Stability of Out-of-Plane Vibration of a Uniform Beam Carrying an End Body and Attached Radially to a Rotating Hub

1999 ◽  
Author(s):  
S. Naguleswaran
Keyword(s):  
Analytical Study ◽  
Natural Frequencies ◽  
Force Distribution ◽  
Sufficient Condition ◽  
Centre Of Mass ◽  
System Parameters ◽  
Plane Vibration ◽  
Uniform Beam ◽  
Out Of Plane ◽  
Zero Frequency

Abstract This paper reports an analytical study on the out-of-plane vibration and stability of a uniform beam attached to a rotating hub and carrying a rigid body at the other end. The parameters which govern the natural frequencies are the hub radius (root offset), speed of rotation of hub, the mass of the end body, its moment of inertia about an axis in the plane of rotation and through the centre of mass, the radial offset of the centre of mass from the beam end It is shown that for certain combinations of the system parameters a ‘tuned’ state (analogous to whirling of a shaft) is possible. It is also shown (hat for some combinations a natural frequency is zero (borderline of instability) even though the axial force distribution in the beam is tensile throughout. Negative centre of mass offset is a necessary but not sufficient condition for zero frequency to occur.

Vibrations of an Intermediately Supported U-Bend Tube

1975 ◽  
Vol 97 (1) ◽  
pp. 23-32 ◽  
Author(s):  
L. S. S. Lee
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Experimental Tests ◽  
Bending Stiffness ◽  
Stiffness Ratio ◽  
Plane Vibration ◽  
Straight Beam ◽  
Out Of Plane ◽  
Straight Segments ◽  
Good Agreement

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

Vibration Analysis and Health Monitoring of Cracks in Composite Disk Rotor Systems

2005 ◽  
Author(s):  
Xin Hai ◽  
George Flowers ◽  
Roland Horvath ◽  
Jerry Fausz
Keyword(s):  
Health Monitoring ◽  
Natural Frequencies ◽  
Experimental Testing ◽  
Vibration Characteristics ◽  
Rotor Systems ◽  
Plane Vibration ◽  
Fea Model ◽  
Rotating Systems ◽  
Out Of Plane ◽  
Composite Disk

Cracks and voids are common defects in rotating systems and are a precursor to fatigue-induced failure. Identifying the presence and growth of cracks is a critical concept for the health monitoring and diagnostics of such systems. A combined computational and experimental study of the vibration characteristics of a composite hub flywheel rotor system with a cracked hub disk is presented. First, experimental testing of both in-plane and out-of-plane vibration characteristics using a rotor with a composite disk hub supporting a relatively massive rim was conducted. A crack was deliberately introduced into the hub disk during fabrication. Based upon these results, a finite element (FEA) model was developed to further explore the relationship between natural frequencies and crack properties. Finally, a simplified theoretical model for the primary in-plane vibration mode was developed and used in a series of parametric studies. Good agreement was found between the model predictions and the experimental results. It was observed that the presence of a crack tends to affect both the magnitudes and distribution of the rotor natural frequencies. Certain primary frequencies for rotors with a crack are smaller than for those without a crack. In addition, the frequency values of associated with the “in-crack” direction are generally smaller than those associated with the “off-crack” direction, introducing a non-symmetry into the rotordynamics which can serve as an indicator for rotor health monitoring.

Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry

2011 ◽  
Vol 226 (5) ◽  
pp. 1254-1262 ◽  
Author(s):  
S-J Jang ◽  
J W Kim ◽  
Y J Choi
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Geometrical Properties ◽  
Plane Vibration ◽  
Numerical Example ◽  
Mass Centre ◽  
Out Of Plane ◽  
Triangular Relationship ◽  
Elastically Supported

The geometrical properties of vibration modes of a single rigid body with one plane of symmetry are presented. When in-plane vibration modes are represented by the axes normal to the plane of symmetry, three intersecting points of those axes and the plane of symmetry constitute two triangles whose orthocentres are coincident with the mass centre and planar couple point, while the induced wrenches of three out-of-plane modes are found to form two triangles whose orthocentres are lying on the mass centre and the perpendicular translation point. Examining these triangles reveals that the triangular areas are proportional to the distributions of the mass and stiffness in the vibrating system and the shapes of the triangles are related to the natural frequencies. A numerical example is provided to verify the proposed findings.

