Resonant Response Characteristics Research Articles

Local defect modelling and nonlinear dynamic analysis for the inter-shaft bearing in a dual-rotor system

• A force model for the inter-shaft bearing with a local defect on surface of the outer or inner race. • The system may resonant in some non-critical-speed region due to the local defect. • Parameters affecting the resonant frequencies and vibration amplitudes of the abnormal resonances. • A comprehensive parametric analysis is carried out to show the nonlinear resonant response characteristics. This paper presents a force model for the inter-shaft bearing with a local defect on the surface of the outer race or the inner race, and the nonlinear dynamic characteristics of a dual-rotor system affected by the local defect are investigated. A simplified dual-rotor system is presented with the consideration of the inter-shaft bearing's nonlinearities such as the Hertzian contact force and the radial clearance. The local defect is considered as a regular dent with a constant depth, thus the radial clearance will increase when rolling elements go through the range of the local defect. The motion equations of the system with eight degrees of freedom are formulated by using the Lagrange's equation. The nonlinear vibration responses of the dual-rotor system affected by the local defect are obtained using numerical method. The results show that there exist four abnormal resonances on the amplitude frequency curves of the system due to the effect of the local defect, apart from the couple of primary resonances excited by the unbalance excitations of the two rotors. With the aid of the characteristic defect frequency analysis, it is revealed that one pair of the abnormal resonances are excited by the characteristic defect frequency, and the other pair of the abnormal resonances are excited by the combination frequency. Furthermore, a comprehensive parametric analysis is carried out to give an insight into the nonlinear resonant response characteristics affected by parameters such as the depth and the span of the defect, the rotation speed ratio, the unbalances of two rotors, the stiffness and the damping of the linear elastic spring, and the radial clearance, the stiffness and the roller number of the inter-shaft bearing. The results show that the vibration amplitudes for the abnormal resonances are mainly determined by the depth and the span of the defect, while the resonant frequencies for the abnormal resonances are mainly influenced by the rotation speed ratio and the roller number of the inter-shaft bearing. However, the rotors’ unbalances mainly affect the corresponding primary resonance rather than the abnormal resonances. The obtained results will contribute to a better understanding of the nonlinear resonant response characteristics of dual-rotor systems with a local defect on the inter-shaft bearing, which are helpful for the fault diagnostics of the inter-shaft bearing in a dual-rotor system.

Somatic versus Dendritic Resonance: Differential Filtering of Inputs through Non-Uniform Distributions of Active Conductances

Synaptic inputs to neurons are processed in a frequency-dependent manner, with either low-pass or resonant response characteristics. These types of filtering play a key role in the frequency-specific information flow in neuronal networks. While the generation of resonance by specific ionic conductances is well investigated, less attention has been paid to the spatial distribution of the resonance-generating conductances across a neuron. In pyramidal neurons – one of the major excitatory cell-types in the mammalian brain – a steep gradient of resonance-generating h-conductances with a 60-fold increase towards distal dendrites has been demonstrated experimentally. Because the dendritic trees of these cells are large, spatial compartmentalization of resonant properties can be expected. Here, we use mathematical descriptions of spatially extended neurons to investigate the consequences of such a distal, dendritic localization of h-conductances for signal processing. While neurons with short dendrites do not exhibit a pronounced compartmentalization of resonance, i.e. the filter properties of dendrites and soma are similar, we find that neurons with longer dendrites ( space constant) can show distinct filtering of dendritic and somatic inputs due to electrotonic segregation. Moreover, we show that for such neurons, experimental classification as resonant versus nonresonant can be misleading when based on somatic recordings, because for these morphologies a dendritic resonance could easily be undetectable when using somatic input. Nevertheless, noise-driven membrane-potential oscillations caused by dendritic resonance can propagate to the soma where they can be recorded, hence contrasting with the low-pass filtering at the soma. We conclude that non-uniform distributions of active conductances can underlie differential filtering of synaptic input in neurons with spatially extended dendrites, like pyramidal neurons, bearing relevance for the localization-dependent targeting of synaptic input pathways to these cells.

