On the change of natural frequencies of a sloshing liquid by movable devices
Sloshing liquid natural frequencies change in cylindrical shell by movable devices, considering immersed thin elastic plate effect
Chang, S.-C.↗
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Natural Frequency Testing and Model Correlation of Rocket Engine Structures in Liquid Hydrogen - Phase I, Cantilever Beam
Many structures in the launch vehicle industry operate in liquid hydrogen (LH2), from the hydrogen fuel tanks through the ducts and valves and into the pump sides of the turbopumps. Calculating the structural dynamic response of these structures is critical for successful qualification of this hardware, but accurate knowledge of the natural frequencies is based entirely on numerical or analytical predictions of frequency reduction due to the added-fluid-mass effect because testing in LH2 has always been considered too difficult and dangerous. This fluid effect is predicted to be approximately 4-5% using analytical formulations for simple cantilever beams. As part of a comprehensive test/analysis program to more accurately assess pump inducers operating in LH2, a series of frequency tests in LH2 were performed at NASA/Marshall Space Flight Center's unique cryogenic test facility. These frequency tests are coupled with modal tests in air and water to provide critical information not only on the mass effect of LH2, but also the cryogenic temperature effect on Young's Modulus for which the data is not extensive. The authors are unaware of any other reported natural frequency testing in this media. In addition to the inducer, a simple cantilever beam was also tested in the tank to provide a more easily modeled geometry as well as one that has an analytical solution for the mass effect. This data will prove critical for accurate structural dynamic analysis of these structures, which operate in a highly-dynamic environment.
Brown, Andrew M.↗
Fortran IV computer program for the evaluation of natural frequencies and unstable values of the thrust frequency for a circular cylindrical shell subjected to a gimbaled periodically-varying end thrust
Fortran IV computer program to evaluate natural frequencies and unstable values of thrust frequency for circular cylindrical shell subjected to periodically varying end thrust
NATURAL FREQUENCY↗
Prediction of natural frequency variability due to uncertainty in material properties
Composite materials are widely used in various types of modern engineering structures. Traditional studies on composite structures have been based on the assumption that the material properties of the composites are characterized by a priori known elastic moduli, and no uncertainties of these moduli have been considered. However, the composite materials are invariably subject to a certain amount of scatter in their measured elastic moduli. To a large extent, the properties of composite materials are dependent on the fabrication process. But even the composite materials manufactured by the same process demonstrate differences in their elastic properties. This paper proposes a new, non-probabilistic method to predict the variability in the natural frequencies of the composite cylindrical shell, resulting from the unavoidable scatter in elastic moduli. The available measurements of elastic moduli are fitted by the four-dimensional uncertainty ellipsoid. The upper and lower bounds of the natural frequency are derived. With these bounds, designers will have a better understanding of the real dynamic behavior of the structure.
Li, Y. W.↗
Natural frequencies of orthotropic circular plates of variable thickness
Differential equations for natural frequencies of orthotropic circular plates of variable thickness
Patel, S. A.↗
Prediction of Natural Frequency and Buckling Load Variability due to Uncertainty in Material Properties by Convex Modeling
Composite materials are widely used in various types of engineering structures. To a large extent, the properties of composite materials are dependent on the fabrication process. But even the composite materials manufactured by the same process may demonstrate differences in their elastic properties. For design purposes, one should be aware of the potential variations in load-carrying capacity and dynamic behavior of such structures that can arise due to the uncertainty in elastic moduli. A more realistic analysis of composite structures should be performed with the variations of the elastic moduli being taken into consideration at the same time. The present paper is a generalization of a study where the influence of uncertainty in elastic moduli on the axial buckling load was discussed. Here, we consider another case of buckling, shells under uniform external pressure. In addition, this paper deals with the variability of natural frequencies by use of convex modeling, which is apparently the first study of this kind in the literature. A numerical approach to the uncertainty problem is nonlinear programming, which we apply to solve the same problem to generate a set of comparable numerical data. The results from both methods show good agreement throughout. Thus, the effectiveness of the analytic convex modeling is clearly demonstrated. The bounds of he natural frequency and the buckling load provide the designer with a better view of the vibrational behavior and the actual load carrying capacities possessed by the composite structure.
