Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Kevin L. Manktelow ◽  
Michael J. Leamy ◽  
Massimo Ruzzene

Wave dispersion in a string carrying periodically distributed masses is investigated analytically and experimentally. The effect of the string's geometric nonlinearity on its wave propagation characteristics is analyzed through a lumped parameter model yielding coupled Duffing oscillators. Dispersion frequency shifts are predicted that correspond to the hardening behavior of the nonlinear chain and that relate well to the backbone of individual Duffing oscillators. Experiments conducted on a string of finite length illustrate the relation between measured resonances and the dispersion properties of the medium. Specifically, the locus of resonance peaks in the frequency/wavenumber domain outlines the dispersion curve and highlights the existence of a frequency bandgap. Moreover, amplitude-dependent resonance shifts induced by the string nonlinearity confirm the hardening characteristics of the dispersion curve. Analytical and experimental results provide a critical link between nonlinear dispersion frequency shifts and the backbone curves intrinsic to nonlinear frequency response functions. Moreover, the study confirms that amplitude-dependent wave properties for nonlinear periodic systems may be exploited for tunability of wave transport characteristics such as frequency bandgaps and wave speeds.

Author(s):  
Sejong Chun ◽  
Jonghan Jin

Wave dispersion is a key element in understanding the pulsating flows in a circular rigid pipe. This study suggests that an extended Taylor’s frozen field hypothesis should make the lumped parameter model be more practical because pressure instead of pressure gradient can be measured with simpler instrumentation. Lumped parameter model as well as wave dispersion is introduced, and then some experimental results with a blood flow simulator were analyzed to validate its idea.


2020 ◽  
Vol 48 (12) ◽  
pp. 2870-2886
Author(s):  
Mehran Mirramezani ◽  
Shawn C. Shadden

Author(s):  
Ruqia Ikram ◽  
Asif Israr

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.


2021 ◽  
Vol 11 (7) ◽  
pp. 3102
Author(s):  
Md. Zakirul Islam ◽  
Seungdeog Choi ◽  
Malik E. Elbuluk ◽  
Sai Sudheer Reddy Bonthu ◽  
Akm Arafat ◽  
...  

The rare-earth (RE) permanent magnets (PM) have been increasingly adopted in traction motor application. However, the RE PM is expensive, less abundant, and has cost uncertainties due to limited market suppliers. This paper presents a new design of a RE-free five-phase ferrite permanent magnet-assisted synchronous reluctance motor (Fe-PMaSynRM) with the external rotor architecture with a high saliency ratio. In such architecture, the low magnetic coercivity and demagnetization risk of the ferrite PM is the challenge. This limits the number of flux barriers, saliency ratio, and reluctance torque. A precise analytical design procedure of rotor and stator configuration is presented with differential evolution numerical optimizations by utilizing a lumped parameter model. A 3.7 kW prototype is fabricated to validate the proposed idea.


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