vortex shedding frequency is locked onto a natural frequency of the structure. In very large structures, typical of those found in some ocean engineering applications, modes are closely spaced, and it is not reasonable to assume total spanwise correlation in the fluid forces or response. The approach used herein avoids the limitations associated with the modal solution of such problems by implementing a solution based on the traveling wave nature of the response. Results presented indicate that the amplitude of response of a long cable is smaller than is predicted by a conventional modal analysis. The drag forces on such a structure may therefore be overestimated by current design approaches.

Damping device using parallel elastic components with respectively positive and negative stiffnesses

Abstract: This damping device has overcome the shortcoming, that the arbitrarily low values of stiffness and natural frequency in general damping devices, made of the elastic component with positive stiffness, can not be achieved easily. The principle of compensating of the positive and negative stiffness each other is used in the device. As the two kind of elastic components with respectively positive and negative stiffnesses are parallelly used in the device, its stiffness can reach arbitrararily low value, and the large regulation of rated load capacity of damping device can be realized by regulating the predeforming value of elastic components with respectively positive and negative stiffnesses, so that the effective measures can be provided for damping, especially for low frequency damping and super-low frequency damping.

Vibrationproofing method using liquid sealing mounting device

Abstract: PURPOSE:To make it possible to exhibit good vibrationproofing effect for input vibration in high frequency band by making an acting member hold elastically against a holding body for making the acting member exhibit a damper action CONSTITUTION:Natural frequency of a mass member 50, which is determined by a spring constant of a coil spring 48 and mass of the member 50 and the liquid in a clearance 52, is set in a higher frequency than a frequency set for the clearance 52 When frequency of input vibration becomes higher than the natural frequency of the mass member 50, buildup of fluid pressure in a chamber portion between 50 and a partition member 32 is suppressed by movement of the mass member 50 to the reverse direction Accordingly, input vibration in high frequency band can be isolated favorably by damper action of the mass member 50 owing to resonance

Vibration damping apparatus for pulse motor

Abstract: A vibration damping apparatus for pulse motor such as linear pulse motors and rotary pulse motors to the first invention composed of a fixed member (2) and a movable member (1) includes a damper (20) mounted on at least one of the fixed member (2) and the movable member (1), the natural frequency of the damper (20) being made substantially equal to the natural frequency of the pulse motor excepting the damper (20) for cancelling out the vibration of the latter motor with the vibration of the former damper. The damper (20) includes a viscoelastic member (21) and a resilient balancer (22), the viscoelastic member (21) being mounted in one end thereof on the movable member (1) while the balancer (22) being mounted on the other end of the viscoelastic member (21).

Method and system for reducing at least one frequency component of a periodic pulsation

Abstract: Pulsations in an electrical parameter on the output of a synchronous generator powered by a Diesel engine at a frequency which differs from that of the synchronous generator's natural frequency are smoothed out, whereby, a controlled variable (X) corresponding to the pulsation is tapped from the stage formed by the Diesel engine (5), the generator (3), and the network (4). From this controlled variable (X) and a reference input (W), a control difference (Δ) is calculated, by means of which a correcting variable (y) is set in the stage indicated for the purpose of control.