## 1 Introduction  
Constrained layer damping (CLD) treatment uses a viscoelastic layer, laid onto the host structure surface covered by a stiff and thin constraining layer, and it can produce energy dissipation relying on the shear deformation of the viscoelastic layer [1]. It is well known that, compared with free-layer damping (FLD) treatment, the CLD generally produces a better damping effect. As an important method of vibration reduction, CLD treatment has been widely used in aeronautics, aerospace, and other engineering domains [2; 3; 4]. Modeling the dynamic behavior of the viscoelastic composite structure is very important for CLD design, and to achieve it, the mechanical parameters of the CLD structure (which are mainly the storage modulus and loss factor of each layer) have to be known in advance. In a CLD structure, the constraining layer is mainly made of metal and its mechanical parameters can be easily found. Therefore, the identification mainly focuses on the mechanical properties of the viscoelastic core layer. It has been well understood that the mechanical properties of viscoelastic materials are influenced by temperature and frequency, and only frequency dependence is taken into account in most studies because of the temperature-frequency superposition principle [5; 6]. Scholars have proposed a variety of constitutive models of viscoelastic material, and those which are commonly used include the complex modulus model [7], the Golla-Hughes-McTavish (GHM) model [8], the anelastic displacement fields (ADF) model [9], and the fractional derivative model [10]. Then, the identification of the parameters of viscoelastic material can be converted in order to obtain the characteristic parameters of the above models. Of the aforementioned models, the fractional derivative model is widely used for its effectiveness in characterizing the mechanical behavior of viscoelastic materials in the frequency and time domains [10; 11; 12]. The core of this paper is studies the method to identify the parameters of the fractional derivative model of the viscoelastic core layer. The inverse method, combining numerical analysis and vibration tests, is an important method to identify the mechanical parameters of viscoelastic materials. The basic principle of the inverse method can be described as follows. The parameters which need to be identified are defined as design variables. To achieve the identification parameters, a matching algorithm (also known as an optimization process) is used to iteratively update the design variables in an analysis model, until the differences between the theoretical and the measured vibration parameters are minimal. Some typical researches were done, for example, based on the response surface optimization technique. [PERSON] et al. [5] identified the mechanical properties of viscoelastic materials characterized using a complex modulus by testing the vibration attenuation response of composite beams. [PERSON] et al. [13] used the numerical optimization method to identify the Young's modulus and loss factor of viscoelastic materials by testing the resonant frequency and modal loss factor of a sandwich beam. The biggest problem of the above researches is that the parameter identifications only focus on the points at a resonant frequency. Thus, the insufficient number of points may lead to the difference between the identified parameters and their true value. For a cantilever beam attached with FLD, [PERSON] and [PERSON] [14] obtained its frequency response function by motivating it with a hammer and used two steps to identify the fractional derivative model parameters. [PERSON] and [PERSON] [6] did a similar study on a cantilever beam with CLD treatment, and identified the mechanical parameters of viscoelastic materials with high damping properties, mainly through minimizing the experimental and theoretical frequency response functions at certain discrete frequency points.