Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform

Author(s):  
Qinghua Liu ◽  
Junyi Cao ◽  
Zehao Hou ◽  
Ying Zhang ◽  
Xingjian Jing
2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.


Author(s):  
Jiapeng Liu ◽  
Ting Hei Wan ◽  
Francesco Ciucci

<p>Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>


1989 ◽  
Vol 18 (2) ◽  
pp. 48-50
Author(s):  
Kallol Bhattacharya ◽  
D. K. Basu ◽  
Ajay Ghosh ◽  
A. K. Chakrabortt

1998 ◽  
Vol 5 (2) ◽  
pp. 101-106
Author(s):  
L. Ephremidze

Abstract It is proved that for an arbitrary non-atomic finite measure space with a measure-preserving ergodic transformation there exists an integrable function f such that the ergodic Hilbert transform of any function equal in absolute values to f is non-integrable.


Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 65
Author(s):  
Benjamin Akers ◽  
Tony Liu ◽  
Jonah Reeger

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.


Actuators ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 87
Author(s):  
Nicholas A. Jones ◽  
Jason Clark

This paper presents a structural geometry for increasing piezoelectric deformation, which is suitable for both micro- and macro-scale applications. New and versatile microstructure geometries for actuators can improve device performance, and piezoelectric designs benefit from a high-frequency response, power density, and efficiency, making them a viable choice for a variety of applications. Previous works have presented piezoelectric structures capable of this amplification, but few are well-suited to planar manufacturing. In addition to this manufacturing difficulty, a large number of designs cannot be chained into longer elements, preventing them from operating at the macro-scale. By optimizing for both modern manufacturing techniques and composability, this structure excels as an option for a variety of macro- and micro-applications. This paper presents an analytical compact model of a novel dual-bimorph piezoelectric structure, and shows that this compact model is within 2% of a computer-distributed element model. Furthermore it compares the actuator’s theoretical performance to that of a modern actuator, showing that this actuator trades mechanical efficiency for compactness and weight savings.


2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.


2020 ◽  
Vol 1706 ◽  
pp. 012107
Author(s):  
V Dankan Gowda ◽  
G Naveena Pai ◽  
S B Sridhara ◽  
K S Shashidhara ◽  
Gangadhara

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