scholarly journals VIBRATONAL MECHANICS AND STOCHASTIC QUASI-RESONANCES

2021 ◽  
Author(s):  
Eugen Kremer
Keyword(s):  
Natural Frequency ◽  
Stochastic Resonance ◽  
High Frequency ◽  
Low Frequency ◽  
Slow Motion ◽  
Excitation Intensity ◽  
Stochastic Excitation ◽  
Primary Interest ◽  
Vibrational Mechanics ◽  
Frequency Properties

The concept of vibrational mechanics was pioneered in the works by Professor I.I. Blekhman and developed by his numerous disciples and coleagues. It is a powerful tool for the study of such systems with fast excitations, in which slow motion is of primary interest. One important application of this approach is the stochastic resonance, the phenomenon of resonance-like response of slow variables to intensity of stochastic excitation. This phenomenon is considered within the framework of vibrational mechanics as forced lowfrequency oscillations near the natural frequency, which evolves under the influence of changing high-frequency stochastic excitation. We propose a generalization of this approach to the case when the evolution of low-frequency properties of the system leads not to the equality of the natural frequency and the frequency of the external slow force, but to the loss of stability in a certain interval of the stochastic excitation intensity. Since in this case, as for stochastic resonance, the external manifestation of the process is the resonance-like response of the system, the considered effect can be called stochastic quasi-resonance, As an example, we consider a rotor with anisotropy of bending stiffness under the action of stochastic angular velocity oscillations.

Secondary signal-induced large-parameter stochastic resonance for feature extraction of mechanical faults

2019 ◽  
Vol 33 (15) ◽  
pp. 1950157 ◽  
Author(s):  
Yunjiang Liu ◽  
Fuzhong Wang ◽  
Lu Liu ◽  
Yamin Zhu
Keyword(s):  
Feature Extraction ◽  
Stochastic Resonance ◽  
High Frequency ◽  
Low Frequency ◽  
Transformation Method ◽  
Scale Transformation ◽  
Large Parameter ◽  
Noise Energy ◽  
Mechanical Faults ◽  
System Output

Aiming to solve the problem that it is difficult to extract large parameter signals from a strong noise background, a novel method of large parameter stochastic resonance (SR) induced by a secondary signal is proposed. The SR mechanism of high-frequency signals is expounded by analyzing the density distribution curve. High-frequency signals are converted to low-frequency signals using the scale transformation method, and then large-parameter SR is induced by the secondary signal. Ultimately, the method is applied to the feature extraction of mechanical faults. Simulation and experimental results indicate that (i) the effect of SR induced by the secondary signal is significantly enhanced when the frequency of the secondary signal is twice that of the signals to be detected after the scale transformation; (ii) when the frequency of secondary signal is twice the maximum frequency of the signals to be detected after the scale transformation, choosing an appropriate amplitude of secondary signal can alleviate the problem that the noise energy is excessively concentrated in the low-frequency channel with regard to the extraction of two-frequency or three-frequency high-frequency signals; and (iii) by adding the secondary signal to the engineering example, the fault power spectrum value of system output is 101% higher than that without the secondary signal.

scholarly journals Effect of Frequency Content of Earthquake on the Seismic Response of Interconnected Electrical Equipment

CivilEng ◽  
2020 ◽  
Vol 1 (3) ◽  
pp. 198-215
Author(s):  
Kashif Salman ◽  
Sung Gook Cho
Keyword(s):  
Seismic Response ◽  
Natural Frequency ◽  
Ground Motion ◽  
High Frequency ◽  
Seismic Analysis ◽  
Response Spectrum ◽  
Low Frequency ◽  
Stable Operation ◽  
Design Spectrum ◽  
Standard Design

To ensure the stable operation of safety-related nuclear power plant (NPP) equipment, they are tested by following the seismic qualification procedures. The in-cabinet response spectrum (ICRS) is used to test the mounted components. However, the ICRS varies significantly with the number of uncertainties that include (1) loaded and unloaded condition of the cabinets, (2) the number of connected cabinets (grouping effects), and (3) higher frequency contents in the seismic inputs. This study focuses on the ICRS generation and alteration induced due to the listed uncertainties. A prototype of an electrical cabinet was experimentally examined. Followed by the numerical modeling of the cabinet, the seismic analysis for the group of cabinets was performed using artificial ground motion compatible with the standard design spectrum and the real accelerograms of high and low frequency contents. The seismic response using finite element (FE) analysis manifests (1) natural frequency of loaded cabinets reduced due to the in-cabinet components while for the unloaded cabinets it increased significantly, (2) a consistent reduction in ICRS due to the grouping effect was recorded when excited by the lower-frequency motion, while it was amplified dramatically due to high-frequency pulses. Interconnected cabinets under the low-frequency input motions have a significant reduction of 50% in the ICRS that corresponds to the higher stiffness of the cabinets, while a 100% increase under the high frequency of ground motion was obtained. High frequency of ground motion, usually above 10 Hz, can cause the interconnected cabinets to resonate as the natural frequency of these equipment lies in this range.

