scholarly journals Spectral Dynamic Analysis of Torsional Vibrations of Thin-Walled Open Section Beams Restrained Against Warping at One End and Transversely Restrained at the Other End

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Chellapilla Kameswara Rao 1 ◽  
Lokavarapu Bhaskara Rao 2
Keyword(s):  
Dynamic Analysis ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
The Other ◽  
Graphical Form ◽  
Open Section ◽  
Torsional Frequency ◽  
Thin Walled ◽  
Spectral Frequency

The present paper deals with spectral dynamic analysis of free torsional vibration of doubly symmetric thin-walled beams of open section. Spectral frequency equation is derived in this paper for the case of rotationally restrained doubly-symmetric thin-walled beam with one end rotationally restrained and transversely restrained at the other end. The resulting transcendental frequency equation with appropriate boundary conditions is derived and is solved for varying values of warping parameter and the rotational and transverse restraint parameter. The influence of rotational restraint parameter, transverse restraint parameter and warping parameter on the free torsional vibration frequencies is investigated in detail. A MATLAB computer program is developed to solve the spectral frequency equation derived in this paper. Numerical results for natural frequencies for various values of rotational and transverse restraint parameters for various values of warping parameter are obtained and presented in both tabular as well as graphical form showing the influence of these parameters on the first fundamental torsional frequency parameter.

Torsional Vibration Analysis of Shafts With Sections of Tapered Diameter

1993 ◽  
Author(s):  
John R. Baker ◽  
Keith E. Rouch
Keyword(s):  
Torsional Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Displacement Function ◽  
The Other ◽  
Mode Shapes ◽  
Axial Distance ◽  
Rotational Degree ◽  
Rotor Systems ◽  
Constant Diameter

Abstract This paper presents the development of two tapered finite elements for use in torsional vibration analysis of rotor systems. These elements are particularly useful in analysis of systems that have shaft sections with linearly varying diameters. Both elements are defined by two end nodes, and inertia matrices are derived based on a consistent mass formulation. One element assumes a cubic displacement function and has two degrees of freedom at each node: rotation about the shaft’s axis and change in angle of rotation with respect to the axial distance along the shaft. The other element assumes a linear displacement function and has one rotational degree of freedom at each node. The elements are implemented in a computer program. Calculated natural frequencies and mode shapes are compared for both tapered shaft sections and constant diameter sections. These results are compared with results from an available constant diameter element. It is shown that the element derived assuming a cubic displacement function offers much better convergence characteristics in terms of calculated natural frequencies, both for tapered sections and constant diameter sections, than either of the other two elements. The finite element code that was developed for implementation of these elements is specifically designed for torsional vibration analysis of rotor systems. Lumped inertia, lumped stiffness, and gear connection elements necessary for rotor system analysis are also discussed, as well as calculation of natural frequencies, mode shapes, and amplitudes of response due to a harmonic torque input.

Dynamic Beam Modification Using Dimples

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
W. N. Cheng ◽  
C. C. Cheng ◽  
G. H. Koopmann
Keyword(s):  
Natural Frequencies ◽  
Design Method ◽  
Frequency Equation ◽  
Search Method ◽  
The Other ◽  
Impedance Method ◽  
Dimple Size ◽  
Straight Beam ◽  
Novel Method ◽  
Force Equilibrium

In this paper, a design method to modify the vibration characteristics of a beam by creating cylindrical dimples on its surface is investigated. In particular, the vibration response of a beam with several dimples is formulated using the impedance method. The dimpled beam is divided into two kinds of structural segments: one, a curved beam that is modeled as the dimple and the other, a straight beam. The frequency equation is derived by assembling the impedance of each structure segment based on conditions of force equilibrium and velocity compatibility. Then a novel method for shifting the natural frequencies of a beam to preassigned values by creating cylindrical dimples on this structure is introduced. The dimple size and its location on the structure can be determined analytically, so the time consuming process using the traditional optimal search method is thereby avoided. Several examples using this technique are demonstrated.

