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.

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.

Fluid Added Mass Effect in the Modal Response of a Pump-Turbine Impeller

2009 ◽  
Author(s):  
Eduard Egusquiza ◽  
Carme Valero ◽  
Quanwei Liang ◽  
Miguel Coussirat ◽  
Ulrich Seidel
Keyword(s):  
Natural Frequencies ◽  
Experimental Tests ◽  
Mass Effect ◽  
Added Mass ◽  
Mode Shapes ◽  
Pump Turbine ◽  
Modal Response ◽  
Surrounding Fluid ◽  
Turbine Impeller ◽  
Good Agreement

In this paper, the reduction in the natural frequencies of a pump-turbine impeller prototype when submerged in water has been investigated. The impeller, with a diameter of 2.870m belongs to a pump-turbine unit with a power of around 100MW. To analyze the influence of the added mass, both experimental tests and numerical simulations have been carried out. The experiment has been performed in air and in water. From the frequency response functions the modal characteristics such as natural frequencies and mode shapes have been obtained. A numerical simulation using FEM (Finite Elements Model) was done using the same boundary conditions as in the experiment (impeller in air and surrounded by a mass of water). The modal behaviour has also been calculated. The numerical results were compared with the available experimental results. The comparison shows a good agreement in the natural frequency values both in air and in water. The reduction in frequency due to the added mass effect of surrounding fluid has been calculated. The physics of this phenomenon due to the fluid structure interaction has been investigated from the analysis of the mode-shapes.

Natural Frequencies and Band Gaps of Periodically Corrugated Beams

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Rhamy Salim Bachour ◽  
Rodrigo Nicoletti
Keyword(s):  
Natural Frequencies ◽  
Periodic Structures ◽  
Dynamic Properties ◽  
Band Gaps ◽  
Transverse Waves ◽  
Large Bandwidth ◽  
Straight Beam ◽  
Propagating Waves ◽  
Corrugated Beam ◽  
Straight Segments

Abstract Structures with geometric periodicity can present interesting dynamic properties like stop and pass frequency bands. In this case, the geometric periodicity has the effect of filtering the propagating waves in the structure, in a similar way to that of phononic crystals and metamaterials (non-homogeneous materials). Hence, by adopting such structures, we can design systems that present dynamic characteristics of interest, e.g., with minimum dynamic response in a given frequency range with large bandwidth. In the present work, we show that corrugated beams also present the dynamic properties of periodic structures due to their periodic geometry only (no need of changing mass or material properties along the beam). Two types of corrugated beams are studied analytically: beams with curved bumps of constant radii and beams with bumps composed of straight segments. The results show that, as we change the proportions of the bump, the natural frequencies change and tend to form large band gaps in the frequency spectrum of the beam. Such shifting of the natural frequencies is related to the coupling between longitudinal and transverse waves in the curved beam. The results also show that it is possible to predict the position and the limits of the first band gap (at least) as a function of the fundamental frequency of the straight beam (without bumps), irrespective of the total length of the corrugated beam.

Managing Vortex Induced Vibration in Well Jumper Systems

2008 ◽  
Author(s):  
Kenneth Bhalla ◽  
Lixin Gong
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Cross Flow ◽  
Mitigation Measures ◽  
Mode Shapes ◽  
Bottom Current ◽  
Vortex Induced Vibration ◽  
Flow Response ◽  
Out Of Plane ◽  
Lock In

The purpose of this paper is to present a method that has been developed to identify if vortex induced vibration (VIV) occurs in well jumper systems. Moreover, a method has been developed to determine when VIV mitigation measures such as strakes are required. The method involves determining the in-plane and out-of-plane natural frequencies and mode shapes. The natural frequencies are then used, in conjunction with the maximum bottom current expected at a given location to determine if suppression is required. The natural frequency of a jumper system is a function of many variables, e.g. span length, leg height, pipe diameter and thickness, buoyancy placement, buoyancy uplift, buoyancy OD, insulation thickness, and contents of the jumper. The suppression requirement is based upon calculating a lower bound lock-in current speed based upon an assumed velocity bandwidth centered about the lock-in current. The out-of-plane VIV cross-flow response is produced by a current in the plane of the jumper; whereas the in-plane VIV cross-flow response is produced by the out-of-plane current. Typically, the out-of-plane natural frequency is smaller than the in-plane natural frequency. Jumpers with small spans have higher natural frequencies; thus small span jumpers may require no suppression or suppression on the vertical legs. Whereas, larger span jumpers may require no suppression, suppression on the vertical legs or suppression on all the legs. The span of jumper systems (i.e. production, water injection, gas lift/injection ...) may vary in one given field; it has become apparent that not all jumper systems require suppression. This technique has allowed us to recognize when certain legs of a given jumper system may require suppression, thus leading to a jumper design whose safety is not compromised while in the production mode, as well as minimizing downtime and identifying potential savings from probable fatigue failures.

