Galerkin methods for natural frequencies of high-speed axially moving beams

2010 ◽  
Vol 329 (17) ◽  
pp. 3484-3494 ◽  
Author(s):  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
High Speed ◽  
Natural Frequencies ◽  
Galerkin Methods ◽  
Axially Moving Beams ◽  
Axially Moving

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.

scholarly journals Parametric Vibrations of Axially Moving Beams with Multiple Edge Cracks

2019 ◽  
Vol 24 (2) ◽  
pp. 241-252 ◽  
Author(s):  
Murat Sarıgül
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Multiple Cracks ◽  
Mean Velocity ◽  
Beam System ◽  
Crack Tips ◽  
Axially Moving Beams ◽  
Edge Cracks ◽  
Axially Moving

Nonlinear transverse vibrations of axially moving beams with multiple cracks is handled studied. Assuming that the beam moves with mean velocity having harmonically variation, influence of the edge crack on the moving continua are investigated in this study. Due to existence of the crack in the transverse direction, the healthily beam is divided into parts. The translational and rotational springs are replaced between these parts so that high stressed regions around the crack tips are redefined with the springs' energies. Thus, the problem is converted to an axially moving spring-beam system. The equations of motion and its corresponding conditions are obtained by means of the Hamilton Principle. In numerical analysis, the natural frequencies and responses of the spring-beam system are investigated for principal parametric resonance in detail. Some important results are obtained; the natural frequencies decreases with increasing crack depth. In case of the beam travelling with high velocities, the effects of crack's depth on natural frequencies seems to be vanished.

Transverse Vibration of Two Axially Moving Beams Connected by an Elastic Foundation

2005 ◽  
Author(s):  
Mohamed Gaith ◽  
Sinan Mu¨ftu¨
Keyword(s):  
Elastic Foundation ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Beam Theory ◽  
Mode Shapes ◽  
Winkler Elastic Foundation ◽  
Canonical State ◽  
Axially Moving Beams ◽  
Axially Moving

Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The system is a model of paper and paper-cloth (wire-screen) used in paper making. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. Due to the effect of translation, the dynamics of the system displays gyroscopic motion. The Euler-Bernoulli beam theory is used to model the deflections, and the governing equations are expressed in the canonical state form. The natural frequencies and associated mode shapes are obtained. It is found that 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 the critical velocity; and, the frequency-velocity relationship is similar to that of a single traveling beam. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams, as well as the effects of the elastic foundation stiffness are investigated.

On the Vibration of Coupled Traveling String and Air Bearing Systems

1996 ◽  
Vol 118 (3) ◽  
pp. 398-405 ◽  
Author(s):  
A. V. Lakshmikumaran ◽  
J. A. Wickert
Keyword(s):  
High Speed ◽  
Natural Frequencies ◽  
Nodal Point ◽  
Fold Increase ◽  
Computational Effort ◽  
Air Pressure ◽  
Mode Shapes ◽  
Air Bearing ◽  
Design Variables ◽  
Axially Moving

Air bearings are used to position and guide such axially-moving materials as high speed magnetic tapes, paper sheets, and webs. In each case, vibration of the moving medium couples with the air bearing’s dynamics, and techniques are developed here to reduce the computational effort that is required to predict the natural frequencies, damping ratios, and vibration modes of the prototypical traveling string and self-pressurized air bearing model. Automatic nodal point allocation reduces the number of nonlinear equations that arise in finding the equilibrium string displacement and air pressure, and in subsequent vibration analysis, the response is obtained in closed form by using the Green’s function for the traveling string. Global discretization of the air pressure alone then yields a matrix eigenvalue problem which is simpler than that obtained through previous methods which required discretization of both displacement and pressure. Overall, essentially a five-fold increase in computational speed is achieved, thus facilitating design and parameter studies. Changes in the natural frequencies, damping ratios, and coupled displacement-pressure mode shapes with respect to several design variables are discussed and compared with experiments.

Dynamic model for high-speed rotors based on their experimental characterization

2017 ◽  
Vol 2 (4) ◽  
pp. 25
Author(s):  
L. A. Montoya ◽  
E. E. Rodríguez ◽  
H. J. Zúñiga ◽  
I. Mejía
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Experimental Characterization ◽  
Rotating Systems ◽  
Computing Performance ◽  
The Impact ◽  
Stiffness Distribution ◽  
Good Agreement

Rotating systems components such as rotors, have dynamic characteristics that are of great importance to understand because they may cause failure of turbomachinery. Therefore, it is required to study a dynamic model to predict some vibration characteristics, in this case, the natural frequencies and mode shapes (both of free vibration) of a centrifugal compressor shaft. The peculiarity of the dynamic model proposed is that using frequency and displacements values obtained experimentally, it is possible to calculate the mass and stiffness distribution of the shaft, and then use these values to estimate the theoretical modal parameters. The natural frequencies and mode shapes of the shaft were obtained with experimental modal analysis by using the impact test. The results predicted by the model are in good agreement with the experimental test. The model is also flexible with other geometries and has a great time and computing performance, which can be evaluated with respect to other commercial software in the future.

scholarly journals Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4705
Author(s):  
Julian Lich ◽  
Tino Wollmann ◽  
Angelos Filippatos ◽  
Maik Gude ◽  
Juergen Czarske ◽  
...  
Keyword(s):  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Fiber Reinforced ◽  
Structural Dynamic ◽  
Spatially Resolved ◽  
Glass Fiber Reinforced ◽  
Vibration Responses ◽  
And Performance

Due to their lightweight properties, fiber-reinforced composites are well suited for large and fast rotating structures, such as fan blades in turbomachines. To investigate rotor safety and performance, in situ measurements of the structural dynamic behaviour must be performed during rotating conditions. An approach to measuring spatially resolved vibration responses of a rotating structure with a non-contact, non-rotating sensor is investigated here. The resulting spectra can be assigned to specific locations on the structure and have similar properties to the spectra measured with co-rotating sensors, such as strain gauges. The sampling frequency is increased by performing consecutive measurements with a constant excitation function and varying time delays. The method allows for a paradigm shift to unambiguous identification of natural frequencies and mode shapes with arbitrary rotor shapes and excitation functions without the need for co-rotating sensors. Deflection measurements on a glass fiber-reinforced polymer disk were performed with a diffraction grating-based sensor system at 40 measurement points with an uncertainty below 15 μrad and a commercial triangulation sensor at 200 measurement points at surface speeds up to 300 m/s. A rotation-induced increase of two natural frequencies was measured, and their mode shapes were derived at the corresponding rotational speeds. A strain gauge was used for validation.

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