Distinctive trembling features following resonance peaks at zero group velocity frequencies in harmonic analysis

The fascinating non-propagating lamb wave modes, Zero-Group-Velocity (ZGV) modes, have ignited profound research curiosity. ZGV modes possess the distinctive attribute of an elapsed group velocity with a finite nonzero wavenumber, indicating a spatially propagating wave package under a motionless envelope. This stationary mode engenders a localized resonance, confining the wave energy in the vicinity. These captivating phenomena have been scrutinized by researchers from the perspective of temporal and spatial domains. Nevertheless, it remains an uncharted frontier that how ZGV modes manifest their peculiarity for steady-state responses in harmonic analysis. Inspired by the unique trembling phenomenon following the appearance of ZGV resonance peaks, this paper aims at revealing the underlying mechanism and fundamental nature of the ZGV trembling phenomena in harmonic analysis, developing a deeper insight into lamb wave modes generation and propagation. The paper commences with the identification and extraction of ZGV modes under the frameworks of analytical analysis, serving as a reference for the subsequent analysis. This is followed by the construction of a finite element model for the implementation of harmonic analysis. Through the meticulous examination of displacement frequency spectra and dispersion curves, the trembling phenomenon following the ZGV resonances is visualized and evaluated. Ultimately, Electro-Mechanical Impedance Spectroscopy (EMIS) is employed to conduct the harmonic tests experimentally to validate the distinct trembling features. The distinct trembling features are attributed to the drastic fluctuations of participation factor for the emerging modes. This paper culminates with summary, concluding remarks, and suggestions for future work.