## 1 Introduction  
The dynamic response of a membrane has been studied since a long time ago. There exist two classic solutions for two extreme situations, one for the case where the membrane is not subjected to internal loads (considered in this case as plate) and the other one when it is under tension (considered as membrane) [1, 2]. Both solutions have proven useful to study a plate and to study a membrane subjected to loads. Many authors have studied and published on this topic. These studies have included different cases of plates and membranes. [PERSON] [1] and [PERSON] [2] have studied vibration of plates and membranes with different shapes; [PERSON] [2] included in their study the energy method for solving the different cases. [PERSON] [3] compiled the studies and publications on vibration of plate in 1969. The first studies on vibrations of circular plates are attributed to [PERSON] [4] and [PERSON] [5]. Subsequently, other authors have contributed to investigate and publish on this topic. [PERSON] [6], [PERSON] and [PERSON] [7] and [PERSON] et al. [8] published studies about free-edge plates; [PERSON] [6] also studied the case of clamped membranes and [PERSON] et al. [8] studied the circular plates vibrating in vacuum and in contact with liquid. Other authors have studied the natural frequencies of circular plates simply supported [9], with elastic edge supports [10] or with non-uniform edge constrains [11]. In the latter case are included the publications of [PERSON] and [PERSON] [12; 13], [PERSON] et al. [14] or [PERSON] and [PERSON] [15]. Others papers research the vibration of circular plates in contact with water [16] or with fluid [17]. It can be concluded that both extreme situations of plate and membrane behaviour are widely covered in the literature. Lesser attention has been paid to the case where the membrane is subjected to a slight level of tension. In these cases, intermediate behaviour is expected between membrane and plate. One of the reasons of the absence of studies in this line is that most of the real situations presented in engineering regarding membrane behaviour responded to one of those extremes. Nevertheless, there are situations under study today that may respond to this intermediate situation. Vibration analysis is important in the study of musical instruments [18; 19; 20; 21] and specifically the case of membrane subjected to tension is important in the study of percussion musical instruments since the component which produce the desired sound it is a material of small thickness subjected to stress [22]. Recently, the use of membrane in microelectronics has made this issue a key point. Small membranes are used in different applications (e.g. as sensor or part of MEMS) which during manufacturing acquire certain level of tension that deviates their expected behaviour form [23; 24; 25; 26; 27]. Another field of study where this effect is manifest is the study of the mechanics of hearing. Based on different experimental studies [28] and simulation of the human hearing system [29] it has been observed that small levels of pre-strain in the system, particularly in the tympanic membrane, causes significant changes in the response. This issue is of great interest for our research group. As the hypothesis origin of this study, we consider that the deviations between expected and tested behaviours may be related the assumption of ideal membrane or plate behaviours in these problems. We have not found a consistent literature that helps us evaluate the influence of the tension level of a membrane with its actual behaviour. There are analytical solutions [30] that developed this question for some regular membrane shapes and some specific situations. The main aim of this work is to approach the study of the influence of pre-strain membranes based on parameters such as its geometric dimensions, type of material and internal stress level. In the present paper, we have conducted a numerical study to evaluate the influence of the level of pre-strain in the circular membrane dynamic response.