Dynamic response of sandwich functionally graded nanoplate under thermal environments and elastic foundations using dynamic stiffness method

Abstract

Abstract The present paper introduces the development of dynamic stiffness method for analyzing small-scale sandwich functionally graded nanoplates resting on elastic foundation in thermal environments. The mathematical formulation is based on classical plate theory in conjunction with nonlocal elasticity theory. The governing equation is derived using Hamilton’s principle. The dynamic stiffness matrix is obtained through the application of the Levy displacement approach and assembled to form the global stiffness matrix. The final matrix is solved for natural frequency of the plates using the Wittrick–Williams algorithm. The proposed methodology is validated against existing literature, demonstrating a strong agreement. Various parametric studies explore the effects of thermal environments, volume fraction index, sandwich configurations, elastic foundation characteristics, nonlocal parameter and boundary conditions. The results show the versatility of the proposed approach in addressing small scaled complex engineering structures. This research significantly contributes to the understanding and analysis of sandwich functionally graded nanoplates, providing valuable insights for applications in aerospace, structural systems, sensors, actuators, and energy harvesting devices.

Keywords

• Nonlocal elasticity theory
• Free vibration
• Plate theory
• Dynamic stiffness method
• Wittrick–Williams algorithm
• Sandwich functionally graded nanoplates (S-FG-nP)