## 1 Introduction
[8] combined ionic technology with a buffer structure at a tunnel entrance and determined that a buffer structure with air slits can effectively reduce the micro-pressure wave amplitude. Furthermore, they developed an analytical model for predicting micro-pressure waves. [PERSON] et al. [9] conducted a comparative study on a variety of buffer structures at 400-km/h high-speed railway tunnel entrances. They proposed to set up an open-hole slant-cut equal-section enlarged section buffer structure of a certain length at the tunnel entrance such that the micro-pressure wave amplitude at tunnel entrances of 5 km and below could satisfy the national regulation standard. In recent years, with the increase in train speed demand, researchers have focused on the phenomenon of high micro-pressure wave amplitude in 600-km/h maglev trains. [PERSON] et al. [10] proposed continuum theory to examine the effect of maglev trains entering tunnels at high Mach numbers on micro-pressure waves. [PERSON] et al. [11] examined the distribution pattern of peak pressure in the tunnel during the rendezvous of 600-km/h maglev trains and concluded that the railway tunnel structure did not satisfy the requirements of high-speed maglev trains passing through the tunnel, and pressure-reducing measures, such as increasing the clear space area of the tunnel or installing additional shafts, should be considered. [PERSON] et al. [12] used the overlapping grid method to investigate the initial compression waves and micro-pressure waves when traversing a tunnel at the head of a 600-km/h high-speed maglev train using three different arch structures: single-arch, double-arch, and triple-arch. They observed that an increase in the arch structure of the maglev train can effectively reduce the initial compression wave gradient in the tunnel and micro-pressure wave amplitude at the tunnel exit. [PERSON] et al. [13] proposed a buffer structure with an arched lattice design that can further dissipate the energy of micro-pressurewaves through a semi-enclosed decompression region formed by the buffer structure. [PERSON] et al. [14] examined the effect of gas deflectors on the aerodynamic effects generated by high-speed maglev trains passing through tunnels at a speed of 600 km/h. They observed that although the deflectors can effectively suppress the pressure between the tunnel wall and train surface, they can only provide limited relief with respect to the micro-pressure wave amplitude. [PERSON] et al. [15] designed and developed the world's only dynamic model test platform for speeds up to 680 km/h. This in turn significantly reduced the cost for testing maglev trains at 600 km/h and improved the accuracy of the test data. [PERSON] et al. [16] used numerical simulations to investigate the aerodynamic effects of maglev trains passing through tunnels at different speeds and observed that the power exponential relationship between the speed of the maglev train and amplitude of the micro-pressure waves increases as the speed of the train increases. Furthermore, they observed sub-reflection waves. The Helmholtz resonator is a chamber installed inside a tunnel comprising a cavity and corresponding neck passage. The pressure wave generated by the train passing at high speed forms a column of air with a certain mass in its neck, which can be considered as a spring oscillator. The air inside the chamber can be considered as a spring, and the neck and chamber form an elastic vibrating system, which resonates when the acoustic frequency of the airflow is similar to the intrinsic frequency of the vibrating system [17]. When a vibrating system resonates, most of its energy dissipates. Each Helmholtz resonator has its own resonant frequency, and [PERSON] et al. [18] and [PERSON] et al. [19] observed that the resonant band of a single-cavity, double-necked Helmholtz resonator system is wider than that of a conventional single-cavity, single-necked Helmholtz resonator.