## 1 Introduction  
Polymers have been a promising damping materials because of their good damping capacity to decrease noise and vibration within their range of glass-transition temperature (\(T_{\mathrm{g}}\)) [1,2]. However, the limited damping temperature range \(\Delta\)T (usually covers 20-30 \({}^{\circ}\)C), the low storage modulus E\({}^{\prime}\) (less than 1 GPa) and the mismatch between the working frequencies and actual required frequencies limit the applications of polymers as damping materials in engineering [3]. The several existing types of damping polymers (such as the polymer blend, copolymer, IPNs) have still not solved these deficiencies [4, 5, 6, 7, 8, 9]. Therefore, damping polymers must be attached onto substrates to work as free damping or constrained damping structures instead of being singly used as structures until now [10, 11, 12]. However, the serious mismatching of modulus between polymers and substrates might cause some interfacial problems such as stress concentration and joint failure after periods of vibration. Gradient materials are composites with continuous variation of properties from one side to another [13], which can decrease some shortcomings of the traditional composites, such as the abrupt changing of stress distributions at interfaces in damping structures and low resistance to temperature shocks. Since the concept of gradient materials was put forward in 1984 [14; 15], lots of papers have been published [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. However, the ambiguous terms \"graded material\", \"thickness gradient\" or \"bilayer material\", which can be found in literatures, are shown in Figure 1 (a detailed comparison between then can be found in Figures S1-S3). Graded material (Figure 1a) is a multi-layered structure, in which the compositions change stepwise from one layer to another along a certain direction, while the compositions in each layer are homogeneous. This kind of graded material is usually generated layer by layer. In addition, the mechanical properties of composites transform orderly from each adjacent sections. Bilayer material (Figure 1b) has a thin-inside transition zone, in which the compositions change sharply. In contrast, the compositions are homogeneous outside the transition zone. There are two different methods to prepare the bilayer material. One is casting different resins into a mold via layer by layer. In addition, the transition region is generated by molecular diffusion during the curing process. The other is using an incomplete self-stratification of resin mixture to form a thin film. Mechanical properties (e.g., storage modulus and stiffness) of this bilayer material in transition region would change sharply. The stress of this bilayer material usually concentrates in this transition zone, which will lead to adhesive failure under tensions along graded direction. Bilayer material cannot be regarded as the truly gradient material because of its limited phase interfacial transition zone. Gradient composite, as shown in Figure 1c, has a continuous changing of compositions from one side to the other (Figure S4 and Table S1). It can be regarded as combinations of infinite ultra-thin layers,  
Figure 1: Schematic diagram of the graded material (**a**); bilayer material (**b**); and the continuous gradient material (**c**). The tonality represents the changing composition ratio. The solid curves (A) and dotted curves (B) in right side figure represent the components ratio used in composite. and each layer is homogeneous in composition. The unique structure endows this kind of composites a plenty of new properties comparing to the traditional polymers. Previous works of this gradient composite mainly focused on the fabricating methods, mechanical analysis or biocompatibility [27; 28]. While, the damping properties of gradient materials are still unclear. Furthermore, the fabricating processes of these gradient materials are usually complex, expensive and time-consuming [29; 30].