The Low-Frequency Behaviour of Response Functions

1989 ◽  
pp. 59-62
Author(s):  
Wilhelm Brenig
Keyword(s):  
Low Frequency ◽  
Response Functions

A Practical Estimation of Frequency Response Functions for System Decoupling Indirectly Using a Variable Cross Section Rod

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Jun Wang ◽  
Tian-Ya Meng ◽  
Ming-Yu Li ◽  
Teik C. Lim ◽  
Wen-Xuan Kuang
Keyword(s):  
Frequency Response ◽  
Cross Section ◽  
Low Frequency ◽  
Coupled System ◽  
Variable Cross Section ◽  
Probe Method ◽  
Variable Cross ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Spatial Limitation

It is of high importance to be able to decouple a system to obtain the dynamic characteristics of its substructures; however, the necessary frequency response functions (FRFs) of the coupling interface are usually challenging to measure due to the limited accessible space and complex geometries. In this paper, a measurement technique in the decoupling process of a coupled system is proposed in order to obtain the FRFs at coupling interface. Specifically, a variable cross section rod is adopted to transmit the dynamic behavior of coupling interface. The proposed technique has three advantages: (a) the thick end with large cross section can provide enough area for applying excitation force like using impact hammer and/or setting up sensors; (b) the slender end with small cross section can break through the spatial limitation more easily; and (c) the convenience that no additional experimental setup is required but just using an available variable cross section rod. Vibrational equation of the variable cross section probe method is derived and then combined with the existing decoupling theories. Finally, the proposed probe method and the new decoupling theory combining probe theory are validated through numerical simulations (FEM) and laboratory experiments, respectively. The results show its great practicability in decoupling process especially in low frequency range.

Use of experimental dynamic substructuring to predict the low frequency structural dynamics under different boundary conditions

2017 ◽  
Vol 23 (11) ◽  
pp. 1444-1455
Author(s):  
Walter D’Ambrogio ◽  
Annalisa Fregolent
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Low Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Different Boundary Conditions ◽  
Rigid Body Modes

Flexible structural components can be attached to the rest of the structure using different types of joints. For instance, this is the case of solar panels or array antennas for space applications that are joined to the body of the satellite. To predict the dynamic behaviour of such structures under different boundary conditions, such as additional constraints or appended structures, it is possible to start from the frequency response functions in free-free conditions. In this situation, any structure exhibits rigid body modes at zero frequency. To experimentally simulate free-free boundary conditions, flexible supports such as soft springs are typically used: with such arrangement, rigid body modes occur at low non-zero frequencies. Since a flexible structure exhibits the first flexible modes at very low frequencies, rigid body modes and flexible modes become coupled: therefore, experimental frequency response function measurements provide incorrect information about the low frequency dynamics of the free-free structure. To overcome this problem, substructure decoupling can be used, that allows us to identify the dynamics of a substructure (i.e. the free-free structure) after measuring the frequency response functions on the complete structure (i.e. the structure plus the supports) and from a dynamic model of the residual substructure (i.e. the supporting structure). Subsequently, the effect of additional boundary conditions can be predicted using a frequency response function condensation technique. The procedure is tested on a reduced scale model of a space solar panel.

A Flow Starvation Model for Tilting Pad Journal Bearings and Evaluation of Frequency Response Functions: A Contribution Toward Understanding the Onset of Low Frequency Shaft Motions

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Luis San Andrés ◽  
Bonjin Koo ◽  
Makoto Hemmi
Keyword(s):  
Frequency Response ◽  
Low Frequency ◽  
Journal Bearings ◽  
Response Functions ◽  
Frequency Range ◽  
Flow Conditions ◽  
Force Coefficients ◽  
Lubricant Flow ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearings

Direct lubrication tilting pad journal bearings (TPJBs) require less oil flow, reduce power consumption, and offer cooler pad temperatures for operation at high surface speeds. Although apparently free of hydrodynamic instability, the literature shows that direct lubrication TPJBs exhibit unexpected shaft vibrations with a broadband low frequency range, albeit small in amplitude. Published industrial practice demonstrates the inlet lubrication type, a reduced supply flow rate causing film starvation, and the bearing discharge conditions (evacuated or end sealed) affect the onset, gravity, and persistency of the subsynchronous vibration (SSV) hash motions. The paper presents a physical model to predict the performance of TPJBs with flow conditions ranging from over flooded to extreme starvation. Lubricant starvation occurs first on an unloaded pad, thus producing a (beneficial) reduction in drag power. As the supplied flowrate decreases further, fluid starvation moves toward the loaded pads and affects the film temperature and power loss, increases the journal eccentricity, and modifies the dynamic force coefficients of each tilting pad and thus the whole bearing. For a point mass rotor supported on a TPJB, the analysis produces eigenvalues and frequency response functions (FRFs) from three physical models for lateral rotor displacements: one with frequency reduced (4 × 4) bearing stiffness (K) and damping (C) coefficients and another with constant K–C–M (inertia) coefficients over a frequency range. The third model keeps the degrees of freedom (DOF) (tilting) of each pad and incorporates the full matrices of force coefficients including fluid inertia. Predictions of rotordynamic performance follow for two TPJBs: one bearing with load between pads (LBP) configuration, and the other with a load on a pad (LOP) configuration. For both examples, under increasingly poor lubricant flow conditions, the damping ratio for the rotor-bearing low frequency (SSV) modes decreases, thus producing an increase in the amplitude of the FRFs. For the LOP bearing, a large static load produces a significant asymmetry in the force coefficients; the rotor bearing has a small stiffness and damping for shaft displacements in the direction orthogonal to the load. A reduction in lubricant flow only exacerbates the phenomenon; starvation reaches the loaded pad to eventually cause the onset of low frequency (SSV) instability. The bearing analyzed showed similar behavior in a test bench. The predictions thus show a direct correlation between lubricant flow starvation and the onset of SSV.