A New Kind of Energy Transfer From the High-Frequency to Low-Frequency Mode in a Composite Laminated Plate

2010 ◽  
Author(s):  
Wei Zhang ◽  
Xiang-Ying Guo ◽  
Qian Wang ◽  
Cui-Cui Liu ◽  
Yun-cheng He
Keyword(s):  
Numerical Simulation ◽  
Natural Frequency ◽  
Thin Plate ◽  
High Frequency ◽  
Low Frequency ◽  
Frequency Mode ◽  
Rectangular Thin Plate ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Low Frequency Mode

This paper focuses on the analysis on a new kind of nonlinear resonant motion with the low-frequency large-amplitude, which can be induced by the high-frequency small-amplitude mode through the mechanism of modulation of amplitude and phase. The system investigated is a simply supported symmetric cross-ply composite laminated rectangular thin plate subjected to parametric excitations. Experimental research has been carried out for the first time. The test plate was excited near the first natural frequency with parametric forces and the above mentioned high-to-low frequency mode has been observed, whose frequency is extremely lower than the first natural frequency. Theoretical job goes to analysis the above phenomenon accordingly. Based on the Reddy’s third-order shear deformation plate theory and the von Karman type equation, the nonlinear governing equations of the simply supported symmetric cross-ply composite laminated rectangular thin plate subjected to parametric excitations are formulated. The Galerkin method is utilized to discretize the governing partial differential equations into a two-degree-of-freedom nonlinear system. Numerical simulation is conducted to investigate this non-autonomous system subsequently. The results of numerical simulation demonstrate that there is a qualitative agreement between the experimental observation and the theoretical result. Besides, the multi-pulse chaotic motions are also reported in numerical simulations.

NONLINEAR INTERACTIONS BETWEEN TWO WIDELY SPACED MODES — EXTERNAL EXCITATION

1993 ◽  
Vol 03 (02) ◽  
pp. 417-427 ◽  
Author(s):  
S.A. NAYFEH ◽  
A.H. NAYFEH
Keyword(s):  
Natural Frequency ◽  
High Frequency ◽  
Analytical Study ◽  
Experimental Studies ◽  
Low Frequency ◽  
Harmonic Excitation ◽  
Frequency Mode ◽  
Large Contribution ◽  
High Frequency Mode ◽  
Two Degree Of Freedom

Recent experimental studies indicate that energy can be transferred from high- to low-frequency modes in structures with weak nonlinearity. In each of these experiments, a high-frequency mode was driven near its natural frequency but the response included a large contribution due to the first mode of the structure. In this paper, an analytical study of the response of a two-degree-of-freedom nonlinear system with widely spaced modes to a simple-harmonic excitation near the natural frequency of its high-frequency mode is presented. This system serves as a paradigm for the interaction of high- and low-frequency modes.

Vibrational and Stochastic Resonance in FitzHugh-Nagumo Neural Model with Time-Delay and Colored Additive Noise

2011 ◽  
Vol 117-119 ◽  
pp. 685-689 ◽  
Author(s):  
Yu Rong Zhou ◽  
Zheng You He
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Adiabatic Approximation ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Low Frequency ◽  
Neural Model ◽  
Vibrational Resonance ◽  
Model Driven ◽  
Delayed Time

The vibrational resonance (VR) and stochastic resonance (SR) phenomena in time-delayed FitzHugh-Nagumo (FHN) neural model, driven by one high-frequency (HF) signal and one low-frequency (LF) signal, with coupled multiplicative and colored additive noise, is investigated. For the case that the frequency of the HF signal is much higher than that of the LF signal, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) with respect to the LF signal is obtained. It is shown that, the SNR is a non-monotonous function of the amplitude and frequency of the HF signal. In addition, the SNR varies non-monotonically with increasing the intensities of the multiplicative and additive noise, with increasing the delayed-time as well as increasing the system parameters of the FHN model. The influence of the correlation time of the colored additive noise and the coupling strength between the multiplicative and additive noise on the SNR is discussed.

scholarly journals Multi-Frequency Weak Signal Decomposition and Reconstruction of Rolling Bearing Based on Adaptive Cascaded Stochastic Resonance

Machines ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 275
Author(s):  
Di Xu ◽  
Jianghua Ge ◽  
Yaping Wang ◽  
Junpeng Shao
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Low Frequency ◽  
Rolling Bearing ◽  
Frequency Noise ◽  
Weak Signal ◽  
Resonance System ◽  
Weak Fault ◽  
High Pass ◽  
Fault Characteristic

