The nonlinearity has significant effect on the ultrasonic therapy using phased arrays.A numerical approach is developed to calculate the nonlinear sound field generated from a phased array based on the Gaussian superposition technique.The parameters of the phased array elements are first estimated from the focal parameters using the inverse matrix algorithm;Then the elements are expressed as a set of Gaussian functions;Finally,the nonlinear sound field can be calculated using the Gaussian superposition technique.In the numerical simulation,a 64×1 phased array is used as the transmitter.In the linear case,the difference between the results of the Gaussian superposition technique and the Fresnel integral is less than 0.5%,which verifies the feasibility of the approach.In the nonlinear case,the nonlinear fields of single-focus modes and double-focus modes are calculated.The results reveal that the nonlinear effects can improve the focusing performance,and the nonlinear effects are related with the source pressures and the excitation frequencies.
On-demand inverse design of acoustic metamaterials(AMs),which aims to retrieve the optimal structure according to given requirements,is still a challenging task owing to the non-unique relationship between physical structures and spectral responses.Here,we propose a probabilistic generation network(PGN) model to unveil this implicit relationship and implement this concept with an acoustic magic-cube absorber.By employing the auto-encoder-like configuration composed of a gate recurrent unit(GRU) and a deep neural network,our PGN model encodes the required spectral response into a latent space.The memory or feedback loop contained in the proposed GRU allows it to effectively recognize sequence characteristics of a spectrum.The method of modeling the inverse problem and retrieving multiple meta structures in a probabilistic generative manner skillfully solves the one-to-many mapping issue that is intractable in deterministic models.Moreover,to meet different sound absorption requirements,we tailored several representative spectra with low-frequency sound absorption characteristics,generating highprecision(MAE<0.06) predicted spectra with multiple meta structures.To further verify the effective prediction of the proposed PGN strategy,the experiment was carried out in a tailored broadband example,whose results coincide with both theoretical and numerical ones.Compared with other 5 networks,the PGN model exhibits higher accuracy and efficiency.Our work offers flexible and diversified solutions for multivalued inverse problems,opening up avenues to realize the on-demand de sign of AMs.
