A Study on the Effect of Piezoelectric Nonlinearity on the Bending Behaviour of Smart Laminated Composite Beam
Abstract
:1. Introduction
2. Mathematical Formulation
2.1. Theoretical Formulation Using HSDT
2.2. Nonlinear Constitutive Relation
2.3. Energy Formulation
2.4. Finite Element Formulation
2.5. Principle of Virtual Work
3. Results and Discussion
3.1. Validation of Results with Unimorph and Bimorph with Linear Piezoelectric Coefficients
3.2. Validation of Nonlinear Analysis of Piezoelectric Cantilever Bimorph and Unimorph
3.3. Nonlinear Analysis of Piezo-Actuated Laminated Composite Beam
3.4. Analysis of Piezo-Actuated Laminated Composite Beam with Different End Conditions
3.5. Nonlinear Analysis for Deflection and Stress Distribution of Composite Laminates
4. Conclusions
Author Contributions
Funding
Informed Consent Statement
Conflicts of Interest
References
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775 | 0.29 | 0.046 cm−2 | 0.046 cm−2 |
FE Tzou/Ye [24] | FE Jiang & Li [4] | FE Present | Theoretical Jiang & Li [4] | |
---|---|---|---|---|
0.02 | 0.132 | 0.136 | 0.138 | 0.138 |
0.04 | 0.528 | 0.545 | 0.552 | 0.552 |
0.06 | 1.19 | 1.226 | 1.242 | 1.242 |
0.08 | 2.11 | 2.18 | 2.208 | 2.208 |
0.1 | 3.30 | 3.41 | 3.45 | 3.45 |
Material | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
PZT [25] | 63 | 63 | 63 | 24.8 | 24.8 | 24.8 | 0.28 | 0.28 | 0.28 | −166 | −166 |
PZT-4 [26] | 81.3 | - | 64.5 | - | 25.6 | 25.6 | - | 0.43 | 0.43 | −122 | −122 |
Al [26] | 68.9 | 68.9 | 68.9 | 27.6 | 27.6 | 27.6 | 0.25 | 0.25 | 0.25 | - | - |
Adhesive [26] | 6.9 | 6.9 | 6.9 | 2.46 | 2.46 | 2.46 | 0.4 | 0.4 | 0.4 | - | - |
T300/934 [26] | 132.38 | - | 107.6 | - | 56.5 | 56.5 | - | 0.24 | 0.43 | - | - |
Material | |||||||||
---|---|---|---|---|---|---|---|---|---|
PZT 3203 HD [11] | 60.24 | 60.24 | 47.62 | 19.084 | 19.084 | 24.04 | 0.494 | 0.494 | 0.253 |
AS/3501 Gr/Ep [25] | 144.8 | 9.65 | - | 5.92 | 7.1 | 7.1 | - | - | 0.3 |
PZT APC 850 [15] | 63 | 63 | 63 | 24.05 | 24.05 | 24.05 | 0.31 | 0.31 | 0.31 |
Silicon [15] | 166 | 166 | 166 | 65.9 | 65.9 | 65.9 | 0.26 | 0.26 | 0.26 |
PZT 3203 HD [11] | −320 | −320 | 650 | −520 | - | ||||
PZT APC 850 [15] | −175 | −175 | - | −1210 | −6.3 |
Elastostriction (%) | Electrostriction (%) | Both (%) | |
---|---|---|---|
Deflection | −86.16 | 691.41 | 9.49 |
Normal Stress | −98.45 | 691.42 | −87.74 |
Shear Stress | −85.81 | 691.32 | 12.23 |
Elastostriction (%) | Electrostriction (%) | Both (%) | |
---|---|---|---|
Deflection | −81.97 | 691.42 | 42.65 |
Normal Stress | −97.98 | 691.42 | −84.038 |
Shear Stress | −82.22 | 691.36 | 43.73 |
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Akhlaq, A.; Shaik Dawood, M.S.I.; Jaffar Syed, M.A.; Sulaeman, E. A Study on the Effect of Piezoelectric Nonlinearity on the Bending Behaviour of Smart Laminated Composite Beam. Materials 2023, 16, 2839. https://doi.org/10.3390/ma16072839
Akhlaq A, Shaik Dawood MSI, Jaffar Syed MA, Sulaeman E. A Study on the Effect of Piezoelectric Nonlinearity on the Bending Behaviour of Smart Laminated Composite Beam. Materials. 2023; 16(7):2839. https://doi.org/10.3390/ma16072839
Chicago/Turabian StyleAkhlaq, Adnan, Mohd Sultan Ibrahim Shaik Dawood, Mohamed Ali Jaffar Syed, and Erwin Sulaeman. 2023. "A Study on the Effect of Piezoelectric Nonlinearity on the Bending Behaviour of Smart Laminated Composite Beam" Materials 16, no. 7: 2839. https://doi.org/10.3390/ma16072839
APA StyleAkhlaq, A., Shaik Dawood, M. S. I., Jaffar Syed, M. A., & Sulaeman, E. (2023). A Study on the Effect of Piezoelectric Nonlinearity on the Bending Behaviour of Smart Laminated Composite Beam. Materials, 16(7), 2839. https://doi.org/10.3390/ma16072839