Narrow Results

In this study, a functionally arranged phononic crystal rod, incorporating sub-periodic structures featuring distinct lattice constants, is designed. This rod seamlessly combines two distinct capabilities: highly efficient broadband vibration suppression and orderly frequency distillation. In the pursuit of this design, the dispersion characteristics of a periodic rod are first analytically calculated to determine the precise cut-on and cut-off frequencies of the resulting band gaps. Following this, the transmission of longitudinal waves traveling through a finite functionally arranged rod is elucidated. Based on these calculations, careful parameter selection yields a compact configuration for a functionally arranged phononic crystal rod, boasting an exceptionally wide band gap spanning frequencies from 100 Hz to 10,000 Hz. Finite element simulations vividly demonstrate its ultra-broadband vibration attenuation capability, nonsymmetrical wave propagation behavior, and orderly frequency distillation phenomenon. Our study underscores the advantages of employing constituent materials with a higher impedance ratio in obtaining a more compact topological structure while preserving the broadband required for vibration attenuation. This research provides essential insights for tackling the need for broadband vibration suppression in engineering and also sets the stage for achieving orderly frequency extraction and energy localization.

The band structure of a two-dimensional phononic crystal, which is composed of four homogenous steel quarter-cylinders immersed in rubber matrix, is investigated and compared with the traditional steel/rubber crystal by the finite element method (FEM). It is revealed that the frequency can then be tuned by changing the distance between adjacent quarter-cylinders. When the distance is relatively small, the integrality of scatterers makes the inner region inside them almost motionless, so that they can be viewed as a whole at high-frequencies. In the case of relatively larger distance, the interaction between each quarter-cylinder and rubber will introduce some new bandgaps at relatively low-frequencies. Lastly, the point defect states induced by the four quarter-cylinders are revealed. These results will be helpful in fabricating devices, such as vibration insulators and acoustic/elastic filters, whose band frequencies can be manipulated artificially.

In this paper, a novel composite acoustical hyperstructure of Bragg structure with local resonator is investigated theoretically for discussing the scattering performance of longitudinal vibration wave, its bandgaps are calculated using the established mathematical model. For confirming the veritable existence of bandgap and verifying the correctness of established mathematical model, the transmission spectrum of composite acoustical hyperstructure is also studied using finite-element method, and comparing the vibration transmission spectrum with bandgaps, the results indicate that the established theoretical model can correctly predict longitudinal wave bandgaps. Moreover, the bandgaps and modes shapes are calculated and compared with an unalloyed Bragg structure for probing the dispersion mechanics of composite acoustical hyperstructure, it turned out that local resonator can add one bandgap at the base of Bragg structure and the total bandgaps can be broadened. Further, for discussing the effect of spring of local resonator on bandgaps, bandgap of local resonator with different spring is calculated, the results showed that the total width of BG is larger when Young’s modulus is 1E and 16E, the total width are 772.48 and 774.30 Hz, respectively; as Young’s modulus is 0.5E and 2E, the width of BG are lower, 753.79 and 754.23 Hz, respectively. In view of longitudinal vibration wave inducing structural distortion and vibration energy conversion, the dynamic properties of composite acoustical hyperstructure are studied via strain energy density, the results indicate that reaction formation of local resonator can dissipate strain energy, when the local resonator is not activated (or waveless along with Bragg structure), un-dissipation strain energy.

A hybrid phononic crystal has been investigated. The characteristic frequency of XY mode, transmission loss and displacement vector have been calculated by the finite element method. There are Bragg scattering band gap and local resonance band gap in the band structures. We studied the influence factors of band gap. There are many flat bands in the eigenfrequencies curve. There are many flat bands in the curve. The band gap covers a large range in low frequency. The band gaps cover more than 95% below 3000 Hz.

Bragg acoustical hyperstructure can scatter elastic wave, local resonance system can fight against vibration by the reaction force with reversed phase in low-frequency range, for improving the scattering performance of Bragg hyperstructure, a novel composite beam of Bragg beam with local resonator is investigated theoretically. Its dispersion relations and bang gaps are calculated by the established theoretical model. In order to confirm the veritable existence of band gaps, the transmission spectrum of flexural vibration waves are also studied by finite-element method, and comparing the relationship of vibration transmission spectrum and band gaps, the results indicate that the proposed theoretical model can accurately predict the band gaps of the proposed composite beam. For probing the dispersion mechanics, comparing the band gaps and modes shapes of the proposed composite beam with an unalloyed Bragg beam, the results denoted that local resonator can add two band gaps at the base of Bragg beam. Further, the changes of the band gaps that depend on the local resonator and on Bragg beam are studied. It is indicated that the total band gaps can be narrowed when the resonance frequency of the local resonators located at the band gaps of the Bragg beam and the branches will become approximately flat. The band gaps will broaden if the branch that depends on the local resonator gets closer to the branch on Bragg beam.

The Bragg scattering of water waves by multiply composite artificial bars was investigated both theoretically and experimentally. Miles' theory is first employed to derive general formulae to calculate Bragg reflection coefficients for multiply composite artificial bars with different shapes, spacings, bar heights, bar footprint, and the number of bars. The theory provides explicit expressions in estimating Bragg reflections over multiply composite bars in practical engineering applications. The undulating oscillation components expanded with respect to the bottom slope and curvature components in the numerical model can increase the accuracy for the simulation of Bragg scattering. Experiments of Bragg reflection over multiply rectangular artificial bars were also conducted in a wave flume. Analytical solutions are in good agreement with numerical simulations of evolution equation of mild-slope equation (EEMSE) and laboratory experiments. Influence parameters that may lead to the optimal combination of a multiple artificial bar to increase the bandwidth of Bragg resonance were studied.

In spatially structured strong laser fields, quantum electrodynamical vacuum behaves like a nonlinear Kerr medium with modulated third-order susceptibility where new coherent nonlinear effects arise due to modulation. We consider the enhancement of vacuum polarization and magnetization via coherent spatial vacuum effects in the photon-photon interaction process during scattering of a probe laser beam on parallel focused laser beams. Both processes of elastic and inelastic four wave-mixing in structured QED vacuum accompanied with Bragg interference are investigated. The phase-matching conditions and coherent effects in the presence of Bragg grating are analyzed for photon-photon scattering.