scholarly journals An analytical formulation to evaluate natural frequencies and mode shapes of high-rise buildings

2021 ◽  
Vol 8 (1) ◽  
pp. 307-318
Author(s):  
Giuseppe Nitti ◽  
Giuseppe Lacidogna ◽  
Alberto Carpinteri
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Shear Walls ◽  
Vertical Axis ◽  
Mode Shapes ◽  
Analytical Formulation ◽  
High Rise ◽  
Open Section ◽  
Stiffness Matrices ◽  
Thin Walled

Abstract In this paper, an original analytical formulation to evaluate the natural frequencies and mode shapes of high-rise buildings is proposed. The methodology is intended to be used by engineers in the preliminary design phases as it allows the evaluation of the dynamic response of high-rise buildings consisting of thin-walled closed- or open-section shear walls, frames, framed tubes, and dia-grid systems. If thin-walled open-section shear walls are present, the stiffness matrix of the element is evaluated considering Vlasov’s theory. Using the procedure called General Algorithm, which allows to assemble the stiffness matrices of the individual vertical bracing elements, it is possible to model the structure as a single equivalent cantilever beam. Furthermore, the degrees of freedom of the structural system are reduced to only three per floor: two translations in the x and y directions and a rigid rotation of the floor around the vertical axis of the building. This results in a drastic reduction in calculation times compared to those necessary to carry out the same analysis using commercial software that implements Finite Element models. The potential of the proposed method is confirmed by a numerical example, which demonstrates the benefits of this procedure.

The Torsional Vibration of Uniform Thin-Walled Beams of Open Section

1969 ◽  
Vol 73 (704) ◽  
pp. 672-674 ◽  
Author(s):  
J. B. Carr
Keyword(s):  
Torsional Vibration ◽  
Characteristic Functions ◽  
Shear Stresses ◽  
Simply Supported ◽  
Open Section ◽  
Torsional Resistance ◽  
Approximate Frequency ◽  
Thin Walled ◽  
Image Position ◽  
Fixed End

The pure torsional vibration of uniform thin-walled beams of open section, which is governed by the differential equation has been extensively analysed by Gere He derived the exact frequency equations for beams with a variety of end conditions. However, these equations are, in most cases, highly transcendental. This note uses an energy approach to obtain approximate frequency equations for the fixed-fixed and the fixed-simply-supported beams. A fixed end is one which allows no twist and no warping and a simply-supported end allows no twist but permits warping to take place freely. The approximating functions used are those corresponding to the exact solution of the problem if the torsional resistance caused by the St Venant system of shear stresses is zero. These functions are similar to the characteristic functions of simple beams in flexure.

Using Torsional Vibration Spectra to Monitor Machinery Rotor Integrity

2003 ◽  
Author(s):  
Gyo¨rgy Sza´sz ◽  
Edward J. Guindon
Keyword(s):  
Torsional Vibration ◽  
Natural Frequencies ◽  
Crack Size ◽  
Lateral Vibration ◽  
Turbine Generator ◽  
Frequency Shifts ◽  
Vibration Spectra ◽  
Hydro Turbine ◽  
Short Notice ◽  
Torsional Frequency

Machine degradation has become a key issue with respect to the operational and maintenance costs associated with industrial and power generation facilities. Current online techniques for monitoring rotor integrity are largely based on lateral overall vibration levels that may provide only a very short notice of impending failure. As an alternative, shifts in rotor torsional natural frequencies could be used as early indicators. Torsional vibration spectra have been gathered on numerous horizontal hydro turbine generator shafts at two Southern Company owned hydro plants. The data was trended for approximately 2 years and changes were compared against findings from visual and nondestructive testing. It was determined that in the very early stages of failure the torsional frequency shifts are minute and may be masked by or be indistinguishable from other phenomena but are detectable. As the degradation progresses, the frequencies shifts may increase greatly with the crack size and are easily discerned. While the degree of early warning capability based on this technique will more than likely vary with each failure occurrence, it should generally outperform existing lateral vibration based techniques.

