Effective Negative Mass Nonlinear Acoustic Metamaterial with Pure Cubic Oscillator

Abstract

Acoustic metamaterial, which can prohibit effectively the elastic wave propagation in the bandgap frequency range, has broad application prospects in the vibration and noise reduction areas. The Lindstedt–Poincaré method was utilized to analyze the dispersion curves of nonlinear metamaterial with a pure Duffing oscillator. The first-order perturbation solutions of acoustic and optical branches were obtained. Both the starting and cutoff frequencies of the bandgap are determined consequently. It was found that the soft/hard characteristics of pure Duffing oscillators could lead to the lower/upper movement of the starting and cutoff frequencies of the bandgap. By further researching the degraded linear system, the conclusion that actual nonlinear metamaterial bandgap region is wider than effective negative mass region is drawn and that both mass and stiffness ratio effect on the starting frequency is obtained. Effective positive mass can also lead to the vibration attenuation in bandgap. For nonlinear metamaterial, the translation effect of the external excitation amplitude on the bandgap range and the zero mass at the nonlinear bandgap cutoff frequency were discussed, and all above conclusion are identified by numerical analysis.

A Novel Elastic Metamaterial with Multiple Resonators for Vibration Suppression

“…Equations ( 10) and ( 11) express the acoustic and optical frequency branches, respectively. Low-frequency and highfrequency dispersive curves are then presented by ω Acoustic and ω Optical , respectively [1]. In the above equations, at the point of qa � ± π, the slope of the dispersion curve, namely, the velocity of the traveling wave, is equal to zero.…”

“…is area is the first Brillouin zone's boundary. Hence, substituting qa � π and qa � 0 into Equations ( 10) and (11), and then solving these expressions, the starting and ending frequencies of the bandgaps for the 1DOF model are extracted [1,20].…”

“…e propagation of waves of different wavelengths is controlled by the low/high-frequency bandgaps generated by the metamaterials. Given this unique property, metamaterials can be used in the field of acoustic insulation, filtration of waves, oscillations reduction, and sonic transmission [1][2][3].…”

Broadband Vibration Attenuation Achieved by 2D Elasto-Acoustic Metamaterial Plates with Rainbow Stepped Resonators

“…The elasto-acoustic metamaterials have the ability of manipulating mechanical waves. Analogous to their counterparts in electromagnetics, the elasto-acoustic metamaterials also possess unique negative properties, such as negative effective mass/density [10][11][12][13], negative bulk modulus [14][15][16], double negativity [17][18][19][20], etc. The very first acoustic metamaterial, developed by Liu et al [21], used fabricated sonic crystals with hard cores and soft coatings arranged in an epoxy matrix.…”

Optimal design of rainbow elastic metamaterials

“…Metamaterials with negative mass/density were most widely mentioned in literature. Yao et al [8,9], Gao et al [10] and Huang et al [11,12] investigated negative mass metamaterial structures with idealized mass-spring systems as resonators. Cselyuszka et al [13], Lee et al [14] and Yang et al [15] presented metamaterials containing elastic membranes that had negative mass/density.…”