Second‐Order Instrumentation Systems with Frequency‐Dependent Stiffness and Damping

1959 ◽  
Vol 31 (11) ◽  
pp. 1457-1462 ◽  
Author(s):  
Eric Rule ◽  
Fred J. Suellentrop ◽  
Thomas A. Perls
Keyword(s):  
Second Order ◽  
Frequency Dependent ◽  
Stiffness And Damping

Frequency-Dependent Second-Order Hyperpolarizability of Carbon Clusters: A Semiempirical Investigation

1995 ◽  
Vol 117 (22) ◽  
pp. 6101-6108 ◽  
Author(s):  
Marianna Fanti ◽  
Giorgio Orlandi ◽  
Francesco Zerbetto
Keyword(s):  
Second Order ◽  
Carbon Clusters ◽  
Frequency Dependent

scholarly journals Rotordynamic Force Coefficients of Pocket Damper Seals

2006 ◽  
Vol 128 (4) ◽  
pp. 725-737 ◽  
Author(s):  
B. Ertas ◽  
A. Gamal ◽  
J. Vance
Keyword(s):  
Dynamic Pressure ◽  
Mechanical Impedance ◽  
Experimental Tests ◽  
Impedance Method ◽  
Force Density ◽  
Frequency Dependent ◽  
Force Coefficients ◽  
Cross Axis ◽  
Positive Direct ◽  
Stiffness And Damping

This paper presents measured frequency dependent stiffness and damping coefficients for 12-bladed and 8-bladed pocket damper seals (PDS) subdivided into four different seal configurations. Rotating experimental tests are presented for inlet pressures at 69 bar (1000 psi), a frequency excitation range of 20–300 Hz, and rotor speeds up to 20,200 rpm. The testing method used to determine direct and cross-coupled force coefficients was the mechanical impedance method, which required the measurement of external shaker forces, system accelerations, and motion in two orthogonal directions. In addition to the impedance measurements, dynamic pressure responses were measured for individual seal cavities of the eight-bladed PDS. Results of the frequency dependent force coefficients for the four PDS designs are compared. The conclusions of the tests show that the eight-bladed PDS possessed significantly more positive direct damping and negative direct stiffness than the 12-bladed seal. The results from the dynamic pressure response tests show that the diverging clearance design strongly influences the dynamic pressure phase and force density of the seal cavities. The tests also revealed the measurement of same-sign cross-coupled (cross-axis) stiffness coefficients for all seals, which indicate that the seals do not produce a destabilizing influence on rotor-bearing systems.

scholarly journals Rotordynamic Force Coefficients of Pocket Damper Seals

2006 ◽  
Author(s):  
B. Ertas ◽  
A. Gamal ◽  
J. Vance
Keyword(s):  
Dynamic Pressure ◽  
Mechanical Impedance ◽  
Impedance Method ◽  
Force Density ◽  
Frequency Dependent ◽  
Force Coefficients ◽  
Direct Stiffness ◽  
Cross Axis ◽  
Positive Direct ◽  
Stiffness And Damping

This paper presents measured frequency dependent stiffness and damping coefficients for 12 and 8 bladed pocket damper seals (PDS) subdivided into 4 different seal configurations. Rotating experimental test are presented for inlet pressures at 69 bar (1,000 psi), a frequency excitation range of 20–300 Hz, and rotor speeds up to 20,200 rpm. The testing method used to determine direct and cross-coupled force coefficients was the mechanical impedance method, which required the measurement of external shaker forces, system accelerations, and motion in two orthogonal directions. In addition to the impedance measurements, dynamic pressure responses were measured for individual seal cavities of the 8 bladed PDS. Results of the frequency dependent force coefficients for the 4 PDS designs are compared. The conclusions of the test show that the 8 bladed PDS possessed significantly more positive direct damping and negative direct stiffness than the 12 bladed seal. The results from the dynamic pressure response tests show that the diverging clearance design strongly influences the dynamic pressure phase and force density of the seal cavities. The tests also revealed the measurement of same-sign cross-coupled (cross-axis) stiffness coefficients for all seals, which indicate that the seals do not produce a de-stabilizing influence on rotor-bearing systems.