Dynamic analysis of thin-walled open section beam under moving vehicle by transfer matrix method

2008 ◽  
Vol 30 (5) ◽  
pp. 603-617 ◽  
Author(s):  
Tianyu Xiang ◽  
Tengfei Xu ◽  
Xinpeng Yuan ◽  
Renda Zhao ◽  
Yuqiang Tong
Keyword(s):  
Dynamic Analysis ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Moving Vehicle ◽  
Open Section ◽  
Thin Walled

A modified Vlasov theory for dynamic analysis of thin-walled and variable open section beams

2000 ◽  
Vol 22 (8) ◽  
pp. 890-900 ◽  
Author(s):  
Ricardo Daniel Ambrosini ◽  
Jorge Daniel Riera ◽  
Rodolfo Francisco Danesi
Keyword(s):  
Dynamic Analysis ◽  
Open Section ◽  
Thin Walled ◽  
Vlasov Theory

Dynamic analysis of thin-walled and variable open section beams with shear flexibility

1995 ◽  
Vol 38 (17) ◽  
pp. 2867-2885 ◽  
Author(s):  
Ricardo Daniel Ambrosini ◽  
Jorge Daniel Riera ◽  
Rodolfo Francisco Danesi
Keyword(s):  
Dynamic Analysis ◽  
Open Section ◽  
Thin Walled

Critical Speeds of Geared Rotors by Including Mesh Stiffness and Using a Continuous System Model

1990 ◽  
Author(s):  
O. Sedat Sener ◽  
H. Nevzat Ozguven
Keyword(s):  
Dynamic Analysis ◽  
High Speed ◽  
Natural Frequencies ◽  
Continuous System ◽  
Transmission Error ◽  
System Model ◽  
Graphical Form ◽  
Critical Speeds ◽  
Gear Mesh ◽  
Dynamic Factors

Abstract Dynamic analysis of high speed gearing for the computation of critical speeds and dynamic factors is a must in a proper design, while some other dynamic characteristics of the system such as dynamic transmission error are to be determined for more critical designs. Numerous different models have been suggested for the dynamic analysis of geared systems. These models differ both in the effects included and in the basic assumptions made. A continuous system model is used in this analysis in order to determine the torsional natural frequencies of a gear shaft system composed of two gears, two shafts and two inertias representing the drive and the load. Gear mesh is modelled as a spring connected between two gears. The natural frequencies of the same system are also calculated by using a four degree of freedom classical discrete model in which shaft masses are ignored. The percentage differences in the natural frequencies calculated with the discrete and continuous system models are determined for several values of some nondimensional system parameters. The results are presented in graphical form in terms of the nondimensional parameters defined. Some conclusions which may be important for designers are drawn.

Free Vibrations of Thin Cylindrical Shells Having Finite Lengths With Freely Supported and Clamped Edges

1955 ◽  
Vol 22 (4) ◽  
pp. 547-552
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Frequency Equation ◽  
The Other ◽  
Lateral Vibration ◽  
Normal Functions ◽  
First Case ◽  
End Conditions ◽  
Good Agreement

Abstract Free vibrations of thin cylindrical shells having finite lengths are investigated on the basis of a set of three differential equations which are derived in a similar manner as Donnell obtained his equations for the bending and buckling problems. The equations can be solved readily after a simplifying assumption is introduced. In this manner the frequency equations are obtained for cylindrical shells with both edges freely supported, with both edges clamped, and with one edge freely supported and the other edge clamped. It is found that the lowest frequency given by the frequency equation is the smallest in the first case, larger in the third, and the largest in the second. The other two frequencies yielded by the frequency equation are approximately the same in all cases. As a result of the approximations, the characteristic equations for the three cases are found to be similar to the frequency equations for the lateral vibration of beams with similar end conditions. For the case of freely supported edges the normal functions obtained are identical in form with those assumed by Flügge and by Arnold and Warburton. For the same case, natural frequencies of one numerical example are computed by means of the present method, and the results are in good agreement with those obtained by these previous authors.

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