Rai Saurabh, Gupta Ankit
School of Engineering, Shiv Nadar Institution of Eminence Deemed to be University, Gautam Buddha Nagar, U.P, 201314, India.
Sci Rep. 2024 Sep 17;14(1):21689. doi: 10.1038/s41598-024-70210-2.
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.
本文介绍了用于分析热环境下弹性基础上的小尺寸夹层功能梯度纳米板的动态刚度法的发展。数学公式基于经典板理论并结合非局部弹性理论。控制方程通过哈密顿原理推导得出。动态刚度矩阵通过应用列维位移法获得，并组装形成全局刚度矩阵。最终矩阵使用维特里克 - 威廉姆斯算法求解板的固有频率。所提出的方法与现有文献进行了验证，显示出高度一致性。各种参数研究探讨了热环境、体积分数指数、夹层配置、弹性基础特性、非局部参数和边界条件的影响。结果表明所提出的方法在处理小尺寸复杂工程结构方面的通用性。这项研究对夹层功能梯度纳米板的理解和分析做出了重大贡献，为航空航天、结构系统、传感器、致动器和能量收集装置等应用提供了有价值的见解。
