The Rotationally Flexible Pendulum Subjected to a High Frequency Excitation

1990 ◽  
Vol 57 (3) ◽  
pp. 725-730 ◽  
Author(s):  
Bertram A. Schmidt
Keyword(s):  
High Frequency ◽  
Harmonic Excitation ◽  
Flexible Parts ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

A high frequency harmonic excitation is applied to the pivot of a rotationally flexible pendulum. It is found that various equilibrium positions occur depending on the stiffness of the flexible parts.

The Radially Flexible Pendulum Subjected to a High-Frequency Excitation

1983 ◽  
Vol 50 (2) ◽  
pp. 443-448 ◽  
Author(s):  
B. A. Schmidt
Keyword(s):  
High Frequency ◽  
Radial Direction ◽  
Harmonic Excitation ◽  
Stable Motion ◽  
Fixed Direction ◽  
Approximate Equilibrium ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

A high-frequency harmonic excitation is applied to a pendulum that is flexible in the radial direction. Approximate equilibrium positions are found when the excitation is in a general and fixed direction. An approximate stable motion is found when the direction of the excitation changes constantly and slowly. It is found that the excitation causes a reduction of the radius.

Experimental Evidence of Vibrational Resonance in a Bi-Stable Twin-Well Mechanical Oscillator

2017 ◽  
Author(s):  
Abdraouf Abusoua ◽  
Mohammed F. Daqaq
Keyword(s):  
Experimental Evidence ◽  
High Frequency ◽  
Harmonic Excitation ◽  
Nonlinear Phenomenon ◽  
Resonant Response ◽  
Mechanical Oscillator ◽  
Vibrational Resonance ◽  
Electrical Systems ◽  
High Frequency Excitation ◽  
Frequency Excitation

Vibrational Resonance (VR) is a nonlinear phenomenon which occurs when a bi-stable system is subjected to a bi-harmonic excitation consisting of a small-amplitude resonant excitation and a large-amplitude high-frequency excitation. The result is that, under some conditions, the high-frequency excitation amplifies the resonant response associated with the slow dynamics. While VR was studied extensively in the open literature, most of the research studies used optical and electrical systems as platforms for experimental investigation. This paper provides experimental evidence that VR can also occur in a mechanical bi-stable twin-well oscillator and discusses the conditions under which VR is possible.

High-Frequency Dynamic Overshoot in Linear and Nonlinear Periodic Media

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Yijing Zhang ◽  
Alexander F. Vakakis
Keyword(s):  
High Frequency ◽  
Harmonic Excitation ◽  
Strong Nonlinearity ◽  
Periodic Media ◽  
Elastic Foundations ◽  
Linear Elastic ◽  
Analytical Approximations ◽  
Linear And Nonlinear ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

We study the transient responses of linear and nonlinear semi-infinite periodic media on linear elastic foundations under suddenly applied, high-frequency harmonic excitations. We show that “dynamic overshoot” phenomena are realized whereby, due to the high-rate of application of the high-frequency excitations, coherent traveling responses are propagating to the far fields of these media; and this, despite the fact that the high frequencies of the suddenly applied excitations lie well within the stop bands of these systems. For the case of a linear one-dimensional (1D) spring-mass lattice, a leading-order asymptotic approximation in the high frequency limit of the suddenly applied harmonic excitation shows that the transient dynamic overshoot is expressed in terms of the Green's function at its free end. Then, a two-dimensional (2D) strongly nonlinear granular network is considered, composed of two semi-infinite, ordered homogeneous granular lattices mounted on linear elastic foundations and coupled by weak linear coupling terms. A high-frequency harmonic excitation is applied to one of the granular lattices—designated as the “excited lattice”, with the other lattice designated as the “absorbing” one. The resulting dynamic overshoot phenomenon consists of a “pure” traveling breather, i.e., of a single propagating oscillatory wavepacket with a localized envelope, resulting from the balance of discreteness, dispersion, and strong nonlinearity. The pure breather is asymptotically studied by a complexification/averaging technique, showing nearly complete but reversible energy exchanges between the excited and absorbing lattices as the breather propagates to the far field. Verification of the analytical approximations with direct numerical simulations is performed.