Li, Y. W.↗
Fortran IV computer program for the evaluation of natural frequencies and unstable values of the thrust frequency for a free- free, circular cylindrical shell subjected to a gimbaled, periodically-varying end thrust
Fortran IV computer program for evaluation of natural frequencies and unstable values of thrust frequency for free-free circular cylindrical shell subjected to end thrust
FORTRAN↗
The vibration of a box-type structure. I - Natural frequencies and normal modes
Box type structure free vibrations investigation by rectangular finite elements, comparing with natural frequencies and normal modes solution
Popplewell, N.↗
Natural frequencies and elastic stability of a simply-supported rectangular plate under linearly varying compressive loads
Natural frequencies and elastic stability of simply supported rectangular plate under linearly varying compressive loads
Fauconneau, G.↗
Natural frequencies of an orbiting space station
The technique of modal synthesis is applied to find the natural frequencies of space stations. The station is modeled as an assemblage of rigid modules, joined by massless elastic constraints, and flexible modules characterized by deformation functions. The equations of motion are derived and system mass and stiffness matrices derived. The method is applied to the Skylab orbiting space station. The frequencies of the lowest 65 modes are given and selected mode shapes illustrated. The technique is feasible for analysis of a complex system and suitable for response studies including damping and attitude control system effects.
Bernstein, E. L.↗
Natural frequency of rotating beams using non-rotating modes
A Lagrangian approach is formulated for predicting the rotating natural frequencies of a beam from the nonrotating modes and frequencies. Using the first two nonrotating mode shapes in one case and the first four such modes in the other case the frequencies of the rotating modes are calculated for a short tapered beam and a typical helicopter blade, respectively. In each case the beam is represented by lumped parameters. The number of mass points representing the beam and the accuracy of the calculated slopes of the nonrotating mode shapes at those points are both shown to affect the accuracy of the resulting frequencies, but the number of stations is shown to be more important.
Loewy, R. G.↗
The natural frequencies of symmetric angle-ply laminates derived from eigensensitivity analysis
In this paper, a new closed-form approximate solution for the natural frequencies of symmetric rectangular angle-ply laminates simply supported on all four edges is derived. The solution, obtained from eigensensitivity analysis, is expressed as a truncated Fourier series in the ply angle. Results show that the prediction for the fundamental frequency is quite accurate for engineering applications, often within 1-2 percent of the true frequency.
Reiss, Robert↗
On the information content of natural frequency spectra associated with different angular numbers
The problem of inferring the speed of sound in a contained spherically symmetric fluid solely from its natural frequencies of vibration is considered. An investigation of the case in which the data consist of the two spectra associated with the angular numbers 0 and 1, suggests the possibility that a one-parameter family of slowness profiles can be constructed. These profiles are compatible with the data, up to first order in the non-uniformity of the fluid. It is conjectured that for other angular numbers, the loss of information increases as the difference between them increases.
Barcilon, V.↗
Design of helicopter rotor blades for desired placement of natural frequencies
The mass and stiffness distributions for helicopter rotor blades are to be tailored in such a way to give a predetermined placement of blade natural frequencies. This optimization problem is addressed in a methodical, step-by-step process in which each aspect of the optimization is studied in detail. Careful consideration is also given to the mathematical formulation of the problem and to the introduction of appropriate constraints.
Peters, D. A.↗
Experimental and Theoretical Deflections and Natural Frequencies of an Inflatable Fabric Plate
Static and vibration tests were performed on an inflatable square fabric plate supported on all edges. Lateral deflections and natural frequencies showed good agreement with calculations made using a linear small-deflection theory.
Stroud, W. Jefferson↗
Design, fabrication, and initial test of a fixture for reducing the natural frequency of the Mod-O wind turbine tower
It was desired to observe the behavior of a two bladed wind turbine where the tower first bending natural frequency is less than twice the rotor speed. The system then passes through resonance when accelerating to operating speed. The frequency of the original Mod-O tower was reduced by placing it on a spring fixture. The fixture is adjustable to provide a range of tower bending frequencies. Fixture design details are given and behavior during initial operation is described.
Winemiller, J. R.↗
Section 1. Method of determining mode shapes and natural frequencies of the NASA unmodified test structure. Section 2. Continuous beam closed from solution to the NASA-LSS astromast torsional vibration, appendix E
The methods used to determine the lower natural frequencies and their corresponding mode shapes of the NASA-LSS Astromast (Unmodified Test Structure), and the mass integrals associated with the mode shapes are illustrated. The test structure is modeled as a cantilever beam with 91 lumped masses and without the tip mass on the free end of the bram. This uncouples the torsion and bending modes and allows for them to be determined separately. The frequency range was limited to an upper bound of 100 rad/sec (15.92 Hz.). In this range from 0.-100. rad/sec, three bending frequencies and one torsion frequency was found.
Source record↗
An estimator for the standard deviation of a natural frequency. I.
A brief review of mean-square approximate systems is given. The case in which the masses are deterministic is considered first in the derivation of an estimator for the upper bound of the standard deviation of a natural frequency. Two examples presented include a two-degree-of-freedom system and a case in which the disorder in the springs is perfectly correlated. For purposes of comparison, a Monte Carlo simulation was done on a digital computer.
Schiff, A. J.↗