Dynamic response of imperfect functionally graded plates: Impact of graded patterns and viscoelastic foundation

Hafida Driz, Amina Attia, Abdelmoumen Anis Bousahla, Farouk Yahia Addou, Mohamed Bourada, Abdeldjebbar Tounsi, Abdelouahed Tounsi, Mohammed Balubaid and S.R. Mahmoud

Abstract

This study presents a methodical investigation into improving structural designs through the analytical examination of the dynamic behavior of functionally graded plates (FGPs) resting on viscoelastic foundations. By employing a four variable first-order shear deformation theory, the study computes non-dimensional frequencies for a variety of porous FGPs with diverse graded patterns and porosity distributions. Different gradient patterns of the plates are considered, and three distinct functions— sigmoid (S-FGM), exponential (E-FGM), and power-law (P-FGM)—are utilized to assess material performance in specific directions. The equations of motion are derived and solved using both Navier's method and Hamilton's principle. Analytical solutions for vibration frequency are provided to validate the proposed methodology against existing literature. Furthermore, a comprehensive parametric analysis is conducted, taking into account various factors such as ceramic material, porosity distribution, gradient index, length-to-thickness ratio, gradient pattern, and damping coefficient. The findings suggest that enhancing the damping coefficient of the viscoelastic foundation can significantly improve the free-vibrational response of functionally graded material plates.

Key Words

behavior; functionally graded plates; viscoelastic foundations

Address

Hafida Driz: Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria Amina Attia: Department of Civil Engineering and Public Works, Engineering and Sustainable Development Laboratory, Faculty of Science and Technology, University of Ain Temouchent, Algeria Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria Farouk Yahia Addou: Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria; Civil Engineering Department, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, Mostaganem, Algeria Mohamed Bourada: Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria Abdeldjebbar Tounsi: Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria; Mechanical Engineering Department, Faculty of Science & Technology, University of Relizane, Algeria Abdelouahed Tounsi: Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia Mohammed Balubaid: Department of Industrial Engineering, King Abdulaziz University, Jeddah, Saudi Arabia S.R. Mahmoud: GRC Department, Applied College, King Abdulaziz University. Jeddah 21589, Saudi Arabia

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