Fig. 1

Schematic diagrams of the metamaterial plate and unit cell: (a) the whole plate; (b) the unit cell; (c) the front view and (d) left view of the unit cell"

Table 1

Geometrical parameters"

Table 2

Material constants"

Fig. 2

The displacements of the mass-beam system (color online)"

Fig. 3

The position of the input point (see the red dot) and output points (see the blue squares) (color online)"

Fig. 4

The transmission spectra of the metamaterial plate at different points (color online)"

Fig. 5

Steady-state modes inside and outside the faceplates (color online)"

Fig. 6

(a) Dispersion surfaces of the metamaterial plate; (b) the upper and lower bound frequencies of the bandgap (color online)"

Fig. 7

Comparison of dispersion surfaces and transmission spectra (color online)"

Fig. 8

Dispersion surfaces under different control voltages (color online)"

Fig. 9

Theoretical upper and lower bound frequencies of the bandgap (color online)"

Fig. 10

Transmission spectra of different output points (color online)"

Fig. 11

Vibration modes of the metamaterial plate under different excitation frequencies and control voltages (color online)"

Fig. 12

Comparison between the theoretical and numerical lower bound frequencies of the bandgap (color online)"

Fig. 13

The relationship between the control gain and the excitation frequency (color online)"

Fig. 14

Transmission spectra under a voltage gain of -2 kV/cm, a dynamic voltage with the frequency-displacement control method, and a voltage gain of 2 kV/cm (color online)"

Fig. 15

Modes of the resonator and plate with and without the frequency-displacement feedback control under an excitation frequency of 47.6 Hz (color online)"