## 1 Introduction  
Metamaterials are artificial composite structures or materials with extraordinary performance that have broad application prospects. Some metamaterials can effectively prevent wave propagation at specific frequencies, and the ranges of these frequencies are called bandgaps. The structures with bandgaps have aroused the research interest of people from diverse fields [1, 2]. Metamaterials are widely used in noise reduction and isolation [3, 4]. For example, the varying geometry or material configuration of the metamaterials to control certain frequencies and reduce vibration [5]. Also, these unique characteristics makes metamaterials ideal candidates for the design of pass-band directional mechanical filters [6] for directional wave transmission [7, 8]. [PERSON], [PERSON] et al. [9] illustrates the possibility of tuning bandgaps with geometric variation. The influence of material properties on the bandgap characteristics of metamaterials has also been widely mentioned [10, 11]. The problem is that the direction of wave propagation and bandgap cannot be tuned after manufacturing. Traditional methods of metamaterial design cannot achieve the continuous control of parameters. Thus, tunable metamaterials have received increasing amounts of attention from scholars. Some studies have considered the influence of magnetic or electric fields on bandgap structures [12, 13]. Piezoelectric materials are also taken into account [14, 15]. [PERSON] al. [16] found that temperature effects could potentially be used for fine-tuning of the phononic bandgap frequency. [PERSON], [PERSON] et al. [17] demonstrated the thermal tuning of phononic bandgaps in the megahertz range. These related studies have important guiding significances for better assisting in the design of tunable devices and tuning mechanisms. The results of some studies indicate that the position and width of the bandgap are affected by the applied deformation [18; 19]. [PERSON], [PERSON] et al. [20] confirms the feasibility of the design of soft tunable phononic crystals and acoustic devices by harnessing uniaxial tension. Structures with bandgaps are to be attenuated in a specific frequency range [21; 22; 23; 24]. Geometry, material properties, and loading conditions all affect the tuning of the bandgap position of phonon crystals in the relevant research of [PERSON] [19; 25; 26]. The soft materials can undergo finite and reversible elastic deformations because of super elasticity. And the porous structures are suitable for shape control. They can be used to make porous phonon crystals [11; 27; 28]. Their configuration can be easily tuned after manufacturing is completed through various methods. Generally, mechanical loading is simple and practical to exert on a structure. Bandgap characteristics will be changed in different geometric configurations with deformed porous materials [20; 26; 29]. Some metamaterial structures can also be deformed under different applied loads such as compression and stretching, which significantly affect their bandgap characteristics [11; 30; 31; 32]. The applied load can close, open, and move the bandgap of the metamaterial structure, which can affect the wave propagation in a specific frequency range [29; 33; 34]. [PERSON], [PERSON] et al. [11] proposed a new configuration-controllable porous metamaterial (CCPM) designed and manufactured using silicone rubber. The bandgap characteristics of CCPM were experimentally and numerically studied. Also, the vibration transmission characteristics of specimens with different deformations were tested, and the influence of the corresponding configuration change in the bandgap characteristics of the structure was studied. Through experimental and numerical analyses, it has been shown that the adjustment of the bandgap of CCPM could be achieved by controlling its configuration. In fact, the initial stress occurs during the configuration-control, and it also affects the bandgap characteristics when the configuration changes [35; 36; 37; 38].