Dynamic Analysis of an Elevator Traveling Cable Using a Singularity-Free Beam Formulation

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
W. Fan ◽  
W. D. Zhu
Keyword(s):  
Dynamic Analysis ◽  
Multibody Dynamics ◽  
Natural Frequencies ◽  
Vertical Motion ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Forced Responses ◽  
Free Beam ◽  
Good Agreement

A round elevator traveling cable is modeled using a singularity-free beam formulation. Equilibria of the traveling cable with different elevator car positions are studied. Natural frequencies and the corresponding mode shapes of the traveling cable are calculated and they are in excellent agreement with those calculated by abaqus. In-plane natural frequencies of the traveling cable do not change much with the car position compared with its out-of-plane ones. Dynamic responses of the traveling cable are calculated and they are in good agreement with those from commercial multibody dynamics software recurdyn. Effects of vertical motion of the car on free responses of the traveling cable and those of in-plane and out-of-plane building sways on forced responses are investigated.

INVESTIGATION OF THE PLANE VIBRATION OF AN ELASTIC PLATE WITH A KINEMATIC VIBRATION PROTECTION SYSTEM

2021 ◽  
Vol 75 (3) ◽  
pp. 44-50
Author(s):  
К. Bissembayev ◽  
◽  
Z. Omyrzhanova ◽  
K. Sultanova ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Natural Frequency ◽  
Elastic Plate ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Rolling Contact ◽  
Seismic Protection ◽  
Geometrical Parameters ◽  
Plane Vibration ◽  
Hamilton Principle

Creation of vibro-protective devices on rolling contact bearings is widely spread in transportation technology and seismic protection. In this work, mathematical modeling of the oscillation movements of the elastic plate will be considered. The equations of motion for elastic plate on vibration supports bounded by high-order rotation surfaces by the Ostrogradsky-Hamilton principle are obtained. The natural frequencies of elastic plate are determined. It is established that the value of the natural frequencies of elastic plate decreases with increasing height and increases with the width of the bases. The ratio of the natural frequency of the second form to the natural frequency of the first form does not depend on the geometrical parameters of the plate.

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.

Effects of Temperature Variation on Vibration of a Cable-Stayed Beam

2017 ◽  
Vol 17 (10) ◽  
pp. 1750123 ◽  
Author(s):  
Yaobing Zhao ◽  
Zhiqian Wang ◽  
Xiaoyu Zhang ◽  
Lincong Chen
Keyword(s):  
Thermal Effect ◽  
Temperature Variation ◽  
Natural Frequencies ◽  
Dominant Role ◽  
Plane Motion ◽  
Tension Force ◽  
Effect Of Temperature ◽  
Stiffness Ratio ◽  
Initial Tension ◽  
Out Of Plane

This paper is concerned with the temperature effect on the vibration of a cable-stayed beam. The thermal effect is considered by using two non-dimensional factors for the cable tension force and sag. The nonlinear in-plane and out-of-plane vibration equations of motion of the cable-stayed beam with thermal effect are derived by using the extended Hamilton’s principle. Eigenvalue analysis is performed to obtain closed-form eigenvalue solutions. It is shown that the effect of temperature variation plays a dominant role on the vibration behavior of the cable-stayed beam, and the effect is closely related with the initial tension force and the stiffness ratio. As to the in-plane motion, both positive and negative correlations between the temperature variations and natural frequencies are found, which depend on the mode order and the stiffness ratio of the cable-stayed beam. However, as to the out-of-plane motion, there only exist negative correlations between the temperature variation and natural frequencies, and the effect of temperature dropping condition seems more obvious. Moreover, both for the in-plane and out-of-plane motions, the locations of veering points between two natural frequencies are shifted under the thermal effect, which can significantly affect the internal resonance between different modes of the cable-stayed beam.

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.

Natural Frequencies of Stator in Induction Motors

1997 ◽  
Author(s):  
Isao Suzuki ◽  
Shinichi Noda ◽  
Kazunobu Itomi ◽  
Fuminori Ishibashi
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Induction Motors ◽  
Fem Analysis ◽  
Stator Core ◽  
Second Stage ◽  
Contact Surfaces ◽  
Natural Frequency Analysis ◽  
Spring Constants ◽  
Good Agreement

Abstract Totally enclosed induction motors in which the stator core is pressed in the frame are in general used in industrial machines and manufactured with similar construction around the world. These motors produce a strong electromagnetic noise, which is caused by resonance between the natural frequencies of the stator core and the harmonics of electromagnetic forces. Therefore, it is very important to estimate its natural frequencies at the stage of design. As the first stage of research to estimate the natural frequencies of the stator core pressed into the motor frame, the dual rings were chosen as the object of studies. They are similar to the motor in construction and are easy to use to solve the problems. The purpose of this study is to investigate the effects of the tight fit to the natural frequencies and to find an analytical method by FEM. The authors have found that the introduction of spring elements with radial and circumferential spring constants at the contact surfaces provides accurate calculated results of the natural frequency by FEM. This paper describes about the spring constants obtained from experiments and analysis. As a result, when the spring constants in the radial direction are infinite and those in the circumferential direction are variable, it is clear that the spring constants for natural frequency analysis by FEM were expressed as a function of contact pressure on the contact surfaces. In the second stage, the measurement and calculation of natural frequency in the actual stator core with a frame was performed, and these results showed good agreement. These spring constants will be useful in FEM analysis of stator cores pressed into cylindrical induction motor frames.

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