ZHONG Zheng and ZHAO Jinfeng et al. publish a paper in Journal of the Mechanics and Physics of Solids

March 27, 2021

Recently, Tongji Professor ZHONG Zheng and Associate Professor ZHAO Jinfeng from the School of Aerospace Engineering and Applied Mechanics, jointly with several other collaborative units, have published a paper in the international authoritative journal of solid mechanics Journal of the Mechanics and Physics of Solids. The research in this article has achieved, for the first time, super-resolution focusing of elastic waves with wide frequency and ultra-high energy density, both experimentally and theoretically.


The typical feature of super-resolution focusing is that the full width at half maximum (FWHM) is less than 0.5 times the wavelength λ0. In existing studies, structures such as negative refractive lenses, super-resolution lenses, and super-surfaces all rely on near-field evanescent waves. Based on phononic crystals, metamaterials or metasurfaces, these structures need to adjust their parameters such as dispersion curves and phases, and mostly have problems of narrow operating frequencies and low signal-to-noise ratio. Although methods such as the time-reversal method and the super-oscillation method do not require the participation of evanescent waves, they experience similar problems. Therefore, wide-frequency and ultra-high energy focusing is of great value in the fields of high-resolution imaging, energy capture, and signal amplification.


Professor ZHONG and Associate Professor ZHAO, together with their collaborative units, through experimental and theoretical studies, have achieved the super-resolution focusing of elastic waves with wide frequency band and ultra-high energy density in the variable-thickness plate acoustic lens. In this structure, increasing the equivalent refractive index plays a key role in achieving the FWHM less than 0.5λ0. In Figure 1, the aluminum plate thickness varies in a gradient along the y-direction, which is equivalent to an acoustic lens, with the central axis equivalent refractive index of n0 = 6.0. In the experiment, the A0 plate wave is excited by a piezoelectric electret film and the wave propagation is measured through a laser Doppler vibrometer.


Figure 1 The top and side views of the variable thickness plate lens sample with the equivalent refractive index n0 = 6.0 in the central axis

Figure 2(a) shows the distribution of the experimentally measured normalized off-plane displacement |w| at the incidence of A0 wave at 50kHz when n0=6.0. Figure 2(b) further displays the experimental (blue line) and numerical (red line) variations of the off-plane displacement |w| along the x-axis. The experimental focus position appears at x=16mm, which is consistent with the numerical results. Figure 2(c) shows the experimental (blue line) and numerical (red line) curves of the respective normalized off-plane displacement |w| (a.u.) along the x-direction. The experimental results show that the FWHM of the central peak is equal to 0.41λ0, which coincides with the numerical result of 0.43λ0. Compared with the incident wave, the displacement and energy density of the focusing position in Figure 2(a) are amplified by 40 and 1000 times respectively, which produces a good focusing effect even if there exists a significant noise signal in the incident wave. In practical engineering, one or several gradient lenses can be used in the flat plate structure to capture the weak signals generated or scattered by the defects, thus providing real-time monitoring of the defect locations. 

Figure 2 When n0=6.0, under the incident condition of A0 wave at 50kHz, (a) the normalized distribution of off-plane displacement |w| and its experimental (blue line) and numerical (red line) curves along (b)x axis; (c) experimental (blue line) and numerical (red line) curves of normalized off-plane displacement |w| (a.u.) along x direction.

 Professor ZHONG is the corresponding author of the paper, Associate Professor ZHAO is the first author, and other participants include Tongji Professor PAN Yongdong and graduate students CUI Xiaodong and Yuan Weitao from the School of Aerospace Engineering and Applied Mechanics. The co-authors of the paper are Professor REN Jie and Professor ZHANG Xiaoqing from the School of Physics Science and Engineering, as well as Professor Bernard Bonello from Sorbonne University and Professor Bahram Djafari-Rouhani from Lille University of Science and Technology.



Written by ZHAO Jinfeng


Link to the paper: https://doi.org/10.1016/j.jmps.2021.104357