A ring locally resonant phononic crystal with an effective optimization scheme is proposed. In order to obtain low-frequency broadband properties, three loops of 2-factor (the two key geometric parameters, i.e., the thickness of elastic beam and the radius of scatterer) and 7-level numerical experiments are designed to perform the response surface methodology (RSM) analysis. The low-frequency band gaps (BGs) of the present structures are calculated using finite element method to obtain enough simulation data for RSM analysis. After calculations, the two relationships can be obtained, i.e., the relationship of the starting frequency of the first BG and the two factors; and the relationship of the total bandwidth of the first two BGs and the two factors. Aiming at the lower starting frequency of the first BG and the wider total bandwidth of the first two BGs, the two key geometric parameters are optimized using interior point method.

In this paper, a comb-like locally resonant phononic crystal (LRPC) with optimal structural parameters, which has good low frequency and broadband band gaps (BGs) between 20–250 Hz, is investigated numerically. With the intention of obtaining the optimal structural parameters, based on the structures with different number of the short elastic beams, 2-factor (the two key structural parameters, i.e. the width of the scatterer and the thickness of elastic beams) and 7-level numerical experiments are designed to obtain simulations data using finite element method (FEM). The functional relationships are further constructed using the response surface method (RSM) analysis, i.e. the relationship of the starting frequency of the first BG and the two factors, the terminating frequency of the second BG and the two factors, and the relationship of the total bandwidth of the first two BG and the two factors. After calculation using interior point method, the BGs of LRPC with optimal structural parameters are determined with lower and wider BGs below 250 Hz.

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A spiral locally resonant phononic crystal (LRPC) with the optimal bandgaps (BGs) between 20 and 250 Hz is proposed. The single factor analysis of three key geometric parameters (the thickness of spiral elastic beams, the side length of square scatterers and the spirals’ turns) are performed to obtain corresponding influences on BGs, two-factor (the thickness of spiral elastic beams and the side length of the square scatterer) and seven-level experiment under the four fixed spirals’ turns are designed to obtain optimal BGs with better low-frequency broadband properties. According to numerical experiments, BG data of present spiral LRPCs can be calculated by finite element method (FEM). Relationships (i.e., the relationship between the starting frequency of the first BG and the two factors, the relationship between the bandwidth of the first BG and the two factors, and the relationship between the bandwidth of the second BG and the two factors) are further obtained using the response surface methodology (RSM). The optimal BGs with better properties are finally calculated using the interior point method.

The vibration problem has a serious impact on modern life. The phononic crystal (PHC) is a periodically arranged composite material, which has good vibration attenuation capability because of its band gap (BG) characteristics. Most of available PHCs are limited to solid structures and the application ranges are limited. In this paper, a new fan-like solid-fluid PHC structure is proposed to supress vibration in special environment. Firstly, the unit cell of fan-like PHC is built and the corresponding band structure is further calulauted by finite element method (FEM). The band structures reveal that this fan-like PHC structure has four BGs below 10000 Hz. In order to illustrate the functionality of the fan-like PHC structure for vibration attenuation, the frequency response function (FRF) of a finite fan-like PHC structure is calculated. The FRF shows that there are strong attenuations in the ranges of BGs. Finally by adjusting the side length of the square inclusion, the influence of the filling rate of the scatterer on BGs is studied. This new PHC provides new ideas for the vibration attenuation of builds at the riverside.