A Flow Starvation Model for Tilting Pad Journal Bearings and Evaluation of Frequency Response Functions: A Contribution Towards Understanding the Onset of Low Frequency Shaft Motions

2017 ◽  
Author(s):  
Luis San Andrés ◽  
Bonjin Koo ◽  
Makoto Hemmi
Keyword(s):  
Frequency Response ◽  
Low Frequency ◽  
Journal Bearings ◽  
Response Functions ◽  
Frequency Range ◽  
Flow Conditions ◽  
Force Coefficients ◽  
Lubricant Flow ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearings

Direct lubrication tilting pad journal bearings (TPJBs) require of less oil flow, reduce power consumption and offer cooler pad temperatures for operation at high surface speeds. Although apparently free of a hydrodynamic instability, the literature shows that direct lubrication TPJBs exhibit unexpected shaft vibrations with a broadband low frequency range, albeit small in amplitude. Published industrial practice demonstrates the inlet lubrication type, a reduced supply flow rate causing film starvation, and the bearing discharge conditions (evacuated or end sealed) affect the onset, gravity and persistency of the sub synchronous (SSV) hash motions. The paper presents a physical model to predict the performance of TPJBs with flow conditions ranging from over flooded to extreme starvation. Lubricant starvation occurs first on an unloaded pad, thus producing a (beneficial) reduction in drag power. As the supplied flowrate decreases further, fluid starvation moves towards the loaded pads and affects the film temperature and power loss, increases the journal eccentricity, and modifies the dynamic force coefficients of each tilting pad and thus the whole bearing. For a point mass rotor supported on a TPJB, the analysis produces eigenvalues and frequency response functions (FRFs) from three physical models for lateral rotor displacements: one with frequency reduced (4×4) bearing stiffness (K) and damping (C) coefficients and another with constant K-C-M (inertia) coefficients over a frequency range. The third model keeps the degrees of freedom (tilting) of each pad and incorporates the full matrices of force coefficients including fluid inertia. Predictions of rotordynamic performance follow for two TPJBs: one bearing with load between pads (LBP) configuration, and the other with a load on a pad (LOP) configuration. For both examples, under increasingly poor lubricant flow conditions, the damping ratio for the rotor-bearing low frequency (SSV) modes decreases, thus producing an increase in the amplitude of the FRFs. For the LOP bearing, a large static load produces a significant asymmetry in the force coefficients; the rotor-bearing has a small stiffness and damping for shaft displacements in the direction orthogonal to the load. A reduction in lubricant flow only exacerbates the phenomenon; starvation reaches the loaded pad to eventually cause the onset of low frequency (SSV) instability. The bearing analyzed showed similar behavior in a test bench. The predictions thus show a direct correlation between lubricant flow starvation and the onset of SSV.

scholarly journals Multiparameter approach in the deep geoelectrics

2021 ◽  
Vol 43 (5) ◽  
pp. 193-207
Author(s):  
I. I. Rokityansky ◽  
A. V. Tereshyn
Keyword(s):  
Electrical Conductivity ◽  
Low Frequency ◽  
Observation Point ◽  
Specific Information ◽  
Response Functions ◽  
Night Time ◽  
Current Harmonics ◽  
Mhd Generator ◽  
Anomalous Field ◽  
Deep Sounding

The main provisions of geoelectrics are described, the importance of taking into account the ambiguity of its inverse problem is emphasized. Three main methods of deep geoelectrics which use natural fields of ionospheric-magnetospheric origin are considered: geomagnetic deep sounding (GDS), magnetotelluric sounding (MTS), and magnetovariational profiling (MVP). The response functions of each method are described. Each response function carries its own specific information about some parameters of the studied object and is characterized by the degree of reliability of the information about the object extracted from it. For example, the most reliable information about electrical conductivity anomalies (if any in the study area) is contained in the MVP response functions. The horizontal tensor of the anomalous field contains information about the electrical conductivity under the observation point, and the tipper (induction vector) contains information from the surrounding areas. In general, MVP information is less susceptible to distortions than MTS information and deserves more trust. Artificial field sources in deep geoelectrics are rarely used due to their high cost. Since 1970, two powerful sources created for other purposes arised on the Kola Peninsula and were used for deep sounding. In the center of these studies found themself young talented geologist-geophysicist and organizer of major projects AbdulkhaiAzimovichZhamaletdinov. The «Khibiny» project with an MHD generator and an ultra-deep well as one of the objects of the study, the «Zeus» low-frequency emitter, the signals of which were recorded in China at a distance of 7000 km, and a number of projects conceived and organized by Zhamaletdinov and executed under his leadership: «Volgograd-Donbass» (1979, 1986), experiments «PHOENIX» (2007, 2009, 2014, 2019) and others. At the same time, methods of interpretation were developed for sounding with artificial EM sources and new response functions were obtained which make it possible to «see» the object of research in a new way. This experience must be preserved, generalized, improved and used, for example as follows. In the area of modern synchronous multipoint MTS-MVP survey, a controlled source composed of two grounded lines emits strong current (harmonics at fixed frequencies and/or pulses) which signal will be recorded by survey instruments during night-time sessions.

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