Study of the Dynamic Behaviour of Circular Membranes with Low Tension

Abstract

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.

Vibroacoustic Characteristics of a Specific Patterned Polymer with Graphene for an Electrostatic Speaker

“…Some peculiarities were apparent in the audible frequency band, particularly the frequency response at a specific voltage to confirm the response in the low-frequency band. Thus, it can be confirmed that the frequency shift is induced in the membrane of the same thickness depending on the type of the substrate, which is due to the change in the resonant frequency and the vibration mode with changing physical properties of the polymer because the elastic and resilience forces are different for each polymer. , …”

“…Thus, it can be confirmed that the frequency shift is induced in the membrane of the same thickness depending on the type of the substrate, which is due to the change in the resonant frequency and the vibration mode with changing physical properties of the polymer because the elastic and resilience forces are different for each polymer. 36,37 Frequency Spectra of Various Polymer Substrates with the Same Thicknesses. It has been previously confirmed that the resonant frequency and frequency shift change with varying substrate diameters.…”

Vibration Analysis of a Piezoelectric Ultrasonic Atomizer to Control Atomization Rate

“…It has been demonstrated that the mechanical vibrating characteristics of the meshed circular thin plate in an ultrasonic atomizer controls the rate atomization [17]. There are two kind of vibrations that can be used to study the mechanical behavior of a homogeneous circular thin plate-namely, free and forced vibrations.…”

A Novel Methodology to Obtain the Mechanical Properties of Membranes by Means of Dynamic Tests

“…Once the experiment procedure was established, different strategies of data post-processing were analyzed, including direct observation and Nyquist diagrams [ 31 ]. The experiment configuration (circular specimens) enables the use of a known analytical solution to describe the dynamic response, which has been widely covered in the literature for extreme cases of plate and membrane behaviors [ 32 , 33 ] and for intermediate situations [ 34 , 35 ]. Finally, experimental displacement measurement at strategic point of the specimen identified a group of main frequencies that, introduced in the analytical formulation, determined the mechanical properties.…”