Frequency-Dependent Second Harmonic Generation in Acentric Chromophoric Self-Assembled NLO Materials

1994 ◽  
Vol 351 ◽  
Author(s):  
Shlomo Yitzchaik ◽  
Paul M. Lundquist ◽  
Weiping Lin ◽  
David R. Kanis ◽  
Mark A. Ratner ◽  
...  
Keyword(s):  
Second Harmonic Generation ◽  
Harmonic Generation ◽  
Self Assembly ◽  
Second Harmonic ◽  
Second Order ◽  
Frequency Dependent ◽  
Aligned Arrays ◽  
Nlo Materials ◽  
Charge Transfer Excitation ◽  
Self Assembled

ABSTRACTAn attractive and challenging approach to the construction of robust, thin film materials with large second-order optical nonlinearities is the covalent self-assembly of aligned arrays of high-β molecular chromophores into multilayer superlattices. In this paper, we describe the dispersion of second harmonic generation (SHG) in a self-assembled (SA) monolayer containing a stilbazolium chromophore. The frequency-dependent measurements were performed on 25 Å thick monolayers on glass using a tunable (0.4–2 μm) light source based on optical parametric amplification (OPA). The SHG spectrum contains a clear two-photon resonance at hω = 1.3eV. The maximum in the second-order susceptibility coincides with a low energy chromophore-centered charge-transfer excitation at 480 nm. The experimental SHG dispersion values compare favorably with theoretical results computed using a sum-over-states (SOS) formalism. However, the measured values exhibit a somewhat broader band response than the theoretical curve, and the origin of this behavior is discussed.

Static- and frequency-dependent NLO properties of dithienothiophene and thienothiophene bridges — A computational investigation

2020 ◽  
Vol 19 (05) ◽  
pp. 2050018
Author(s):  
Sagar B. Yadav ◽  
Nagaiyan Sekar
Keyword(s):  
Density Functional ◽  
Nonlinear Optical ◽  
Chemical Reactivity ◽  
Second Order ◽  
Basis Sets ◽  
Frequency Dependent ◽  
Nlo Properties ◽  
Reactivity Descriptors ◽  
Hartree Fock ◽  
Perturbation Potential

We have explored detailed linear and nonlinear optical properties of push-pull systems bearing thienothiophene and dithienothiophene spacers. By using density functional theory (DFT), frequency-dependent strategies were applied to examine the polarizability ([Formula: see text] and hyperpolarizability ([Formula: see text] and [Formula: see text]. The set of global and range-separated hybrid functionals with different Hartree–Fock (HF) exchange percentage at two basis sets cc-pVDZ and cc-pVTZ were used to evaluate the nonlinear optical (NLO) properties. The observed trends in the absorption maxima supported by perturbation potential analysis; as the absorption maxima increases, the respective amplitude potential decreases. For the investigated compounds, [Formula: see text]-conjugation along with the type of substituted acceptor plays a crucial role in the enhancement of NLO properties. The presence of acceptor group and length of conjugation increase between the D and A group; the first- and second-order intrinsic hyperpolarizability increases, leads to enhanced first- as well as second-order hyperpolarizability. Bond length alternation (BLA)/bond order alteration (BOA) exploration suggested that compounds attain cyanine limit. The trends in NLO properties for investigated compounds are supported by chemical reactivity descriptors, hardness and hyperhardness analysis. The polarizability is linearly correlated with the hyperpolarizability parameters ([Formula: see text] and [Formula: see text] and shows a good regression coefficient by figures of merit analysis.

Transfer Function Coefficients Calculation of the High Pass Frequency-Dependent Second-Order Components Using Special Phase Frequency Response Values

2021 ◽  
Vol 105 ◽  
pp. 161-166
Author(s):  
Hanna Ukhina ◽  
Ivan Afanasyev ◽  
Valerii Sytnikov ◽  
Oleg Streltsov ◽  
Pavel Stupen
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Digital Filter ◽  
Second Order ◽  
Robotic Systems ◽  
Frequency Dependent ◽  
Digital Frequency ◽  
Order Components ◽  
High Pass

In this work, adjustable second-order digital frequency-dependent components that are used in robotic systems are considered. The obtained approximations of the PFR dependence on the ripple level allow us to find the digital filter transfer function denominator coefficients' values that result contributes to a more rapid rearrangement of their responses in robotic systems.