THE EFFECT OF TIDE LEVEL ON THE TSUNAMI RESPONSE OF COASTAL HARBORS

The tsunamis generated by the February 27, 2010 Chilean earthquake and the great Japan Tohoku earthquake on March 11, 2011 arrived at several Pacific Coast harbors when the tide levels were at low tides and persisted for several tidal cycles. Despite the significant difference in the recorded wave amplitude observed at Crescent City harbor between these two events, the energy spectrum as a function of frequency has been found to contain several spikes corresponding to the frequency range of 3×〖10〗^(-4)~10×〖10〗^(-4) Hz. This pattern in spectral density is different from several prior tsunamis observed and analyzed for Crescent City Harbor as presented by Lee, Xing and Magoon (2008). In the present study we present the reasons behind the differences in the response behavior associated with these two events. We prove that they are due to the effect of tide levels. We also show that in order to correctly decipher the resonant response characteristics to incident wave the response curves should be expressed as a function of the dimensionless wave number. The tsunami waves recorded at tide gauge station in San Diego Harbor (Southern California) are also analyzed and discussed.

Resonant Response of a Tapered Beam and Its Implications to Blade Vibration

The resonant response characteristics of a tapered beam are studied using Euler–Bernoulli beam theory. The sensitivity of the beam’s maximum stress to variations in its geometry is studied for three types of harmonic pressure loading. The implications to the response of airfoil chordwise bending modes are discussed.

Resonant Response Characteristics of a Group of Blades. (3rd Report. Methodologies for Research on "Coupled Natural Vibration of Axial Deflection and Torsion of a Finite Group of Blades" and "its Resonant Response Characteristics").

In a continuation of our research on resonant response characteristics of a group of blades, other aspects of which were reported by sister papers (1), (2) and (3), coupled vibrations of axial deflection and torsion of a group of blades are thoroughly investigated in the present work. From the results, we explicity and quantitatively determine the resonant stress increasing and decreasing effects in such coupled vibrations and we provide a theoretical explanation of the cause of those effects. Our whole research, consisting of two series of studies, that is, the former study(1)∼(3)on uncoupled ibration of only tangential deflection and the present on coupled vibration of axial deflection and torsion, is aimed at elucidating the essence of resonant stress increasing and decreasing effects in a group of turbine blades; it should be a contribution to rotating machine's dynamics. In this paper, the first of the new series, methodologies are presented for the investigation on the resonant response characteristics of such coupled vibration, comparing with the methodologies adopted in sister papers(1), (2)and(3).

Resonant Response Characteristics of Group of Blades. 5th Report. Survey of Phenomena Related to "Resonant Stress Increasing and Decreasing Effects of Grouping" of "Coupled Natural Vibration of Axial Deflection and Torsion of a Finite Group of Blades".

Based on the fundamental characteristics of coupled natural vibration of axial deflection and torsion, which were presented for a finite group of blades in the 4th Report, its resonant response characteristics are thoroughly investigated. The numerous phenomena related to resonant stress increasing and decreasing effects are put in order for the coupled vibration, and the plural factors controlling such effects in this case are deduced. In the case of uncoupled tangential flexural vibration, a single factor controlled such effects.

Resonant Response Characteristics of a Group of Blades. 4th Report. Fundamental Characteristics of "Coupled Natural Vibration of Axial Deflection and Torsion of a Finite Group of Blades".

Prior to investigating the resonant response characteristics of a finite group of blades, such as resonant stress increasing and decreasing effects, fundamental characteristics of the natural vibration in question must be elucidated. By means of the method described in Chapter 6 of the 3rd report, natural Vibration of axial deflection and torsion is solved for the shroud/blade thickness ratio which is purposely changed from zero to infinity. The results are analyzed and itemized in comparison with tangential flexural vibration. Thus, the fundamental characteristics of natural vibration of such a coupled vibration are clearly shown.

Resonant Response Characteristics of Group of Blades. 2nd Report. Theoretical Investigation into the Cause of Resonant Stress Increasing and Decreasing Effect of Grouping.

