Nonlinear Vibration of Sheet Metal Plates Under Interacting Parametric and External Excitation During Manufacturing

2005 ◽  
Vol 127 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Chung Hwan Kim ◽  
Chong-Won Lee ◽  
N. C. Perkins
Keyword(s):  
Sheet Metal ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Synergistic Effects ◽  
Broad Band ◽  
Metal Plate ◽  
Time Dependent ◽  
Single Frequency ◽  
Cubic Nonlinearity ◽  
External Excitation

This study is motivated by the vibrations that plague coating processes used in the manufacturing of coated sheet metal. These vibrations arise from time-dependent tension fluctuations within the sheet metal plate as well as from the eccentricity of the rollers used to transport the plate. The time-dependent tension is observed to be rather broad-band and creates multi-frequency parametric excitation. By contrast, the roller eccentricity is largely single-frequency (synchronized with the roller speed) and creates single-frequency external excitation. The plate and excitation sources are studied herein using a single-degree-of-freedom model with a cubic nonlinearity, subject to combined parametric and external excitation. In our study, we investigate the resonances that arise from the synergistic effects of multi-frequency parametric excitation and single-frequency external excitation. For the simpler case of single-frequency parametric excitation, we observe both sum and difference combination resonances in addition to principal parametric resonance. For the case of multi-frequency parametric excitation, we observe a frequency shift for the parametric resonance that derives from the cubic nonlinearity and external excitation. Moreover, the phase relationships of the external and each parametric excitation source have a significant effect on the resulting response amplitude. We use these analyses to explain the resonance mechanisms observed in experiments conducted on an example sheet metal coating process.

Nonlinear Vibration of Sheet Metal Plates Under Interacting Parametric and External Excitation During Manufacturing

2003 ◽  
Author(s):  
Chung Hwan Kim ◽  
Chong-Won Lee ◽  
N. C. Perkins
Keyword(s):  
Sheet Metal ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Synergistic Effects ◽  
Broad Band ◽  
Metal Plate ◽  
Time Dependent ◽  
Single Frequency ◽  
Cubic Nonlinearity ◽  
External Excitation

This study in motivated by the vibrations that plague coating processes used in the manufacturing of coated sheet metal. These vibrations arise from time-dependent tension fluctuations within the sheet metal plate as well as from the eccentricity of the rollers used to transport the plate. The time-dependent tension is observed to be rather broad-band and creates multi-frequency parametric excitation. By contrast, the roller eccentricity is largely single-frequency (synchronized with the roller speed) and creates single-frequency external excitation. The plate and excitation sources are studied herein using a single-degree-of-freedom model with a cubic nonlinearity, subject to combined parametric and external excitation. In our study, we investigate the resonances that arise from the synergistic effects of multi-frequency parametric excitation and single-frequency external excitation. For the simpler case of single-frequency parametric excitation, we observe both sum and difference combination resonances in addition to principal parametric resonance. For the case of multi-frequency parametric excitation, we observe a frequency shift for the parametric resonance that derives from the cubic nonlinearity and external excitation. Moreover, the phase relationships of the external and each parametric excitation source have a significant effect on the resulting response amplitude. We use these analyses to explain the resonance mechanisms observed in experiments conducted on an example sheet metal coating process.

Energy Harvesting From Droplet Interface Bilayers

2015 ◽  
Author(s):  
Ashok K. Kancharala ◽  
Eric Freeman ◽  
Michael K. Philen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Harvesting ◽  
Nonlinear Finite Element ◽  
Time Dependent ◽  
External Excitation ◽  
Biologically Inspired ◽  
Element Analysis ◽  
Interfacial Membrane ◽  
Membrane Deflection

Biologically inspired droplet interface bilayers have found applications in the development of hair cell sensors and other mechanotransduction applications. In this research, the flexoelectric capability of the droplet bilayers under external excitation is explored for energy harvesting. Traditionally, membrane capacitance models are being used for inferring the magnitude of the membrane deflection which do not account for the relation between the applied force or deflection and the deflection of the interfacial membrane and time dependent variations. In this work, the dynamic behavior of the droplets under external excitation has been modeled using nonlinear finite element analysis. A flexoelectric model including mechanical, electrical, and chemical sensitivities has been developed and coupled with the calculated bilayer deformations to predict the mechanotransductive response of the droplets under excitation. Using the developed framework, the possibilities of energy harvesting for different droplet configurations have been investigated and reported.

