Energy Transfer From High-to Low-Frequency Modes in a Flexible Structure via Modulation

1994 ◽  
Vol 116 (2) ◽  
pp. 203-207 ◽  
Author(s):  
S. A. Nayfeh ◽  
A. H. Nayfeh
Keyword(s):  
Cross Section ◽  
High Frequency ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Low Frequency ◽  
Cantilever Beams ◽  
Axially Symmetric ◽  
Internal Resonances ◽  
Planar Motions ◽  
High Frequency Modes

An experimental study of the response of axially-symmetric (i.e., circular cross-section) cantilever beams to planar external excitations is presented. Because of the axial symmetry, one-to-one internal resonances occur at each natural frequency. These resonances cause the planar motions to lose stability and nonplanar (whirling) motions are observed. Under certain conditions, periodically-and chaotically-modulated motions may occur. In addition, when the beam is excited near one of its high natural frequencies, large first-mode responses accompanied by slow modulations of the amplitudes and phases of high-frequency modes are observed. This interaction between high-and low-frequency modes may be extremely dangerous because the amplitudes of the responses of the low-frequency modes can be very large compared with those of the directly excited high-frequency modes.

Bending Vibrations of Variable Section Beams

1956 ◽  
Vol 23 (1) ◽  
pp. 103-108
Author(s):  
E. T. Cranch ◽  
Alfred A. Adler
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Beam Theory ◽  
Cantilever Beams ◽  
Constant Depth ◽  
Bending Vibrations ◽  
Variable Section

Abstract Using simple beam theory, solutions are given for the vibration of beams having rectangular cross section with (a) linear depth and any power width variation, (b) quadratic depth and any power width variation, (c) cubic depth and any power width variation, and (d) constant depth and exponential width variation. Beams of elliptical and circular cross section are also investigated. Several cases of cantilever beams are given in detail. The vibration of compound beams is investigated. Several cases of free double wedges with various width variations are discussed.

Transverse Vibrations of Cantilever Beams Having Unequal Breadth and Depth Tapers

1977 ◽  
Vol 44 (4) ◽  
pp. 737-742 ◽  
Author(s):  
B. Downs
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Distribution Patterns ◽  
Continuous Systems ◽  
Cantilever Beams ◽  
Transverse Vibrations ◽  
Discretization Technique

Natural frequencies of doubly symmetric cross section, isotropic cantilever beams, based on both Euler and Timoshenko theories, are presented for 36 combinations of linear depth and breadth taper. Results obtained by a new dynamic discretization technique include the first eight frequencies for all geometries and the stress distribution patterns for the first four (six) modes in the case of the wedge. Comparisons are drawn wherever possible with exact solutions and with other numerical results appearing in the literature. The results display outstanding accuracy and demonstrate that it is possible to model with high precision the dynamic behaviour of continuous systems by discretization on to a strictly limited number of degrees of freedom.

Systematic design of cantilever beams for muscle research

1977 ◽  
Vol 42 (5) ◽  
pp. 786-794 ◽  
Author(s):  
R. J. McLaughlin
Keyword(s):  
Elastic Modulus ◽  
Cross Section ◽  
Experimental Studies ◽  
Circular Cross Section ◽  
Design Procedure ◽  
Structural Materials ◽  
Thick Wall ◽  
Beam Parameter ◽  
Thin Wall ◽  
Cantilever Beams

Experimental studies of muscle contraction often involve difficult problems in the design of cantilever beams for movable levers, transducers, or mechanical supports. Equations are presented for the calculation of mass, inertia, stress distribution, strain, deflection curve, compliance, and resonant frequency of uniform or nonuniform cantilever beams made of structural materials of different density or elastic modulus. Formulas are listed for solid, thick-wall, and thin-wall uniform beams of rectangular and circular cross section. Physical properties including density, elastic and torsional moduli, stress and strain limits, thermal expansion coefficients, Poisson's ratio, and certain elastic-modulus-to-density ratios are tabulated for structural materials including common metals, glass, plastic, and wood. A graphical design procedure is presented based on a chart containing loci of constant beam parameter values as a function of beam length and height or diameter, for the simple geometries. The choice of structural material is discussed for design problems with typical constraints, and examples are given of the design of beams of nonuniform cross section. Methods for extending the design chart to other geometries and materials are included.