Resonant Response Characteristics of Group of Blades. 2nd Report. Theoretical Investigation into the Cause of Resonant Stress Increasing and Decreasing Effect of Grouping.

Resonant Response Characteristics of Group of Blades. 1st Report. Phenomena Related to Resonant Stress Increasing and Decreasing Effect of Grouping.

Resonant Response Characteristics of Group of Blades. 1st Report. Phenomena Related to Resonant Stress Increasing and Decreasing Effect of Grouping.

Maximum Resonant Response of Mistuned Bladed Disks

The turbomachinery bladed disks used in today’s advanced turbine engines must meet strict standards with regard to aeroelastic stability and forced resonant response. One structural characteristic of bladed disks that can significantly impact both of these areas is that of bladed disk mistuning. Mistuning occurs when some circumferential asymmetry exists in the bladed disk. This asymmetry can be due to such things as mass or stiffness eccentricity or slight variations in the individual blade properties and occurs in all bladed disks to a greater or lesser extent. One important structural phenomenon resulting from mistuning is the splitting of the bladed disk’s diametral modes of vibration into “twin” or “dual” modes. The presence of dual mode characteristics in a bladed disk can significantly affect either or both of its aeroelastic stability and resonant response characteristics. The present paper, expanding upon the earlier works of Tobias and Arnold [1] and of Ewins [2] addresses the prediction of the maximum resonant response of a mistuned bladed disk having closely spaced dual modes as a function of mode mistuning and modal damping. A closed form expression is derived for the maximum forced resonant response. A discussion of mistune and damping characteristics of typical turbomachinery bladed disks is also presented.

Low wavenumber wall pressure measurements using a rectangular membrane as a spatial filter

The response of a rectangular membrane to a convecting random pressure field is interpreted to reveal the inherent wavenumber filtering characteristics of the device. After experimental determination of its resonant response characteristics, one such membrane is used to measure the low wavenumber components of the wall pressure fluctuations beneath a plane turbulent boundary layer. The measurements were made at wavenumbers far below the convective region ( k 1 = ω/ U c ) but above the acoustic region ( k 1 ⩽ ω/ c o ). Possible contamination by acoustic and convective ridge effects is considered. The low wavenumber measurements are also compared with values of the wavenumber-frequency pressure spectral density Φ p( k,ω) obtained by Fourier transforming cross-spectral density data obtained by Blake in the same wind tunnel. From this comparison it is seen that this transformation of Blake's data (based on a Corcos model) grossly overestimates the magnitude of Φ p( k,ω) in the low-wavenumber region. The measured values of Φ p( k, c o) are about 36 dB down from convective ridge levels at the same frequency. The data are also compared with earlier results obtained by Jameson. In a similar frequency range the current data levels are approximately 10 dB higher than those of Jameson.

Vibration of Steam Turbine Blade : 1st Report, On Resonant Response Characteristics of Tangential Flexural Vibration of a Group of Several Blades

In designing steam turbine blades and analyzing blade failures, it is not reasonable to consider every possible resonance to be equally harmful, and we must find out which is harmful under giving condition among all possible resonances. In this report, the coefficients of normal mode of tangential flexural vibration of a group of several blades are obtained by the Rayleigh method, and it is proved that resonant response characteristics depend on 1). number of blades per group, 2).'blade pitch'/'pitch of pulsating steam force', viz. D'/D, and 3). normal mode ; and resonant response characteristics are represented quantitatively in the form of dimensionless function named by the author as "timing factor". As the result, it is found that when D'/D is not close to zero or integers, a remarkable "effect of decreasing amplitude by grouping" is produced on the resonance of fixed free type mode, and on the contrary, an "effect of increasing amplitude by grouping" is produced on the resonance of fixed supported type mode ; and also it is found that an analogy is applicable to axial flexural vibration and torsional vibration. Hence, it is found that the failures of short blades which we experienced are attributable to the resonance between nozzle wake and "tangential flexural first order fixed supported type vibration "or" axial flexural first order vibration having many nodes on shroud".