Tubuloglomerular feedback dynamics and renal blood flow autoregulation in rats

1991 ◽  
Vol 260 (1) ◽  
pp. F53-F68 ◽  
Author(s):  
N. H. Holstein-Rathlou ◽  
A. J. Wagner ◽  
D. J. Marsh
Keyword(s):  
Blood Flow ◽  
Arterial Pressure ◽  
Renal Blood Flow ◽  
Slow Component ◽  
Broad Band ◽  
Experimental Results ◽  
Tubuloglomerular Feedback ◽  
Single Frequency ◽  
Vascular Control ◽  
Arterial Blood

To decide whether tubuloglomerular feedback (TGF) can account for renal autoregulation, we tested predictions of a TGF simulation. Broad-band and single-frequency perturbations were applied to arterial pressure; arterial blood pressure, renal blood flow and proximal tubule pressure were measured. Data were analyzed by linear systems analysis. Broad-band forcings of arterial pressure were also applied to the model to compare experimental results with simulations. With arterial pressure as the input and tubular pressure, renal blood flow, or renal vascular resistance as outputs, the model correctly predicted gain and phase only in the low-frequency range. Experimental results revealed a second component of vascular control active at 100-150 mHz that was not predicted by the simulation. Forcings at single frequencies showed that the system behaves linearly except in the band of 33-50 mHz in which, in addition, there are autonomous oscillations in TGF. Higher amplitude forcings in this band were attenuated by autoregulatory mechanisms, but low-amplitude forcings entrained the autonomous oscillations and provoked amplified oscillations in blood flow, showing an effect of TGF on whole kidney blood flow. We conclude that two components can be detected in the dynamic regulation of renal blood flow, i.e., a slow component that represents TGF and a faster component that most likely represents an intrinsic vascular myogenic mechanism.

Parametric Resonance of a Self-Excited System Under External Force and Time Delay Influence

2013 ◽  
Author(s):  
Jerzy Warminski ◽  
Anna Warminska
Keyword(s):  
Time Delay ◽  
External Force ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Multiple Time ◽  
Frequency Locking ◽  
Scale Method ◽  
Rayleigh Function ◽  
Excited System ◽  
Multiple Time Scale Method

Vibrations of a nonlinear self-excited system driven by parametric excitation are presented in the paper. The considered model with one DOF includes a self-excitation term represented by a nonlinear Rayleigh function and also a periodically varied stiffness coefficient which represents parametric excitation. The influence of the external force or/and time delay, treated as a control signal, is demonstrated. Nonlinear parametric resonance is determined numerically and analytically by the multiple time scale method. The influence of time delay on the resonance zones and the frequency locking phenomenon is analysed.

scholarly journals Analysis of Forming Limits in Sheet Metal Forming with Pattern Recognition Methods. Part 2: Unsupervised Methodology and Application

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 1892 ◽  
Author(s):  
Christian Jaremenko ◽  
Emanuela Affronti ◽  
Andreas Maier ◽  
Marion Merklein
Keyword(s):  
Pattern Recognition ◽  
Sheet Metal ◽  
Optical Measurement ◽  
Unsupervised Classification ◽  
Evaluation Methods ◽  
Time Dependent ◽  
Measuring System ◽  
Forming Limit ◽  
Element Analysis

The forming limit curve (FLC) is used in finite element analysis (FEA) for the modeling of onset of sheet metal instability during forming. The FLC is usually evaluated by achieving forming measurements with optical measurement system during Nakajima tests. Current evaluation methods such as the standard method according to DIN EN ISO 12004-2 and time-dependent methods limit the evaluation range to a fraction of the available information and show weaknesses in the context of brittle materials that do not have a pronounced constriction phase. In order to meet these challenges, a supervised pattern recognition method was proposed, whose results depend on the quality of the expert annotations. In order to alleviate this dependence on experts, this study proposes an unsupervised classification approach that does not require expert annotations and allows a probabilistic evaluation of the onset of localized necking. For this purpose, the results of the Nakajima tests are examined with an optical measuring system and evaluated using an unsupervised classification method. In order to assess the quality of the results, a comparison is made with the time-dependent method proposed by Volk and Hora, as well as expert annotations, while validated with metallographic investigations. Two evaluation methods are presented, the deterministic FLC, which provides a lower and upper limit for the onset of necking, and a probabilistic FLC, which allows definition of failure quantiles. Both methods provide a necking range that shows good correlation with the expert opinion as well as the results of the time-dependent method and metallographic examinations.

