scholarly journals Calculation of natural frequencies and damping coefficients of a multi-layered composite using homogenization theory ⁎ ⁎This work was supported by the Russian Science Foundation under grant 16-11-10343.

2018 ◽  
Vol 51 (2) ◽  
pp. 126-131 ◽  
Author(s):  
Alexey S. Shamaev ◽  
Vladlena V. Shumilova
Keyword(s):  
Natural Frequencies ◽  
Layered Composite ◽  
Homogenization Theory ◽  
Russian Science ◽  
Damping Coefficients

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads

2010 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul E. Allaire ◽  
John C. Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to non-synchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are considered using a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced non-synchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

scholarly journals Rayleigh Damping Coefficients of Laminated Rubber Bearing

2019 ◽  
Vol 8 (4) ◽  
pp. 12294-12300
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Ground Structure ◽  
Damping Coefficients ◽  
Rubber Bearing ◽  
Stability And Instability ◽  
Laminated Rubber Bearing

In isolating the ground structure and the above ground structure from seismic loads, a significant device called laminated rubber bearing is usually found in structure. The complexity of the material which is made up from a combination of rubber and steel shim plates in alternate layer, has made it difficult to measure damping value. Damping is a dissipation of energy or energy losses in the vibration of the structure. Measuring the accurate amount of damping is fundamental as damping plays a crucial role in fixing the borderline between stability and instability in structural systems. Therefore, to determine the damping value including dynamic properties in any materials, modal analysis can be used. Hence, the main objective of this research is to determine the Rayleigh’s damping coefficients α and β and to evaluate the performance of the laminated rubber bearing using finite element and experimental modal analysis. Finding shows that, the finite element modal analysis with the addition of Rayleigh’s damping coefficients α and β, shows a good agreement with the experimental modal analysis in term of natural frequencies and mode shapes. Findings show that, the values of natural frequencies reduced when precise Rayleigh’s damping coefficient added in the finite element modal analysis. It can be concluded that both finite element and experimental modal analysis method can be used to estimate the accurate values of damping ratio and to determine the Rayleigh’s damping coefficients α and β as well.

Dynamics of a Three Level Rotor System Using Solid Elements

2003 ◽  
Author(s):  
J. S. Rao ◽  
R. Sreenivas
Keyword(s):  
Natural Frequencies ◽  
Rotor System ◽  
Support Structures ◽  
Campbell Diagram ◽  
Critical Speeds ◽  
Spin Speed ◽  
Damping Coefficients ◽  
Stiffness And Damping

This paper discusses the interaction of support structures on the dynamics of a dual rotor system. The system considered is a dual rotor, supported on flexible bearings, which are in turn mounted in a flexible casing. ANSYS® is used for modeling and meshing the dual rotors and the casing. The rotors are modeled using solid elements. The bearings are simulated as springs, wherein the direct and cross coupled stiffness and damping coefficients are applied. The casing is also modeled and meshed in ANSYS® using solid elements. Different spin speeds are applied to the dual rotor system. The casing is also rotated at a zero spin speed. The Stress stiffening and spin softening options are also set on for the dual rotor system. The system natural frequencies are obtained for different spin speeds and the Campbell diagram of the system is plotted. The critical speeds due to per revolution excitations are then extracted from the Campbell diagram.

Dynamic Properties of a Heliostat Structure Determined by Numerical and Experimental Modal Analysis

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
J. Felipe Vásquez-Arango ◽  
Reiner Buck ◽  
Robert Pitz-Paal
Keyword(s):  
Modal Analysis ◽  
Vortex Shedding ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Simple Approach ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Fe Model ◽  
Damping Coefficients ◽  
Operating Points

An experimental and numerical modal analysis was performed on an 8 m2 T-shaped heliostat structure at different elevation angles. The experimental results were used to validate a finite element (FE) model by comparing natural frequencies and mode shapes. The agreement between experiments and simulations is good in all operating points investigated. In addition, damping coefficients were determined experimentally for each mode, in order to provide all necessary information for the development of a dynamic model. Furthermore, potentially critical operating conditions caused by vortex shedding were identified using a simple approach.

scholarly journals Computation of Rayleigh damping coefficient of a rectangular submerged floating tunnel (SFT)

2020 ◽  
Vol 2 (5) ◽  
Author(s):  
Md. Hafizur Rahman ◽  
Chhavi Gupta
Keyword(s):  
Dynamic Analysis ◽  
Modal Analysis ◽  
Fundamental Frequency ◽  
Significant Role ◽  
Analytical Study ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Damping Coefficients ◽  
Rayleigh Damping ◽  
Submerged Floating Tunnel

