## 1 Introduction  
Deployable structures have been widely applied to the aerospace industry [1; 2; 3], such as aperture antennas [4; 5; 6; 7; 8], solar arrays [9; 10], space masts [11; 12], and so on. One of the most important advantages is the perfect package property [13] of deployable structures so as to store in the fairing of launch vehicle and deploy into structures in orbit. This way can enormously reduce the weight and enlarge the size of these pay-load structures. However, the stiffness and dynamic properties of structures are greatly decreased along with the weight reduction and size expansion [14; 15]. Therefore, the improvement of dynamic properties is an essential study on deployable structures in working state for the further applications. Different with common structures, the deployable structure generally has the drastically structural transformations from folded state to deployed state [13]. In order to fulfill this function, the deployable mechanism is necessarily employed by segmented bodies, kinematic pairs, and driving devices. These components may damage the structural integrity or lead to the nonlinear response and weaken structures [16; 17]. Thus, the accurate evaluation of dynamic properties is a significant but difficult part to study deployable structures in work state. Previous studies on dynamic properties of deployable structures have mainly focused on simplified models. [PERSON] [18] developed a simplified mathematical model of a NASA solar array fight experiment configuration to investigate the free vibration and force-response behavior by the Galerkin method for the truncated set of second-order differential equations. [PERSON] et al. [16] conducted the experiment of a deployable truss structure to explore the effects of joints on structural dynamics. The results reflected the complex nonlinear dynamic behavior and reduction of dynamic performances. [PERSON] et al. [19] established the FEM of an experimental deployable truss structure with considering the clearance joint by ANSYS to study the transient dynamic analysis based on a virtual experimental model analysis method. [PERSON] et al. [17] developed a cantilever beam model containing linear joints based on FEM to analyze the influence of joint on natural frequencies and mode shapes. It was shown that nonlinear effects of free play and hysteresis lead dynamic responses switch from one resonance frequency to another when the amplitude exceed demarcation values. [PERSON] et al. [20] proposed an optimization method with a dynamic constraint for the maximum stiffness/mass ratio to develop a new large cable-rib deployable antenna. These studies explore the dynamic properties of deployable structures in order to deeply develop the applications. Because these deployable structures on the satellites suffer from the vibrations, especially during the satellite attitude adjustment, the flexibility of deployed structures may bring trouble for the dynamic controls. However, research about the structural dynamics seldom pays attention to deployable solid-surface reflector antennas. Thereinto, the Petal-type Deployable Solid-surface Reflector (PDSR) has been widely utilized in the aerospace applications [13; 21; 22; 23; 24]. The parabolic reflector is generally divided into the central hub and several petals with the connections by the deploying mechanism. The deploying mechanism can fulfill the petal deploying from folded state to deployed state; meanwhile, it may also bring about the unstableness [13]. In regard to not only the deploying process but also the deployed state, the dynamic properties should be paid attention to for the stability of reflector surface accuracy [25; 26]. Especially in deployed working state, the reflector structure showing apparent flexibility may cause the flexible vibration or the resonance with the satellite. Therefore, for this paper, a PDSR in deployed state was modeled to deeply explore its structural dynamic properties. The design of this reflector is presented in detail below.