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. 2022 Mar 2;12(3):288.
doi: 10.3390/membranes12030288.

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

Antonia Lima-Rodriguez  1 , Jose Garcia-Manrique  1 , Wei Dong  2 , Antonio Gonzalez-Herrera  1
Affiliations

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

Antonia Lima-Rodriguez et al. Membranes (Basel). .

Abstract

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.

Keywords: experiment; finite element model; membrane characterization.

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Conflict of interest statement

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Figures

Figure 1
Figure 1
Configuration setup.
Figure 2
Figure 2
Modal shapes of the first 9 vibration modes.
Figure 3
Figure 3
Center point of a membrane of 40 µm. Velocity magnitude at different positions of the source: (a) 90° and (b) 45°.
Figure 4
Figure 4
Point y = 0 x = radio/2 for a membrane of 40 µm. Velocity magnitude at different positions of the source: (a) 90° and (b) 45°.
Figure 5
Figure 5
Center point for membranes of 60 µm. Velocity magnitude for the positions of the source at 90° for different damping values: 1%, 5%, 10%, 20%, 30% and 40%.
Figure 6
Figure 6
Surface responses of some representative points for a membrane of 40 µm, 90° source angle and 1 Pa of pressure in the source.
Figure 7
Figure 7
Candidate points from the surface of the membrane for a membrane with a thickness of 40 microns and with an angle of 90°. Modes 1, 3, 4, 7, 8 and 9.
Figure 8
Figure 8
Nyquist diagrams. Application of the circular fit method for two resonance frequencies (a,b).
Figure 9
Figure 9
Disposition of the different elements in the experiment (a,b). Measurement at the center of the membrane (c). Measurement at a support point (d).
Figure 10
Figure 10
Membrane velocity transfer function. Responses of membranes with diameters of 5 mm (a), 10 mm (b), and 15 mm (c) for the center location (blue curve) and edge location (green curve). Responses at the edge location are scaled up to 10 x.
Figure 11
Figure 11
Nyquist diagram for membranes with diameters of 5 mm (a), 10 mm (b), and 15 mm (c) for the center location (blue curve) and edge location (green curve).
Figure 12
Figure 12
Membrane acceleration transfer function. Responses of membranes with diameters of 5 mm (a), 10 mm (b), and 15 mm (c) for the center location (blue curve) and edge location (green curve). Resonant frequencies added at the center (red line) and at the border (grey line).
Figure 13
Figure 13
Young’s modulus determination for membranes with diameters of 5 mm (a), 10 mm (b), and 15 mm (c).
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