Adaptive Boundary Control of Out-of-Plane Cable Vibration

1998 ◽  
Vol 65 (4) ◽  
pp. 963-969 ◽  
Author(s):  
H. Canbolat ◽  
D. Dawson ◽  
C. Rahn ◽  
S. Nagarkatti
Keyword(s):  
Boundary Control ◽  
Parametric Uncertainty ◽  
Adaptive Controller ◽  
Cable Tension ◽  
Flexible Cable ◽  
System Parameters ◽  
Plane Vibration ◽  
Exact Model ◽  
Out Of Plane ◽  
Adaptive Boundary Control

This paper develops active controllers for the out-of-plane vibration of a flexible cable using boundary actuators and sensors. An exact model knowledge controller exponentially stabilizes the cable displacement assuming known system parameters. An adaptive controller asymptotically stabilizes the cable displacement while compensating for parametric uncertainty in the actuator mass and cable tension. The performance of the controllers is experimentally demonstrated.

Free Out-of-Plane Vibration of a Ring Elastically Supported at Several Points

1982 ◽  
Vol 49 (4) ◽  
pp. 854-860 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
H. Okada
Keyword(s):  
Differential Equation ◽  
Infinite Series ◽  
Natural Frequencies ◽  
Circular Ring ◽  
Mode Shapes ◽  
Matrix Differential Equation ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Matrix Differential ◽  
Elastically Supported

An analysis is presented for the free out-of-plane vibration of a circular ring elastically supported against deflection, rotation, and torsion at several points located at equal angular intervals. The equations of out-of-plane vibration of the ring is expressed as a matrix differential equation by using the transfer matrix, the solution to which is conveniently given by infinite series. The vibrations arising in the ring are classified into several types, for each of which the natural frequencies and the mode shapes are calculated numerically up to higher modes.

FREE VIBRATIONS OF SHEAR DEFORMABLE CIRCULAR CURVED BEAMS RESTING ON ELASTIC FOUNDATIONS

2002 ◽  
Vol 02 (01) ◽  
pp. 77-97 ◽  
Author(s):  
BYOUNG KOO LEE ◽  
SANG JIN OH ◽  
KWANG KYOU PARK
Keyword(s):  
Shear Deformation ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Rotary Inertia ◽  
Transverse Shear Deformation ◽  
Curved Beams ◽  
System Parameters ◽  
Elastic Foundations ◽  
Out Of Plane ◽  
Shear Deformable

The governing differential equations for the out-of-plane, free vibration of circular curved beams resting on elastic foundations are derived and solved numerically. The formulation takes into consideration the effects of rotary inertia and transverse shear deformation. The lowest three natural frequencies are calculated for beams with hinged–hinged, hinged-clamped, and clamped–clamped end constraints. The effects of various system parameters as well as rotary inertia and shear deformation on the natural frequencies are investigated.

On the Natural Frequencies of a Flexible Manipulator with a Tip Payload

2005 ◽  
Vol 219 (11) ◽  
pp. 1199-1205 ◽  
Author(s):  
D C D Oguamanam ◽  
M Arshad
Keyword(s):  
Free Vibration ◽  
Parametric Study ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
Flexible Manipulator ◽  
Centre Of Mass ◽  
Bernoulli Beam ◽  
Torsional Deformation ◽  
Out Of Plane ◽  
Euler Bernoulli Beam

The free vibration of a flexible manipulator that is carrying a rigid payload at the tip is examined. The centre of mass of the payload may not coincide with the point of attachment to the manipulator. The manipulator is modelled as an Euler-Bernoulli beam and it undergoes both out-of-plane and in-plane elastic flexural deformations in conjunction with torsional deformation. The explicit expression of the characteristic (or frequency) equation is presented and a parametric study is provided.

Out-of-Plane Vibrations of a Stepped Euler-Bernoulli Beam Clamped to a Rotating Hub

2001 ◽  
Author(s):  
S. Naguleswaran
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Unit Length ◽  
Frequency Equation ◽  
Bernoulli Beam ◽  
System Parameters ◽  
Out Of Plane ◽  
Finite Element Procedure ◽  
Euler Bernoulli Beam

Abstract This paper is concerned with the vibrations of an Euler-Bernoulli stepped cantilever, clamped to a hub rotating at a constant speed. The system parameters are: the speed of rotation of the hub, the position of the step, the ratio of the mass per unit length of the two portions of the beam and the ratio of the flexural rigidity. Analytical solution of the mode shape differential equations for out-of-plane vibrations (normal to the plane of rotation) is developed. The frequency equation is expressed as a 4th order determinant equated to zero. A scheme is presented to derive the natural frequencies. The first three frequencies are tabulated for various combinations of the system parameters. Published results (which were obtained via finite element procedure) are compared with the analytical results.

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.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

Sign in / Sign up

Export Citation Format

Share Document