Predictions for Non-Contacting Mechanical Face Seal Vibration With External Excitation From Pump Vibration: Part I — Flexibly Mounted Stator

2018 ◽  
Author(s):  
Clay S. Norrbin ◽  
Dara W. Childs
Keyword(s):  
Excitation Frequency ◽  
Mechanical Seal ◽  
Seal Ring ◽  
External Excitation ◽  
Frequency Dependent ◽  
Frequency Independent ◽  
Mechanical Face Seal ◽  
Stiffness And Damping ◽  
Damping Model ◽  
Independent Model

Stability and response predictions are presented for a Flexibly Mounted Stator (FMS) mechanical seal ring using the model developed by Childs in 2018. The seal ring is excited by external vibration from the rotor/housing. The model includes a frequency dependent stiffness and damping model for the O-ring and a frequency independent model for the fluid film. The dynamic coefficients depend on both speed and excitation frequency. Data used in defining the model are representative of a typical FMS mechanical seal. Parameters for radius and O-Ring placement are varied. The predictions show an insignificant dependency on speed. The predictions are strongly frequency dependent with a critical speed of 90 kRPM. The FMS is predicted to be stable to frequencies below 140 kRPM. The distance between the O-Ring and seal ring inertia center doz couples lateral and pitch-yaw motion of the seal ring. Overall, if doz is kept small, the seal ring is predicted to not have any stability or response issues.

Measured and Predicted Transfer Functions Between Rotor Motion and Pad Motion for a Rocker-Back Tilting-Pad Bearing in LOP Configuration

2011 ◽  
Author(s):  
Jason C. Wilkes
Keyword(s):  
Transfer Functions ◽  
Analytical Models ◽  
Single Frequency ◽  
Frequency Dependent ◽  
Damping Coefficients ◽  
Operating Region ◽  
Direct Measurements ◽  
Trailing Edges ◽  
Tilting Pad ◽  
Stiffness And Damping

Many researchers have compared predicted stiffness and damping coefficients for tilting-pad journal bearings (TPJBs) to measurements. Most have found that direct damping is consistently overpredicted. Continuing to test TBJBs in the same fashion is not likely to produce an explanation for the discrepancies between measured and predicted damping. Most analytical models for TPJBs are based on the assumption that explicit dependence on pad motion can be eliminated by assuming a solution for rotor motion such that the amplitude and phase of pad motions are predicted by rotor-pad transfer functions. Direct measurements of pad motion during test excitation are needed to produce measured transfer functions between rotor and pad motion, and a comparison between these measurements and predictions is needed to identify model discrepancies. A test setup was designed to fulfill these objectives. Motion probes were added to the loaded pad to obtain accurate measurement of pad radial and tangential motion, as well as tilt, yaw and pitch. For the remainder of this work, the loaded pad refers to the pad whose pivot sits on the static load line. Testing was performed primarily at low speeds and high loads, since this is the operating region for which predictions are most erroneous. Single frequency excitations were performed ranging from 10–350 Hz, producing rotor and pad motion, acceleration, and force vectors. This motion was used to determine frequency-dependent bearing impedances and rotor-pad transfer functions. A new pad perturbation model is proposed including the effects of pad angular, radial, and circumferential pad motion. This model was implemented in a Reynolds-based TPJB code to predict the frequency-dependent bearing impedances and rotor-pad transfer functions. These predictions are compared with measurements and discussed. Good agreement was found between the amplitude of the measured and predicted transfer functions concerning tilt and radial motions for low to moderate loads, but deviated in accuracy at the highest loaded case. Circumferential (sliding) pad motion was predicted and observed; however, the effect of this degree of freedom on dynamic bearing coefficients has not been quantitatively assessed. For the bearing investigated, radial motion accounted for more than 67% of total motion of the fluid-film height at the leading and trailing edges of the pad when operating at 4400 rpm under heavily loaded conditions. The measurements show that predicting TPJB stiffness and damping coefficients without accounting for pad pivot deformation will not produce satisfactory outcomes.

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