Lateral Vibrations of a Damped Laminated Hollow Circular Cross-Section Beam

1974 ◽  
Vol 96 (3) ◽  
pp. 845-852
Author(s):  
R. A. Ditaranto
Keyword(s):  
Cross Section ◽  
Viscoelastic Material ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Material Loss ◽  
Simply Supported ◽  
Elastic Beams ◽  
Mass Moment ◽  
Elastic Layers ◽  
Loss Factors

The free lateral bending vibrations of an “infinitely” long or simply-supported thin-walled circular cross-section beams having elastic-viscoelastic-elastic layers are investigated to determine the natural frequencies and associated composite loss factors. The analysis considers the inner and outer beams to behave as elastic beams in which the mass and mass-moment of inertia are both considered along with the interaction of the two elastic beams through the viscoelastic material. The results indicate that there are two natural frequencies. The lower one associated with the two elastic beams moving together so that little damping is obtained in this mode of vibration; the higher mode in which the two elastic beams vibrate in opposite directions so that there is an amount of damping comparable to the material loss factor of the viscoelastic material. A simplified model analysis is performed which is used to corroborate the trends obtained in the computer solutions of the more rigorous analysis. A series of curves are obtained for equal thickness elastic layers which can be used to obtain natural frequencies and composite loss-factors for a realistic range of geometrical and physical properties of a laminated circular cross-section simply supported beam.

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

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.

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.

scholarly journals Elliptical Crack Identification in a Nonrotating Shaft

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
B. Muñoz-Abella ◽  
L. Rubio ◽  
P. Rubio ◽  
L. Montero
Keyword(s):  
Cross Section ◽  
Direct Problem ◽  
Natural Frequencies ◽  
Fatigue Cracks ◽  
Circular Cross Section ◽  
Crack Identification ◽  
Bernoulli Beam ◽  
Bending Vibration ◽  
Euler Bernoulli Beam ◽  
Cracked Shaft

It is known that fatigue cracks are one of the most important problems of the mechanical components, since their propagation can cause severe loss, both personal and economic. So, it is essential to know deeply the behavior of the cracked element to have tools that allow predicting the breakage before it happens. The shafts are elements that are specially affected by the described problem, because they are subjected to alternative compression and tension stresses. This work presents, firstly, an analytical expression that allows determining the first four natural frequencies of bending vibration of a nonrotating cracked shaft, assumed as an Euler–Bernoulli beam, with circular cross section under pinned-pinned conditions, taking into account the elliptical shape of the crack. Second, once the direct problem is known, the inverse problem is approached. Genetic Algorithm technique has been used to estimate the crack parameters assuming known the natural frequencies of the cracked shaft.

Natural Frequencies of Out-of-Plane Vibration of Arcs

1982 ◽  
Vol 49 (4) ◽  
pp. 910-913 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
K. Tanaka
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Plane Vibration ◽  
Out Of Plane

The natural frequencies of out-of-plane vibration based on the Timoshenko beam theory are calculated numerically for uniform arcs of circular cross section under all combination of boundary conditions, and the results are presented in some figures.

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