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An effective method for determination of elastic constants of materials using multiresolution analysis

International Journal on Smart Sensing and Intelligent Systems
Volume 18 (2025): Issue 1 (January 2025)
By:
Open Access
|Aug 2025

Figures & Tables

Figure 1:

Flow diagram of the experimental setup.
Flow diagram of the experimental setup.

Figure 2:

(A) Experimental setup, (B) SS SA 240 Gr 304 with eight clamps at corners, and (C) copper plate with eight clamps at corner.
(A) Experimental setup, (B) SS SA 240 Gr 304 with eight clamps at corners, and (C) copper plate with eight clamps at corner.

Figure 3:

Free ball impact test setup.
Free ball impact test setup.

Figure 4:

Proposed techniques.
Proposed techniques.

Figure 5:

Decomposition process of a signal using DWT [13]. DWT, discrete wavelet transform.
Decomposition process of a signal using DWT [13]. DWT, discrete wavelet transform.

Figure 6:

SS plate Level 2. SS, stainless steel.
SS plate Level 2. SS, stainless steel.

Figure 7:

Copper plate level 2.
Copper plate level 2.

Figure 7:

(A) The SS specimen sheet with dimensions 220 mm × 220 mm × 1.3 mm. Through ANSYS analysis, the fundamental frequency for the first modal vibration is determined to be 144.19 Hz, considering clamping along eight edges. (B) The copper specimen sheet measuring 220 mm × 220 mm × 1 mm. Utilizing ANSYS, the natural frequency of the first modal vibration is identified as 107.04 Hz when considering clamping along eight edges. SS, stainless steel.
(A) The SS specimen sheet with dimensions 220 mm × 220 mm × 1.3 mm. Through ANSYS analysis, the fundamental frequency for the first modal vibration is determined to be 144.19 Hz, considering clamping along eight edges. (B) The copper specimen sheet measuring 220 mm × 220 mm × 1 mm. Utilizing ANSYS, the natural frequency of the first modal vibration is identified as 107.04 Hz when considering clamping along eight edges. SS, stainless steel.

Figure 7:

(A) The stainless steel specimen sheet measuring 220 mm × 220 mm × 1.3 mm. In ANSYS analysis, the first modal natural frequency is found to be 144.19 Hz when considering clamping along eight edges. (B) The copper specimen sheet sized 220 mm × 220 mm × 1 mm, with the ANSYS analysis revealing a first modal natural frequency of 107.04 Hz for eight clamp edges. (C) The stainless steel specimen sheet with the same dimensions (220 mm × 220 mm × 1.3 mm), clamping along four edges. 60.51 Hz. (D) The copper specimen sheet of dimensions 220 mm × 220 mm × 1 mm, similarly clamped along four edges, with ANSYS indicating a first modal natural frequency of 45.12 Hz.
(A) The stainless steel specimen sheet measuring 220 mm × 220 mm × 1.3 mm. In ANSYS analysis, the first modal natural frequency is found to be 144.19 Hz when considering clamping along eight edges. (B) The copper specimen sheet sized 220 mm × 220 mm × 1 mm, with the ANSYS analysis revealing a first modal natural frequency of 107.04 Hz for eight clamp edges. (C) The stainless steel specimen sheet with the same dimensions (220 mm × 220 mm × 1.3 mm), clamping along four edges. 60.51 Hz. (D) The copper specimen sheet of dimensions 220 mm × 220 mm × 1 mm, similarly clamped along four edges, with ANSYS indicating a first modal natural frequency of 45.12 Hz.

