Low-frequency Wave Attenuation Research Articles

Flexural wave attenuation by metamaterial beam with compliant quasi-zero-stiffness resonators

A novel metamaterial beam with embedded quasi-zero-stiffness (QZS) resonator is proposed to realize wave attenuation in very low-frequency band gaps. The configuration of the QZS resonator is developed by using compliant mechanism with design optimization, and the feature of quasi-zero stiffness is achieved under proper pre-compression. Then, the dispersion relations of the metamaterial beam are derived by the transfer matrix method (TMM) to predicate the band gap theoretically. Additionally, the dynamic responses of the metamaterial beam are obtained by the spectral element method (SEM) to evaluate the transmittance of the flexural wave. Finally, the prototype of the metamaterial beam is fabricated by additive manufacturing, and the experimental investigation is conducted to verify the formation mechanism of the band gaps, which shows very low-frequency band gaps. Therefore, the QZS metamaterial beam should be promising in application for very low-frequency wave attenuation.

Enhanced suppression of low-frequency vibration transmission in metamaterials with linear and nonlinear inerters

This study proposes the use of a linear and geometrically nonlinear inerter-based resonator in locally resonant acoustic metamaterials (LRAMs) and evaluates the performance on low-frequency wave attenuation. The LRAM is modeled as a 1D chain system composed of mass-in-mass unit cells connected by springs, and the geometrical nonlinearity is achieved by two lateral inerters linking the resonator and lumped mass symmetrically with respect to the horizontal springs. For the nonlinear inerter-based LRAM, the dispersion relation is analytically derived by a complex Fourier transform and the harmonic balance method. Compared with the linear inerter-based LRAM, the proposed nonlinear inerter-based structure has the property of a low-frequency bandgap with sufficient width for longitudinal wave propagation without being sensitive to changes in the inertance ratio. The nonlinearity can extend the original material parameter restrictions, leading to a lower-frequency bandgap. The results of dispersion properties are validated by wave transmittance and vibration power flow diagrams obtained by using the method of effective mass. It is shown that an adequate number of unit cells can achieve better wave attenuation performance.

атухание низкочастотных электромагнитных волн в нижней ионосфере земли под влиянием сильного локального возмущения в атмосфере.

The value and duration of attenuation of low frequency waves (1...10 kHz) in the presence of a strong local disturbance of the atmosphere have been estimated. Sources of significant local disturbances of the atmosphere are, for example, precipitation of energetic particles of radiation belts; electromagnetic pulses of lightning discharges; radiation of powerful low-frequency ground-based transmitters; invasion of large meteors. Strong local disturbances lead to an increase of ionization (concentration of free electrons) of the environment by several orders of magnitude in the region of space whose characteristic dimensions are comparable to the length of the wave (tens and hundreds of kilometers). As such a disturbance, we use the previously developed macroscopic model of an instantaneous, point release of a relatively large amount of energy in the atmosphere below the ionosphere. This model makes it possible to estimate the features of the propagation of low-frequency waves through the disturbed layer of the lower ionosphere by changing only two initial parameters: the disturbance energy and its initial height. It is shown that the attenuation value is almost independent of frequency and geo- and heliophysical conditions. For initial heights up to 50 km, the fading duration does not exceed ~ 2 min. With an increase of the initial altitude, the attenuation in the lower ionosphere becomes extremely large. However, for heights of 50 ... 70 km (depending on the value of energy), the horizontal size of the disturbance decreases significantly, which leads to a decrease in the fading time to tens of seconds for initial heights of more than 80 km.

Bending-wave localization and interaction band gaps in quasiperiodic beams

Aperiodic metamaterials can host topological or localized wave modes, and gradually changing structures are known to induce conversion between elastic wave types. This work describes a family of one dimensional, aperiodic elastic structures that can host localized modes or achieve low-frequency attenuation by varying a single geometrical parameter, i.e., the ratio between the sizes of two interacting periodic structures. Two periodic sets of slits on the top and bottom of a slender beam scatter bending waves. The thickness profile and cross section of beams with a period ratio close to 1 varies slowly, resulting in localized wave modes. The localization happens because of spatially confined band gaps and is only triggered for certain excitation locations, unlike wave localization due to a local defect. If the periods differ more, broad band gaps appear at wave numbers equal to linear combinations of the individual Brillouin zone edges of each set of slits. We call these interaction band gaps, since they result from the interplay between two periodic sets of slits. Low-frequency wave attenuation is achieved while maintaining a high overall bending stiffness.

Issues in design of one-dimensional metamaterials for seismic protection

Metamaterials provide an unprecedented solution for seismic hazard mitigation by blocking seismic wave transmission. This paper investigates the wave attenuation capability of one-dimensional binary seismic metamaterials. Variations in the bandgaps of metamaterials are studied analytically with different material combinations. Results indicate that large contrasts in mass densities and wave velocities between the two constituent materials are desirable in consideration of gap width and central frequency, and increasing the contrast in mass density is relatively more effective. Reducing the filling ratio of the soft and light material is also beneficial to seismic wave attenuation. However, several practical challenges are also highlighted. For example, attenuation of low frequency waves inevitably leads to low global stiffness of seismic metamaterials because the use of soft constituent material is indispensable. Despite enhancement of the attenuation effect in the whole frequency range, material damping weakens the band structure. In addition, the vibration in front of the metamaterial is amplified to a certain degree due to wave reflections. These may present several practical conundrums in the application of seismic metamaterials.