On Using a Strong High-Frequency Excitation for Parametric Identification of Nonlinear Systems

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Abdraouf Abusoua ◽  
Mohammed F. Daqaq
Keyword(s):  
High Frequency ◽  
Nonlinear Models ◽  
Modulation Frequency ◽  
Parametric Method ◽  
Harmonic Excitation ◽  
Restoring Force ◽  
Nonlinear Parameters ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Slow Modulation

This paper describes a new parametric method for the development of nonlinear models with parameters identified from an experimental setting. The approach is based on applying a strong nonresonant high-frequency harmonic excitation to the unknown nonlinear system and monitoring its influence on the slow modulation of the system's response. In particular, it is observed that the high-frequency excitation induces a shift in the slow-modulation frequency and a static bias in the mean of the dynamic response. Such changes can be directly related to the amplitude and frequency of the strong excitation offering a unique methodology to identify the unknown nonlinear parameters. The proposed technique is implemented to identify the nonlinear restoring-force coefficients of three experimental systems. Results demonstrate that this technique is capable of identifying the nonlinear parameters with relatively good accuracy.

Equation for the evolution of trapped hydrogen in an elastic rod subjected to high-frequency harmonic excitation

2016 ◽  
Vol 227 (5) ◽  
pp. 1515-1518 ◽  
Author(s):  
Alexander K. Belyaev ◽  
Iliya I. Blekhman ◽  
Vladimir A. Polyanskiy
Keyword(s):  
High Frequency ◽  
Harmonic Excitation ◽  
Elastic Rod ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

Stiffening Effects of High-Frequency Excitation: Experiments for an Axially Loaded Beam

1999 ◽  
Vol 67 (2) ◽  
pp. 397-402 ◽  
Author(s):  
J. S. Jensen ◽  
D. M. Tcherniak ◽  
J. J. Thomsen
Keyword(s):  
High Frequency ◽  
Harmonic Excitation ◽  
General Tendency ◽  
Beam Model ◽  
Very High Frequency ◽  
Simple Analytical Expression ◽  
Theoretical Predictions ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Very High

According to theoretical predictions one can change the effective stiffness or natural frequency of an elastic structure by employing harmonic excitation of very high frequency. Here we examine this effect for a hinged-hinged beam subjected to longitudinal harmonic excitation. A simple analytical expression is presented, that relates the effective natural frequencies of the beam to the intensity of harmonic excitation. Experiments performed with a laboratory beam confirm the general tendency of this prediction, though there are discrepancies that cannot be explained in the framework of the linear Galerkin-discretized beam model. [S0021-8936(00)01302-7]

scholarly journals Early Fault Detection Method for Rotating Machinery Based on Harmonic-Assisted Multivariate Empirical Mode Decomposition and Transfer Entropy

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 873 ◽  
Author(s):  
Zhe Wu ◽  
Qiang Zhang ◽  
Lixin Wang ◽  
Lifeng Cheng ◽  
Jingbo Zhou
Keyword(s):  
Fault Detection ◽  
Empirical Mode Decomposition ◽  
High Frequency ◽  
Rotating Machinery ◽  
Transfer Entropy ◽  
Multivariate Empirical Mode Decomposition ◽  
Mode Decomposition ◽  
Coupling Characteristics ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

It is a difficult task to analyze the coupling characteristics of rotating machinery fault signals under the influence of complex and nonlinear interference signals. This difficulty is due to the strong noise background of rotating machinery fault feature extraction and weaknesses, such as modal mixing problems, in the existing Ensemble Empirical Mode Decomposition (EEMD) time–frequency analysis methods. To quantitatively study the nonlinear synchronous coupling characteristics and information transfer characteristics of rotating machinery fault signals between different frequency scales under the influence of complex and nonlinear interference signals, a new nonlinear signal processing method—the harmonic assisted multivariate empirical mode decomposition method (HA-MEMD)—is proposed in this paper. By adding additional high-frequency harmonic-assisted channels and reducing them, the decomposing precision of the Intrinsic Mode Function (IMF) can be effectively improved, and the phenomenon of mode aliasing can be mitigated. Analysis results of the simulated signals prove the effectiveness of this method. By combining HA-MEMD with the transfer entropy algorithm and introducing signal processing of the rotating machinery, a fault detection method of rotating machinery based on high-frequency harmonic-assisted multivariate empirical mode decomposition-transfer entropy (HA-MEMD-TE) was established. The main features of the mechanical transmission system were extracted by the high-frequency harmonic-assisted multivariate empirical mode decomposition method, and the signal, after noise reduction, was used for the transfer entropy calculation. The evaluation index of the rotating machinery state based on HA-MEMD-TE was established to quantitatively describe the degree of nonlinear coupling between signals to effectively evaluate and diagnose the operating state of the mechanical system. By adding noise to different signal-to-noise ratios, the fault detection ability of HA-MEMD-TE method in the background of strong noise is investigated, which proves that the method has strong reliability and robustness. In this paper, transfer entropy is applied to the fault diagnosis field of rotating machinery, which provides a new effective method for early fault diagnosis and performance degradation-state recognition of rotating machinery, and leads to relevant research conclusions.

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