High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

Propagation Characteristics of Flexural Wave in One-Dimensional Phononic Crystals Based on Lattice Dynamics Model

In this paper, we establish discrete flexural lattice chain models of Bragg and locally resonant phononic crystals by setting mass defect atoms and local resonant elements on the flexural lattice chain. The bandgap characteristics of flexural wave in phononic crystals are studied by establishing the governing equations of the model. The results from models show that with the change of the mass ratio of defective atoms to normal atoms, the bandgap of the flexural wave produced by Bragg scattering shows a certain rule. When the local resonant bandgap and Bragg scattering bandgap are close to each other, the two bandgaps will be coupled to form a wider flexural wave bandgap. The effect of axial strain on bending wave propagation is only the shift of bandgap position. The effect of material damping on the propagation of a bending wave is only energy dissipation at high frequency. In addition, we use finite element simulation to calculate the bandgap of flexural wave in phononic crystals with mass defects, and the results are consistent with lattice chain model. This shows that lattice chain model can effectively guide the bandgap design of phononic crystals. This comprehensive study may help to elucidate the rule of bandgap generation of flexural wave in one-dimensional phononic crystals.