Nonlinear free vibration impact on the smart small-scale thermo-mechanical sensors for monitoring the information in sports application

This paper presents an in-depth analysis of the nonlinear vibration of microbeams, with a particular emphasis on their application in sports monitoring systems. The research utilizes classical beam theory, modified couple stress theory, and von-Kármán nonlinear parameters to explore the behavior of microbeams. These microbeams are characterized by a nonuniform geometry, with materials that continuously change along the beam radius and a thickness that varies along the beam length. The main contribution lies in its exploration of the stability of smart sensors in sports structures, particularly those with non-uniform geometries. The research findings indicate that these non-uniform microbeams, when used in smart systems made of functionally graded temperature-dependent materials, can operate effectively in thermal environments. The smart system developed in this study demonstrates significant potential for use in sports applications, particularly in monitoring and gathering information. The insights gained from this research contribute to the understanding of the performance and optimization of microbeams in sports applications, particularly in the context of non-uniform geometries. This research, therefore, provides a foundation for the development of advanced, reliable, and efficient monitoring systems in sports applications.