Dynamic Stability of Simply Supported Beams With Multi-Harmonic Parametric Excitation

2020 ◽  
pp. 2150027
Author(s):  
Chao Xu ◽  
Zhengzhong Wang ◽  
Baohui Li
Keyword(s):  
Parametric Resonance ◽  
Parametric Excitation ◽  
Dynamic Instability ◽  
Elastic Structures ◽  
Simply Supported ◽  
Response Characteristics ◽  
Positive Effects ◽  
Excited Vibration ◽  
Mdof Systems ◽  
Instability Regions

Determination of the regions of dynamic instability has been an important issue for elastic structures. Under the extreme climate, the external load acting on structures is becoming more and more complicated, which can induce dynamic instability of elastic structures. In this study, we explore the dynamic instability and response characteristics of simply supported beams under multi-harmonic parametric excitation. A numerical approach for determining the instability regions under multi-harmonic parametric excitation is developed here by examining the eigenvalues of characteristic exponents of the monodromy matrix based on the Floquet theorem, and the fourth-order Runge–Kutta method is used to calculate the dynamic responses. The accuracy of the method is verified by the comparison with classical approximate boundary formulas of dynamic instability regions. The numerical results reveal that Bolotin’s approximate formulas are only applicable to the low-order instability regions with a small value of the excitation parameter of simple parametric resonance. Multi-harmonic parametric excitation can significantly change the dynamic instability regions, it may cause parametric resonance on beams for longitudinal complex periodic loads. The influence of frequency and number of multiply harmonics on the parametrically excited vibration of the beam is explored. High-order harmonics with low-frequency have positive effects on the stable response characteristics for multi-harmonic parametric excitation. This paper provides a new perspective for the vibration suppression of parametric excitation. The developed procedure can be used for multi-degree-of-freedom (MDOF) systems under complex excitation (e.g. tsunami waves and strong winds).

scholarly journals Dynamics of entanglement entropy of interacting fermions in a 1D driven harmonic trap

2018 ◽  
Vol 175 ◽  
pp. 03002
Author(s):  
Joshua R. McKenney ◽  
William J. Porter ◽  
Joaquín E. Drut
Keyword(s):  
Thermal Behavior ◽  
Parametric Resonance ◽  
Cold Atoms ◽  
Particle System ◽  
Entanglement Entropy ◽  
Harmonic Trap ◽  
Time Dependent ◽  
One Dimension ◽  
Recent Analysis ◽  
Contact Interactions

Following up on a recent analysis of two cold atoms in a time-dependent harmonic trap in one dimension, we explore the entanglement entropy of two and three fermions in the same situation when driven through a parametric resonance. We find that the presence of such a resonance in the two-particle system leaves a clear imprint on the entanglement entropy. We show how the signal is modified by attractive and repulsive contact interactions, and how it remains present for the three-particle system. Additionaly, we extend the work of recent experiments to demonstrate how restricting observation to a limited subsystem gives rise to locally thermal behavior.

Analytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches

2003 ◽  
Vol 125 (1) ◽  
pp. 73-79 ◽  
Author(s):  
Dimitris S. Sophianopoulos ◽  
George T. Michaltsos
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Dynamic Stability ◽  
Parametric Excitation ◽  
Stability Problem ◽  
Axial Loading ◽  
Time Dependent ◽  
Analytical Treatment ◽  
Simply Supported ◽  
Forced Motion

The present work offers a simple and efficient analytical treatment of the in-plane undamped vibrations of simply supported parabolic arches under parametric excitation. After thoroughly dealing with the free vibration characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P=P0+Pt cos θt are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed. An illustrative example based on Bolotin’s approach produces results validating the proposed method.

scholarly journals A Laser-Based Optical Sensor for Broad-Band Measurements of Building Earthquake Drift

2017 ◽  
Vol 33 (4) ◽  
pp. 1573-1598 ◽  
Author(s):  
David McCallen ◽  
Floriana Petrone ◽  
Jason Coates ◽  
Nicholas Repanich
Keyword(s):  
Broad Band ◽  
Strong Motion ◽  
Structural Member ◽  
Time Dependent ◽  
Position Sensor ◽  
Computational Simulations ◽  
Earthquake Excitation ◽  
Seismic Demands ◽  
Building Systems ◽  
Traditional Approaches

Accurate measurements of the time-dependent deformations of a building during earthquake excitation are essential for interpretation of the dynamic response of the as-built system and for quantifying the seismic demands. Traditional approaches for monitoring building systems are based on strong motion accelerometers mounted at selected elevations. However, accelerometer-based systems do not directly measure the deformations of the structure, and can have significant limitations that make it challenging to correctly measure deformations, particularly permanent deformations from inelastic response. In the study described herein, computational simulations and experiments were combined to evaluate the potential of a new optically based sensor to directly measure time-dependent deformations of a building, including inelastic deformations. The sensor methodology includes corrections for localized structural member rotations and can provide estimates of the absolute accelerations at each floor. A laser-based system utilizing a recently developed discrete diode position sensor (DDPS) is evaluated, and the ability of such a system to measure earthquake induced transient deformations characterized by building interstory drift is demonstrated.

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