The difficulty to estimate the mechanical properties of the tympanic membrane (TM) is a limitation to understand the sound transmission mechanism. In this paper, based on finite element calculations, the sensitivity of the human hearing system to these properties is evaluated. The parameters that define the bending stiffness properties of the membrane have been studied, specifically two key parameters: Young's modulus of the tympanic membrane and the thickness of the eardrum. Additionally, it has been completed with the evaluation of the presence of an initial prestrain inside the TM. Modal analysis is used to study the qualitative characteristics of the TM comparing with vibration patterns obtained by holography. Higher-order modes are shown as a tool to identify these properties. The results show that different combinations of elastic properties and prestrain provide similar responses. The presence of prestrain at the membrane adds more uncertainty, and it is pointed out as a source for the lack of agreement of some previous TM elastic modulus estimations.

The dynamic behaviour of membranes has been widely studied by well-known authors for a long time. A clear distinction can be made between the behaviour of membranes without tension (plate case) and membranes subjected to large tension or pre-strain in their plane (membrane case). In classical theories, less attention has been paid to membranes subjected to a low level of tension, which solution is between both extreme cases. Recently, certain fields of research are demanding solutions for this intermediate behaviour. It is the case of membranes present in MEMS and sensor or the response of the tympanic membrane in mammals hearing system. In this paper, the behaviour of plates and circular membranes with boundary conditions clamped in the edges has been studied. The natural frequencies for both cases (plate and membrane) have been calculated using the solutions of the traditional theories and these have been compared with the numerical frequencies calculated by finite element analysis. The dynamic response of membrane with low tension, corresponding to a transition between these extreme behaviours, has also been calculated. A theoretical solution has been used complemented with a wide set of numerical finite elements calculations. The analytical and numerical solutions are very close, being the error made using both methods very low; nevertheless, there are no analytical solutions for the entire transition zone between the plate and membrane behaviour. Therefore, this range has been completed using finite element analysis. Broad ranges of geometric configurations have been studied. The transition behaviour of the membrane has been clearly identified. The main practical consequences of these results have been discussed, in particular focused on the response of the tympanic membrane.

A new, non-destructive methodology is proposed in this work in order to determine the mechanical properties of membrane using vibro-acoustic tests. This procedure is based on the dynamic analysis of the behavior of the membrane. When the membrane is subjected to a sound excitation it responds by vibrating based on its modal characteristics and this modal parameter is directly related to its mechanical properties. The paper is structured in two parts. First, the theoretical bases of the test are presented. The interaction between the sound waves and the membrane (mechano-acoustic coupling) is complex and requires meticulous study. It was broadly studied by means of numerical simulations. A summary of this study is shown. Aspects, such as the position of the sound source, the measuring points, the dimensions of the membrane, the frequency range, and the magnitudes to be measured, among others, were evaluated. The validity of modal analysis curve-fitting techniques to extract the modal parameter from the data measures was also explored. In the second part, an experimental test was performed to evaluate the validity of the method. A membrane of the same material with three different diameters was measured with the aim of estimating the value of the Young’s modulus. The procedure was applied and satisfactory results were obtained. Additionally, the experiment shed light on aspects that must be taken account in future experiments.

Recent studies have allowed us to identify a narrow region of the thickness of the crack front in fracture problems that presents interesting characteristics for the numerical-experimental correlation. Taking the three-dimensional distribution of the stress intensity factor (K) as a reference, we observe how it remains invariant and independent of the main factors influencing this type of analysis. This article presents a summary of how to identify this point through the numerical simulation of the problem and its relationship with parameters such as thickness, load level or angle of curvature. The simulations are carried out with the ANSYS software in an aluminium CT specimen subjected to a fracture loading process in mode I.