Free Vibration of Thick FGM Plates under TSDT and Thermal Environment

Authors

  • Chih-Chiang Hong Department of Mechanical Engineering, Hsiuping University of Science and Technology, Taichung, Taiwan

DOI:

https://doi.org/10.46604/peti.2021.6580

Keywords:

TSDT, FGM, frequency, nonlinear, homogeneous

Abstract

Three parameters of thermal environment, varied calculated shear correction, and third-order shear deformation theory (TSDT) of displacement are important in the frequency study. These three effects have been studied on the non-dimensional and dimensional frequencies of thick FGM plates. An additional c1 displacement term in nonlinear coefficient of TSDT is used to present the frequency of vibration into the simply homogeneous equation of thick FGM plates. The determinant of the coefficient matrix containing the c1 displacement term in dynamic differential equilibrium equations can be derived into the five degree polynomial free vibration equation. The non-dimensional and dimensional of natural frequency can be obtained. The effects of plate thickness, temperature of environment and power law index of FGM on the non-dimensional and dimensional frequency of FGM plates are investigated.

 

References

K. K. Żur, M. Arefi, J. Kim, and J. N. Reddy, “Free Vibration and Buckling Analyses of Magneto-Electro-Elastic FGM Nanoplates Based on Nonlocal Modified Higher-Order Sinusoidal Shear Deformation Theory,” Composites Part B, vol. 182, 107601, February 2020.

H. M. Ouakad, A. Valipour, K. K. Żur, H. M. Sedighi, and J. N. Reddy, “On the Nonlinear Vibration and Static Deflection Problems of Actuated Hybrid Nanotubes Based on the Stress-Driven Nonlocal Integral Elasticity,” Mechanics of Materials, vol. 148, 103532, September 2020.

A. Ghobadi, H. Golestanian, Y. T. Beni, and K. K. Żur, “On the Size-Dependent Nonlinear Thermo-Electro-Mechanical Free Vibration Analysis of Functionally Graded Flexoelectric Nano-Plate,” Communications in Nonlinear Science and Numerical Simulation, in press.

A. Ghobadi, Y. T. Beni, and K. K. Żur, “Porosity Distribution Effect on Stress, Electric Field and Nonlinear Vibration of Functionally Graded Nanostructures with Direct and Inverse Flexoelectric Phenomenon,” Composite Structures, in press.

H. Guo, T. Yang, K. K. Żur, and J. N. Reddy, “On the Flutter of Matrix Cracked Laminated Composite Plates Reinforced with Graphene Nanoplatelets,” Thin-Walled Structures, vol. 158, 107161, January 2021.

M. Babaei, M. H. Hajmohammad, and K. Asemi, “Natural Frequency and Dynamic Analyses of Functionally Graded Saturated Porous Annular Sector Plate and Cylindrical Panel Based on 3D Elasticity,” Aerospace Science and Technology, vol. 96, 105524, January 2020.

A. Alaimo, C. Orlando, and S. Valvano, “Analytical Frequency Response Solution for Composite Plates Embedding Viscoelastic Layers,” Aerospace Science and Technology, vol. 92, pp. 429-445, September 2019.

B. Safaei, R. Moradi-Dastjerdi, Z. Qin, and F. Chu, “Frequency-Dependent Forced Vibration Analysis of Nanocomposite Sandwich Plate under Thermo-Mechanical Loads,” Composites Part B, vol. 161, pp. 44-54, March 2019.

L. Sun and X. Wei, “A Frequency Domain Formulation of the Singular Boundary Method for Dynamic Analysis of Thin Elastic Plate,” Engineering Analysis with Boundary Elements, vol. 98, pp. 77-87, January 2019.

M. Vinyas, K. K. Sunny, D. Harursampath, T. Nguyen-Thoi, and M. A. R. Loja, “Influence of Interphase on the Multi-Physics Coupled Frequency of Three-Phase Smart Magneto-Electro-Elastic Composite Plates,” Composite Structures, vol. 226, 111254, October 2019.

A. S. Rezaei, A. R. Saidi, M. Abrishamdari, and M. H. Pour Mohammadi, “Natural Frequencies of Functionally Graded Plates with Porosities via a Simple Four Variable Plate Theory: An Analytical Approach,” Thin-Walled Structures, vol. 120, pp. 366-377, November 2017.

M. Yao, W. Hu, and W. Zhang, “Nonlinear Frequency Responses of the Bistable Piezoelectric Plate,” Procedia IUTAM, vol. 22, pp. 208-215, 2017.

D. K. Jha, T. Kant, and R. K. Singh, “Free Vibration Response of Functionally Graded Thick Plates with Shear and Normal Deformations Effects,” Composite Structures, vol. 96, pp. 799-823, February 2013.

N. D. Duc, J. Lee, T. Nguyen-Thoi, and P. T. Thang, “Static Response and Free Vibration of Functionally Graded Carbon Nanotube-Reinforced Composite Rectangular Plates Resting on Winkler–Pasternak Elastic Foundations,” Aerospace Science and Technology, vol. 68, pp. 391-402, September 2017.

C. C. Hong, “GDQ Computation for Thermal Vibration of Thick FGM Plates by Using Fully Homogeneous Equation and TSDT,” Thin-Walled Structures, vol. 135, pp. 78-88, February 2019.

S. H. Chi and Y. L. Chung, “Mechanical Behavior of Functionally Graded Material Plates Under Transverse Load, Part I: Analysis,” International Journal of Solids and Structures, vol. 43, no. 13, pp. 3657-3674, June 2006.

S. J. Lee, J. N. Reddy, and F. Rostam-Abadi, “Transient Analysis of Laminated Composite Plates with Embedded Smart-Material Layers,” Finite Elements in Analysis and Design, vol. 40, no. 5-6, pp. 463-483, March 2004.

S. J. Lee and J. N. Reddy, “Non-Linear Response of Laminated Composite Plates Under Thermomechanical Loading,” International Journal of Non-Linear Mechanics, vol. 40, no. 7, pp. 971-985, September 2005.

J. M. Whitney, “Structural Analysis of Laminated Anisotropic Plates,” U.S.A: CRC Press, 1987.

J. N. Reddy, “Energy Principles and Variational Methods in Applied Mechanics,” New York: Wiley, 2017.

H. S. Shen, “Nonlinear Thermal Bending Response of FGM Plates due to Heat Condition,” Composites Part B: Engineering, vol. 38, pp. 201-215, 2007.

S. D. Conte and C. de Boor, “Elementary Numerical Analysis, an Algorithmic Approach,” 3rd ed. U.S.A.: McGraw-Hill Book Company, 1980.

Y. W. Kim, “Temperature Dependent Vibration Analysis of Functionally Graded Rectangular Plates,” Journal of Sound and Vibration, vol. 284, no. 3-5, pp. 531-549, June 2005.

V. Ungbhakorn and N. Wattanasakulpong, “Thermo-Elastic Vibration Analysis of Third-Order Shear Deformable Functionally Graded Plates with Distributed Patch Mass Under Thermal Environment,” Applied Acoustics, vol. 74, no. 9, pp. 1045-1059, September 2013.

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Published

2021-01-20

How to Cite

[1]
C.-C. Hong, “Free Vibration of Thick FGM Plates under TSDT and Thermal Environment”, Proc. eng. technol. innov., vol. 17, pp. 21–31, Jan. 2021.

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