Effect of Slenderness Ratio on the Natural Frequencies of Pre-Twisted Cantilever Beams of Uniform Rectangular Cross-Section

1971 ◽  
Vol 13 (1) ◽  
pp. 51-59 ◽  
Author(s):  
B. Dawson ◽  
N. G. Ghosh ◽  
W. Carnegie
Keyword(s):  
Differential Equations ◽  
Shear Deformation ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Slenderness Ratio ◽  
Twist Angle ◽  
Equations Of Motion ◽  
Rotary Inertia ◽  
Cantilever Beams

This paper is concerned with the vibrational characteristics of pre-twisted cantilever beams of uniform rectangular cross-section allowing for shear deformation and rotary inertia. A method of solution of the differential equations of motion allowing for shear deformation and rotary inertia is presented which is an extension of the method introduced by Dawson (1)§ for the solution of the differential equations of motion of pre-twisted beams neglecting shear and rotary inertia effects. The natural frequencies for the first five modes of vibration are obtained for beams of various breadth to depth ratios and lengths ranging from 3 to 20 in and pre-twist angle in the range 0–90°. The results are compared with those obtained by an alternative method (2), where available, and also to experimental results.

Dynamic Analysis of the Rotating Composite Thin-Walled Cantilever Beams with Shear Deformation

2013 ◽  
Vol 690-693 ◽  
pp. 309-313
Author(s):  
Yong Sheng Ren ◽  
Qi Yi Dai
Keyword(s):  
Shear Deformation ◽  
Cross Section ◽  
Fiber Orientation ◽  
Model Comparison ◽  
Natural Frequencies ◽  
Theoretical Study ◽  
Equations Of Motion ◽  
Cantilever Beams ◽  
The Finite Element Method ◽  
Rotating Speed

This paper presents a theoretical study of the dynamic characteristics of rotating composite cantilever beams. Considering shear deformation and cross section warping, the equations of motion of the rotating cantilever beams are derived using Hamilton’s principle. The Galerkin’s method is used in order to analysis the free vibration behaviors of the model. Comparison of the theoretical solutions has been made with the results obtained from the finite element method, which prove the validity of the model presented in this paper. Natural frequencies are obtained for circular tubular composite beams. The effects of fiber orientation, rotating speed and structure parameters on modal frequencies are investigated.

Natural Frequencies of In-Plane Vibration of Arcs

1983 ◽  
Vol 50 (2) ◽  
pp. 449-452 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
K. Tanaka
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Plane Vibration

The natural frequencies of in-plane vibration are presented for uniform arcs with circular cross section under all combinations of boundary conditions.

Axially Symmetric Waves in Elastic Rods

1960 ◽  
Vol 27 (1) ◽  
pp. 145-151 ◽  
Author(s):  
R. D. Mindlin ◽  
H. D. McNiven
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Elastic Rod ◽  
One Dimensional ◽  
Axial Shear ◽  
Wave Numbers ◽  
Complex Wave

A system of approximate, one-dimensional equations is derived for axially symmetric motions of an elastic rod of circular cross section. The equations take into account the coupling between longitudinal, axial shear, and radial modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite rod is explored in detail and compared with the analogous solution of the three-dimensional equations.

Concentration Fluctuation Spectra in Turbulent Slurry Pipeline Flow

1989 ◽  
Vol 111 (3) ◽  
pp. 317-323 ◽  
Author(s):  
R. J. Sumner ◽  
C. A. Shook ◽  
M. C. Roco
Keyword(s):  
Cross Section ◽  
Electrical Resistance ◽  
High Frequency ◽  
Particle Diameter ◽  
Low Frequency ◽  
Frequency Spectra ◽  
Concentration Time ◽  
Solids Concentration ◽  
Slurry Flows ◽  
Effective Domain

Using probes responding to changes of slurry electrical resistance with concentration, time spectra of longitudinal concentration fluctuations in turbulent slurry flows have been measured. The sensors, with an effective domain approximately 1 mm in diameter, showed the spectra to be relatively insensitive to location within the pipe cross section. High frequency spectra were found to be relatively insensitive to slurry concentration and particle diameter. Low frequency spectra showed fluctuation amplitudes which increased with solids concentration.

scholarly journals VIBRATORY SEPARATION OF GRAIN FROM THE EAR: PROBLEMS AND PERSPECTIVES

2020 ◽  
Author(s):  
V.I. Pakhomov ◽  
◽  
S.V. Braginets ◽  
O.N. Bakhchevnikov ◽  
D.V. Rudoy ◽  
...  
Keyword(s):  
High Frequency ◽  
Natural Frequencies ◽  
Low Frequency ◽  
Mechanical Resonance ◽  
High Frequency Oscillations ◽  
Low Frequency Oscillations ◽  
Oscillation Frequencies

The method of vibratory separation of grain from ear is validated in article. It is set that transferring to a stalk with ear low frequency oscillations in the range 18…100 Hz corresponding to natural frequencies of its oscillations are possible to achieve damage of ear or its detachment from a stalk as a result of a resonance. But this interval of oscillation frequencies does not provide separation of grains from ear as does not lead to damage of perular scales. Transmission to ear of high-frequency oscillations in the range 100…14000 Hz matching its natural frequencies of oscillations is perspective for this purpose. The mechanical resonance generate to grain separation owing to break off perular scales from ear can result from such vibratory influence.

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