Abstract The dynamic behaviors of the submerged floating tunnel, a buoyant structure of high slenderness, are a matter of concern since it is surrounded by the huge hazardous effects called hydrodynamic, seismic and functional action. Modal analysis and Rayleigh damping coefficients play a significant role in dynamic analysis, but it is not sufficiently simple to predict the reasonable damping coefficients named α and β. The present paper outlines the modal analysis and the calculation of Rayleigh damping coefficients that provide the natural frequencies, mode shapes, mode’s motion as well as coefficients α and β. To compute the Rayleigh damping coefficients, 2–10% damping to the critical damping has been assumed for this analytical study. For the analysis, an FEA-based software ANSYS is utilized successfully. It has been seen that the fundamental frequency and Rayleigh damping coefficients (α = 0.946 and β = 0.00022) of the SFT are reasonably high and it is under noticeable damping.

Dynamics of Continuous-Mode Icebreaking by a Polar-Class Hull—Part 2: Spectral Analysis

1989 ◽  
Vol 33 (03) ◽  
pp. 236-251
Author(s):  
Frederick Stern ◽  
Robert Ettema ◽  
Javier Lazaro
Keyword(s):  
Reasonable Agreement ◽  
Natural Frequencies ◽  
Ice Sheet ◽  
Added Mass ◽  
Dominant Frequency ◽  
Towing Tank ◽  
Damping Coefficients ◽  
Series Of Experiments ◽  
The Mean ◽  
Scale Data

Part 2 of this two-part paper presents additional results from an ice towing-tank study of a Polar-Class hull for two conditions: for one, the hull was free to pitch, heave, and undergo limited roll (free hull); for the other, the hull was restrained from motions (fixed hull). Measurements were made of resistance as well as motions and restraining forces and moments for the free-and fixed-hull conditions, respectively. In Part 1, the values of the mean and standard deviation for both conditions are compared and related to observed patterns of icebreaking. In Part 2, the spectral densities are examined with regard to the natural frequencies of hull motions and frequencies associated with icebreaking pattern to determine the dominant cycles of resistance and motions. A series of experiments was conducted to determine values of zero-speed natural frequencies and added-mass and damping coefficients for ice-covered conditions. The presence of an ice sheet significantly reduces the natural frequencies and increases the added-mass and damping coefficients. It was found that hull motions and icebreaking pattern determined the dominant cycles of resistance for the free hull. Icebreaking frequency, the frequency of individual breaking events, was significant only for thin ice such that significant heave and pitch did not occur. When w b was less than the natural frequencies of coupled heave and pitch amid ice, w the dominant frequency of resistance and motions occurred at integral fractions of usually b/2. The frequencies, (b/n, are associated with the icebreaking pattern, that is, cyclic manner by which hull trim changed as the hull broke and cleared a track through an ice sheet. When b equaled or exceeded to„, the dominant frequency of resistance coincided with The fixed hull responded at higher frequencies than the free hull, usually at u>0. Also, available full-scale data are shown to be in reasonable agreement with the present results for the free hull. Lastly, the principal conclusions of the overall study are summarized and the implications of the present work with regard to the development of prediction methods are discussed.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness, and Different Pad Preloads

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Timothy Dimond ◽  
Amir A. Younan ◽  
Paul Allaire ◽  
John Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to nonsynchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are compared to a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced nonsynchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two-degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part II: Effect of Tilt-Pad Bearings and Foundation Dynamics

1987 ◽  
Vol 109 (1) ◽  
pp. 8-14 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Critical Speed ◽  
Natural Frequencies ◽  
State Of The Art ◽  
Dynamic Properties ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Speed Prediction ◽  
Bearing Stiffness ◽  
Stiffness And Damping

This is the second of two papers describing results of a research project directed at verifying computer programs used to calculate critical speeds of turbomachinery. This part describes measurements made to determine the characteristics of tilt-pad bearings and foundation dynamics. Critical speeds of a 166 kg laboratory rotor on tilt-pad bearings are then compared with predictions from a state-of-the-art damped eigenvalue computer program. Measured natural frequencies of a steam turbine are also compared with computer predictions. Accuracy of critical speed prediction is shown to depend on accuracy of 1) the “free-free” rotor models, 2) the bearing stiffness and damping coefficients, and 3) the dynamic properties of the foundation, which can be represented by an impedance that must be determined by experimental measurements.

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