Figure 8:

(A) The power spectral density of SS specimen sheet and copper specimen sheet, both measuring 220 mm × 220 mm × 1.3 mm, obtained using Coiflet wavelets. (B) The power spectral density of SS and Copper specimen sheets is depicted, with the analysis performed using Daubechies Wavelets. (C) A typical power spectral plot for SS and copper specimen sheets, each sized 220 mm × 220 mm × 1.3 mm, employing Symlets wavelets. (D) A similar depiction showcases the typical power spectral plot for SS and Copper specimen sheets, again measuring 220 mm × 220 mm × 1.3 mm, but utilizing BiorSplines wavelets. SS, stainless steel.
(A) The power spectral density of SS specimen sheet and copper specimen sheet, both measuring 220 mm × 220 mm × 1.3 mm, obtained using Coiflet wavelets. (B) The power spectral density of SS and Copper specimen sheets is depicted, with the analysis performed using Daubechies Wavelets. (C) A typical power spectral plot for SS and copper specimen sheets, each sized 220 mm × 220 mm × 1.3 mm, employing Symlets wavelets. (D) A similar depiction showcases the typical power spectral plot for SS and Copper specimen sheets, again measuring 220 mm × 220 mm × 1.3 mm, but utilizing BiorSplines wavelets. SS, stainless steel.

Figure 10:

Location of the acceleration sensor on specimen sheets, 37.24 mm from center.
Location of the acceleration sensor on specimen sheets, 37.24 mm from center.

Average estimated error value of SS specimen sheet_

SNR input signal (dB)db4coif4sym3bior2.2
808.271013.31385.20916.6665

Different wavelet estimated frequency and average error for specimen sheets of SS and copper with dimensions 220 mm × 220 mm × 1_3 mm and 220 mm × 220 mm × 1 mm using 200 g ball

Name of wavelet familySS specimen plateCopper specimen plate
Frequency obtained by FEM (ANSYS software)Estimated frequency using proposed methodFrequency obtained by FEM (ANSYS software)Estimated frequency using proposed method
Daubechies wavelets144.19151.7107.0497.80
Coiflet wavelet 146.10 105.7
Symlets wavelet 156.6 81.41
BiorSplines wavelet 156.8 117.6

Elastic constant for SS specimen sheet_

Sr no.SS specimen plateCopper specwimen plate
Height of impact in cmFrequency obtained by FEM (ANSYS software)Estimated frequency using proposed methodError (%)Average error (%)Frequency obtained by FEM (ANSYS software)Estimated frequency using proposed methodError (%)Average error (%)
150144.19146.601.641.30%107.04105.71.261.18%
270 146.021.25 105.81.17
390 146.801.77 105.61.36
4110 145.600.96 105.41.55
5130 145.801.10 106.20.80
6150 145.801.10 106.00.98
Average frequency and error146.101.30 105.781.18

Average estimated error value of copper specimen sheet_

Sr. no.SS specimen plateCopper specimen plate
Height of impact in cmFrequency obtained by FEM (ANSYS software)Estimated frequency using proposed methodError (%)Average error (%)Frequency obtained by FEM (ANSYS software)Estimated frequency using proposed methodError (%)Average error (%)
150144.19146.601.641.30%107.04105.71.261.18%
270 146.021.25 105.81.17
390 146.801.77 105.61.36
4110 145.600.96 105.41.55
5130 145.801.10 106.20.80
6150 145.801.10 106.00.98
Average frequency and error146.101.30 105.781.18

The calculated error copper and SS plate frequency

SS plate size of 220 mm × 220 mm × 1.3 mm
ParameterFundamental frequency (Hz)Young’s modules (N/m2)Stiffness (N/m2)
FEM by ANSYS144.19187.6917.06
Multiresolution method146.10191.3917.20
Average error (%)1.301.970.14

Elastic constant for copper specimen sheet

Copper plate size of 220 mm × 220 mm × 1 mm
ParameterFundamental frequency (Hz)Young’s modules (N/m2)Stiffness (N/m2)
FEM by ANSYS107.04133.8212.55
Multiresolution method105.78129.4912.34
Average error (%)1.192.330.21
DOI: https://doi.org/10.2478/ijssis-2025-0044 | Journal eISSN: 1178-5608
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Language: English
Submitted on: Mar 5, 2025
Published on: Aug 23, 2025
Published by: Professor Subhas Chandra Mukhopadhyay
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Young Modules,
FEA,
stiffness
Related subjects:
Engineering,
Introductions and overviews,
Engineering, other

© 2025 Vijaykumar R. Bhanuse, Sanika S. Patankar, Jayant V. Kulkarni, published by Professor Subhas Chandra Mukhopadhyay
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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