Natural Frequencies of a Railroad Track

1987 ◽  
Vol 54 (2) ◽  
pp. 299-304 ◽  
Author(s):  
S. P. Patil
Keyword(s):  
Natural Frequency ◽  
Elastic Layer ◽  
Natural Frequencies ◽  
Unit Length ◽  
Added Mass ◽  
Winkler Foundation ◽  
Railroad Track

The natural frequency of an infinite railroad track was first determined by Timoshenko as ωR = √k/m, where k is the constant for the massless Winkler foundation and m is the mass per unit length of the rail. The natural frequencies of the track are determined here by modeling the track as a beam resting on a 3-D inertial elastic layer. It is shown that the mass of the supporting foundation has a significant effect on the natural frequencies of a railroad track. Finally, the concept of “added mass” is introduced in order to determine the natural frequency in a desired mode of vibration, by modeling the track as a beam on the massless Winkler foundation and adding the mass of the foundation to the beam.

Mode Coupling in Torsional and Longitudinal Shafting Vibrations

1983 ◽  
Vol 20 (03) ◽  
pp. 257-271
Author(s):  
Michael G. Parsons
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Longitudinal Vibration ◽  
Added Mass ◽  
Mode Shapes ◽  
Regression Equations ◽  
Vibration Problem ◽  
Vibratory Response ◽  
Marine Propulsion ◽  
Coupling Characteristics

The effect of propeller coupling on the torsional and longitudinal vibration of marine propulsion shafting is studied. Recent research on the nature and computation of propeller added mass and damping is reviewed. It is now possible to estimate the inertia coupling and velocity coupling characteristics which couple the torsional and longitudinal vibration of a marine propeller. Regression equations suitable for estimating the torsional and longitudinal added mass and damping of 4-, 5-, 6-, and 7-bladed Wageningen B-Series propellers are presented in the Appendix. The torsional and longitudinal modeling of a typical marine propulsion plant is reviewed. The numerical techniques and computer programs used in solving the free vibration problem for natural frequencies and mode shapes and the forced vibration problem for vibratory response are introduced. Results for a realistic numerical example are presented to compare the natural frequencies, mode shapes, and vibratory response which are obtained when the propeller coupling is neglected with those obtained with the propeller coupling included. In general, the natural frequencies are shown to change by less than 2 percent. The modes shapes can show significant change. Vibratory response can be either increased or decreased. Some cases show that neglecting the propeller coupling can result in more than a 50 percent underprediction of the vibratory response. The coupling effects are greatest when a torsional natural frequency obtained with the propeller coupling neglected and a longitudinal natural frequency obtained with the propeller coupling neglected converge.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

scholarly journals A Vibration-Based Structural Health Monitoring System for Transmission Line Towers

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 515 ◽  
Author(s):  
Long Zhao ◽  
Xinbo Huang ◽  
Ye Zhang ◽  
Yi Tian ◽  
Yu Zhao
Keyword(s):  
Structural Health Monitoring ◽  
Transmission Line ◽  
Natural Frequency ◽  
Health Monitoring ◽  
Structural Changes ◽  
Natural Frequencies ◽  
Transmission Tower ◽  
Health Monitoring System ◽  
Wind Speeds ◽  
Before And After

In this paper, we present a vibration-based transmission tower structural health monitoring system consisting of two parts that identifies structural changes in towers. An accelerometer group realizes vibration response acquisition at different positions and reduces the risk of data loss by data compression technology. A solar cell provides the power supply. An analyser receives the data from the acceleration sensor group and calculates the transmission tower natural frequencies, and the change in the structure is determined based on natural frequencies. Then, the data are sent to the monitoring center. Furthermore, analysis of the vibration signal and the calculation method of natural frequencies are proposed. The response and natural frequencies of vibration at different wind speeds are analysed by time-domain signal, power spectral density (PSD), root mean square (RMS) and short-time Fouier transform (STFT). The natural frequency identification of the overall structure by the stochastic subspace identification (SSI) method reveals that the number of natural frequencies that can be calculated at different wind speeds is different, but the 2nd, 3rd and 4th natural frequencies can be excited. Finally, the system was tested on a 110 kV experimental transmission line. After 18 h of experimentation, the natural frequency of the overall structure of the transmission tower was determined before and after the tower leg was lifted. The results show that before and after the tower leg is lifted, the natural frequencies of each order exhibit obvious changes, and the differences in the average values can be used as the basis for judging the structural changes of the tower.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

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.

