Enhancing responses of Lamb waves to bias electric fields by flexoelectricity

2021 ◽  
pp. 1-14
Author(s):  
Sihao Lv ◽  
Wenjun Yang ◽  
Qian Deng ◽  
Shengping Shen
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Strain Gradient ◽  
Acoustic Waves ◽  
Lamb Waves ◽  
Gradient Elasticity ◽  
High Sensitivity ◽  
Strain Gradient Elasticity ◽  
Voltage Sensors ◽  
Bias Electric Field

Abstract In this work, responses of Lamb waves to a bias electric field in a nanoplate with the consideration of piezoelectricity, flexoelectricity, and strain gradient elasticity are investigated. Firstly, governing equations and boundary conditions of acoustic waves propagating in bias fields are derived. Then, dispersion equations under a bias electric field are obtained and solved numerically. Numerical solutions indicate that flexoelectricity can enhance the response of Lamb waves to external bias electric fields. It is also found that the competition between flexoelectricity and strain gradient elasticity leads to a complex variation of the voltage sensitivity with respect to the wavelength and frequency of Lamb waves. Our work may provide a way of resolving the contradiction between high sensitivity and miniaturization in the conventional voltage sensors based on surface acoustic waves. The theoretical results can guide a new design of voltage sensors with high sensitivity.

Bernoulli–Euler Dielectric Beam Model Based on Strain-Gradient Effect

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Xu Liang ◽  
Shuling Hu ◽  
Shengping Shen
Keyword(s):  
Electric Field ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Beam Theory ◽  
Field Strain ◽  
Beam Model ◽  
Strain Gradient Elasticity ◽  
Cantilever Beams ◽  
Size Dependent ◽  
Classical Beam Theory

The theoretical investigation of the size dependent behavior of a Bernoulli–Euler dielectric nanobeam based on the strain gradient elasticity theory is presented in this paper. The variational principle is utilized to derive the governing equations and boundary conditions, in which the coupling between strain and electric field, strain gradient and electric field, and strain gradient and strain gradient are taken into account. Different from the classical beam theory, the size dependent behaviors of dielectric nanobeams can be described. The static bending problems of elastic, pure dielectric (nonpiezoelectric), and piezoelectric cantilever beams are solved to show the effects of the electric field-strain gradient coupling and the strain gradient elasticity. Comparisons between the classical beam theory and the strain gradient beam theory are given in this study. It is found that the beam deflection predicted by the strain gradient beam theory is smaller than that by the classical beam theory when the beam thickness is comparable to the internal length scale parameters and the external applied voltage obviously affects the deflection of the dielectric and piezoelectric nanobeam. The presented model is very useful for understanding the electromechanical coupling in nanoscale dielectric structures and is very helpful for designing devices based on cantilever beams.

Nonlinear Acoustoelastic Interactions of Lamb Waves with LiNbO3 Films Deposited on Sapphire Substrates

2004 ◽  
Vol 261-263 ◽  
pp. 263-268 ◽  
Author(s):  
H. Liu ◽  
K.C. Shin ◽  
J.J. Lee ◽  
Z.M. Cai
Keyword(s):  
Electric Field ◽  
Acoustic Waves ◽  
Lamb Waves ◽  
Piezoelectric Plate ◽  
Surface Acoustic Waves ◽  
Bias Field ◽  
Film Structure ◽  
Voltage Sensors ◽  
Sapphire Substrates ◽  
Piezoelectric Structure

The influence of a biasing electric field on the propagation of the lowest-order antisymmetrical a0 Lamb wave modes in a bi-layered piezoelectric plate is investigated in this paper. It is found that the velocity shifts for the a0 mode due to presence of the bias field on the 10- µm LiNbO3 film structure are comparable with those observed in surface acoustic waves and Lamb waves in LiNbO3 plates. The fractional change in phase velocity of the layered piezoelectric structure is a linear function of the biasing electric field and can be used in voltage sensors.

SIZE-DEPENDENT PIEZOELECTRICITY AND ELASTICITY DUE TO THE ELECTRIC FIELD-STRAIN GRADIENT COUPLING AND STRAIN GRADIENT ELASTICITY

2013 ◽  
Vol 05 (02) ◽  
pp. 1350015 ◽  
Author(s):  
LIANG XU ◽  
SHENGPING SHEN
Keyword(s):  
Electric Field ◽  
Strain Gradient ◽  
Present Model ◽  
Gradient Elasticity ◽  
Beam Theory ◽  
Field Strain ◽  
Strain Gradient Elasticity ◽  
Size Dependent ◽  
Beam Thickness ◽  
Gradient Coupling

A size-dependent nonclassical Bernoulli–Euler beam model based on the strain gradient elasticity is proposed for piezoelectric nanowires. The governing equations and the corresponding boundary conditions are naturally derived from the variational principle. Different from the classical piezoelectric beam theory, the electric field–strain gradient coupling and the strain gradient elasticity are both taken into account. Static bending problem of a cantilever piezoelectric nanobeam is solved to illustrate the effect of strain gradient. The present model contains material length scale parameters and can capture the size dependent piezoelectricity and elasticity for nanoscale piezoelectric structures. The numerical results reveal that the deflections predicted by the present model are smaller than that by the classical beam theory and the effective electromechanical coupling coefficient is dramatic enhanced by the electric field–strain gradient coupling effect. However, the differences in both the deflections and effective EMC coefficient between the two models are very significant when the beam thickness is very small; they are diminishing with the increase of the beam thickness. This model is helpful for understanding the electromechanically coupling mechanism and in designing piezoelectric nanowires based devices.

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