In the present study, a modular mass oscillator elastic metasurface (MMEM) is proposed to manipulate the wavefield of flexural waves by assembling and replacing mass-oscillator-like functional units. Based on the bandgap analysis of phononic crystals, the MMEMs were found to achieve a full 2 π range of phase shift with relatively high transmission using functional unit arrangements of varying sizes (masses). According to the generalized Snell’s law, the modulation of abnormal refraction, lens focusing, and beam self-acceleration can be realized. To broaden the operating frequency domain, we present the idea of a multiple mass oscillator array design, which can control flexural waves at broadband frequencies of 13–41 kHz by adding/removing mass oscillators within a functional unit. This study presents a method to realize tunable metasurfaces and provides an innovative concept for broadening the operating frequency of elastic metasurfaces.

Considering the manufacturing difficulty and tunability, a one-dimensional phononic crystal-type metastructure is proposed in this paper. By adjusting the distance between the mass oscillators installed on the connecting bar, that is, changing the length of the phononic crystal unit, the phase shift of the flexural wave can span over a full range of 0–2π and then the phenomena such as abnormal refraction, beam focusing, and self-acceleration can be realized based on the generalized Snell’s law. In addition, the method of multiple mass oscillator array design is used to broaden the operating frequency domain by increasing or decreasing the number of mass oscillators. This proposed method provides an innovative concept for realizing broadband tunable metastructures and has potential applications in the fields of vibration control, energy harvesting, and noise isolation.

In this paper, a simple mass oscillator metasurface is designed, which can regulate the phase shift of flexural wave covering 0-2π by adjusting the number of mass oscillators on the connecting bar. Based on the forced vibration theory, there is a simple approximately linear relationship between the number and phase shift of mass oscillators, which can more intuitively and accurately predict the phase of different number of mass oscillators, and then realize the metasurface design of mass oscillators with different requirements. Therefore, arbitrary regulation of flexural waves, such as abnormal refraction, beam focusing, and self-acceleration, can be realized by reasonably arranging the number of mass oscillators. The results show that the proposed metasurface can be greatly simplified both in the establishment of phase shift relation and in the fabrication of structure configuration, and will have broad application potential in the engineering field.

In this paper, we design a tunable asymmetric transmission structure consisting of a one-dimensional phononic crystal metastructure and a simple mass oscillator metasurface. By reasonably adjusting the width of the supercell in the metasurface, transmission control of the flexural wave can be achieved. According to the generalized Snell's law, anomalous refraction occurs when the flexural wave is obliquely incident, while total reflection will occur when the flexural wave is vertically incident. The one-dimensional phononic crystal metastructure can be used to deflect the perpendicularly incident flexural wave. In combination with the metasurface, the asymmetric transmission of flexural waves over a quite wide frequency range can be achieved. The designed asymmetric transmission structure has both tunability and broadband capability. Adjusting the distance of the mass oscillators in the metastructure and the phase distribution of the metasurface can realize the modulation of refraction angles, while increasing or decreasing the number of mass oscillators can further expand the operating frequency domain of the tunable asymmetric transmission structure. Numerical results show that the proposed structure can achieve asymmetric transmission of flexural waves in the frequency domain of 13-25 kHz or even wider.

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