PNEUMATIC VIBROISOLATION SYSTEM OF THE BASE DESK WITH NATURAL FREQUENCY REGULATION

2021 ◽  
Vol 113 ◽  
pp. 91-100
Author(s):  
Radka JÍROVÁ ◽  
Lubomír PEŠÍK
Keyword(s):  
Natural Frequency ◽  
Automotive Industry ◽  
Natural Frequencies ◽  
Dynamical Behaviour ◽  
Operating Conditions ◽  
Frequency Regulation ◽  
The Stability ◽  
Short Time

Vibroisolation systems of base desks for machine and testing facilities usually cannot effect efficient changing of their own frequencies according to operating conditions. Especially in the case of the automotive industry, the possibility of changing natural frequencies is very desirable. During varying operating conditions, the vibroisolation system needs to be regulated easily and quickly regarding the minimisation of dynamical forces transmitted to the ground and to ensure the stability of the testing process. This paper describes one of the options of tuning the base desk at a relatively short time and by sufficient change of own frequencies, which decides the dynamical behaviour of the whole system.

scholarly journals Identification of Corrosion on a Hollow Tube Using Vibration

2014 ◽  
Vol 564 ◽  
pp. 176-181
Author(s):  
S.T. Cheng ◽  
Nawal Aswan Abdul Jalil ◽  
Zamir A. Zulkefli
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Impact Loading ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Localized Corrosion ◽  
Free Boundary Conditions ◽  
The Impact ◽  
Impact Vibration

Vibration based technique have so far been focused on the identification of structural damage. However, not many studies have been conducted on the corrosion identification on pipes. The objective of this paper is to identify corrosion on pipes from vibration measurements. A hollow pipe, 500 mm in length with 63.5 mm in diameter was subjected to impact loading using an impact hammer to identify the natural frequency of the tube in two conditions i) without any corrosion and ii) with an induced localized 40 mm by 40 mm corrosion at the middle of the pipe. The shift of natural frequencies of the structures under free boundary conditions was examined for each node of excitation. The results showed that there is a shift in natural frequency of the pipe, between 3 and 4 Hz near to the corrosion area. It can suggested that that the impact vibration is capable of identifying of localized corrosion on a hollow tube.

A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

1962 ◽  
Vol 66 (616) ◽  
pp. 240-241 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Present Note ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Electronic Digital Computer ◽  
Isotropic Plates ◽  
Four Corners ◽  
Square Plate

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

Speed Dependency of Coupled Rotor-Blade Torsional Natural Frequencies

2013 ◽  
Author(s):  
Ulrich Ehehalt ◽  
Balazs Becs ◽  
Xiaoping Zhou ◽  
Stefan Güllenstern
Keyword(s):  
Natural Frequency ◽  
Rotor Blade ◽  
Natural Frequencies ◽  
Low Pressure ◽  
Campbell Diagram ◽  
Calculation Results ◽  
Measured Speed ◽  
High Level ◽  
Blade Model ◽  
Proper Analysis

The natural frequencies of blades depend on the rotational speed of the rotor train as the stiffness changes with centrifugal loading. In the case of low pressure turbines with shrunk-on-disc design the coupled rotor-blade torsional natural frequencies can also show this property. For proper analysis of the speed dependency, a complete rotor-blade model which takes the elasticity of the blades into account is required. In this paper the torsional natural frequencies calculated with a complete rotor-blade model are compared with those calculated with a model in which blade elasticity is not included. The analysis clearly demonstrates that calculations without blade elasticity lead to different natural frequencies. By modeling the complete rotor and taking blade elasticity into account, it is demonstrated that the torsional natural frequencies of a complete rotor-blade model can also become speed dependent. As a consequence, a distinction between the natural frequencies at nominal speed and natural frequency at critical speeds becomes necessary. In the following, measured torsional natural frequencies at different rotating speeds of an individual low pressure rotor are presented. A comparison of the measured speed dependency of the torsional natural frequency with calculation results thereby taking the blade elasticity into account is conducted. The analysis shows that the measured speed dependency can be predicted with a high level of accuracy and can become important for modes which are dominated by the blades of the last stages. As a consequence of this analysis, a clear distinction between natural frequency at nominal and at critical speed has to be made for certain rotor and blade designs. It is shown that the use of the Campbell diagram is highly beneficial for designing rotor trains with large blades with regard to their torsional vibration behavior.

Lateral Vibration of Two Axially Translating Beams Interconnected by a Winkler Foundation

2006 ◽  
Vol 129 (3) ◽  
pp. 380-385 ◽  
Author(s):  
Mohamed Gaith ◽  
Sinan Müftü
Keyword(s):  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Mode Shapes ◽  
Winkler Foundation ◽  
Axial Tension ◽  
Winkler Elastic Foundation ◽  
Critical Tension ◽  
Divergence Instability ◽  
Axially Moving Beams ◽  
Axially Moving

Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. The natural frequencies and associated mode shapes are obtained. The natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at a critical velocity and a critical tension; and, divergence and flutter instabilities coexist at postcritical speeds, and divergence instability takes place precritical tensions. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams are presented.

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