The nonlinearity has significant effect on the ultrasonic therapy using phased ar- rays. 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.