In engineering practice, the bearing fault signal is composed of a series of complex multi-component signals containing multiple fault characteristics information. In the early stage of fault sprouting and evolution, the fault features are easily disturbed by noise and irrelevant signals, eliminating the fault signals in the strong background noise. To overcome the influence of noise on the signal, this study proposes multi-frequency weak signal decomposition and reconstruction of rolling bearing based on adaptive cascaded stochastic resonance. First, the original signal is passed through the Hilbert transform to obtain the envelope signal. The envelope signal is high-pass filtered to eliminate the interference of low-frequency components on the response of the stochastic resonance system. Secondly, cascaded stochastic resonance system parameters are adaptively optimized by the quantum particle swarm algorithm (QPSO). The high-pass filtered signal input to the adaptive cascaded stochastic resonance system (ACSRS) can further enhance the weak fault characteristics, allowing the gradual transfer of high-frequency noise energy to the low-frequency fault characteristic components. Finally, the signal is decomposed using the variational mode decomposition (VMD) method to jointly determine the location of the fault characteristic frequencies in the intrinsic mode functions (IMF) component by the energy loss coefficient and correlation coefficient to achieve the reconstruction of multi-frequency weak signals. Through simulation and experimental validation, the effectiveness and superiority of the method for multi-frequency weak signal detection in bearings are verified. The results show that the method not only achieves the adaptive optimization of the stochastic resonance system parameters gradually removing the high-frequency noise in the signal and improving the energy of the low-frequency signal but also reduces the number of decomposition layers of the VMD, enhances the fault characteristic information in the weak signal, and effectively identifies the early weak fault characteristics of rolling bearings.

Pendulum Quasi-Static Drift Effect at Suspension Point Excitation by High-Frequency Polyharmonic Multiple Frequency Vibration

2021 ◽  
pp. 4-16
Author(s):  
O.N. Tushev ◽  
D.S. Chernov
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Slow Motion ◽  
External Action ◽  
Frequency Component ◽  
Vertical Coordinate ◽  
Harmonic Components ◽  
The Individual ◽  
Fast Oscillations ◽  
Research Show

The paper dwells upon the dynamic behavior of a 2d pendulum under polyharmonic vibration. The study shows that the angles between the vertical coordinate axis and the directions of the individual harmonic components effects are generally different. Relying on the well-known approach, we solved the problem in two approximations. The movement of the pendulum contains two components: the "low-frequency" component and the "high-frequency" one. As the frequencies are not multiple, the movement is essentially an aperiodic process. Hence, when deriving the basic relations, it is impossible to use an effective method of averaging the solution within a period of fast oscillations. Dividing the solution by the frequencies of oscillations, we obtained an equation describing the slow motion and an approximate formula based on it for determining the pendulum quasi-static displacement, i.e., the "drift effect". The result is generalized by taking energy dissipation into account. Findings of research show that near the quasi-static position of the pendulum, loss of stability is possible as a result of parametric resonance at the combination frequencies of the external action. The paper gives an example in which an approximate solution is compared with an exact numerical simulation and shows the results of this comparison

Stochastic resonance as the averaged response to random broadband excitation and its possible applications

2019 ◽  
Vol 233 (23-24) ◽  
pp. 7476-7488 ◽  
Author(s):  
I Blekhman ◽  
E Kremer
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Dynamic Properties ◽  
Low Frequency ◽  
Universal Curve ◽  
Two Dimensional ◽  
Suspension Point ◽  
Low Frequency Oscillations ◽  
Stochastic Oscillations ◽  
Stochastic Analog

Within the framework of vibrational mechanics, a stochastic analog of the Stephenson–Kapitza pendulum with random two-dimensional oscillations of the suspension point was considered and the dynamic properties of its averaged motion were studied. It is shown that, unlike the ordinary Stephenson–Kapitsa pendulum with deterministic vertical oscillations of the suspension point, both an increase and a decrease in the effective natural frequency are possible under the influence of high-frequency stochastic oscillations. A formula is derived for the amplitude of low-frequency oscillations as a function of the intensity of high-frequency stochastic oscillations and the possibility of a stochastic resonance in this system is shown. The dependence of the stochastic resonance on the mass and the damping coefficient is analyzed. It is shown that the points of the stochastic resonance lie in the plane of parameters “intensity of stochastic excitation” and “amplitude of low-frequency oscillation” on a universal curve that is independent of the mass of the pendulum. Peculiar self-oscillations in a system for which stochastic oscillations are produced by a technological load and, therefore, depend monotonically on the amplitude of low-frequency oscillations are discussed. A schematic diagram of these phenomena is proposed. The motion of the machine is described by the same equations as the stochastic analog of the Stephenson–Kapitza pendulum with random two-dimensional oscillations of the suspension point. A strategy of control for such a vibro-machine is proposed with the aim of maintaining it at resonance and providing an energetically efficient mode of operation.

Simulations of high-resolution images of amorphous silicon films

1986 ◽  
Vol 44 ◽  
pp. 544-545
Author(s):  
G. Y. Fan ◽  
J. M. Cowley
Keyword(s):  
Electron Microscope ◽  
High Frequency ◽  
Fourier Transformation ◽  
Amorphous Materials ◽  
Low Frequency ◽  
Chromatic Aberration ◽  
Structure Information ◽  
Frequency Components ◽  
High Resolution Images ◽  
Spatial Frequency Spectrum

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.

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