Effect of grain size on the natural frequencies of high-strength steel HT-80

Ultrafine-grained steels offer the prospect of high strength compared with traditional steel. In this article, the vibration responses of a beam as a function of the grain size of the material in HT-80 steel are investigated by an analytical approach. First, the relation between Young’s modulus and grain diameter in HT-80 steel is obtained based on the experimental results using curve fitting in the form of a mathematical equation. Then, governing equations of the cantilever beam and also associated boundary conditions are derived based on Hamilton’s principle using obtaining the total kinetic and potential energies of the system. After that, the natural frequencies of the system are determined using an analytical approach. Finally, numerical results of the natural frequencies of the system are presented concerning different values of the system parameters such as thickness, width, length, and grain size of the material. The obtained results show that the grain diameter of the material and also the dimensions of the beam such as thickness in the micro-scale have significant effects on the vibration response of the system. The presented approach can be used to estimate the vibration characteristics of ultrafine-grained steels and also microsystems such as piezoelectric cantilever-based MEMS sensors.