Document Type : Research Paper

Authors

• H Benaddi ¹
• B Rebai ¹
• K Mansouri ²
• N M Seyam ³
• Ashraf M. Zenkour ^{4, 5}

¹ Faculty of Sciences & Technology, Civil Eng Department, University Abbes Laghrour, Khenchela 40000, Algeria

² b Faculty of Sciences & Technology, Mechanic Eng Department, University Abbes Laghrour, Khenchela 40000, Algeria

³ Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia

⁴ Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

⁵ Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

Abstract

This comprehensive study investigates the behavior of functionally graded (FG) nanoplates, providing insights into their characteristics and important design considerations. By examining factors such as homogenization models (Voigt Reuss, LRVE, and Tamura), volume fraction laws (power-law model, Viola-Tornabene four-parameter model, trigonometric model), eigenmode, aspect ratios, index material, and small-scale length parameters, the study evaluates their influence on the natural frequency response of simply supported nanoplates. A novel twisting function is introduced and its accuracy in predicting natural frequencies in FG square nanoplates is rigorously validated through numerical comparisons with existing literature. The findings obtained from this research offer valuable guidance for optimizing the design of FG nanoplates and significantly contribute to advancing our understanding of their dynamics and practical applications.

Keywords

• Functionally graded materials
• small-scale length parameter
• homogenization models
• volume fraction laws
• vibrational behavior

Main Subjects

• Acoustics & Vibration