Thermo-mechanical analysis of FG nanobeam with attached tip mass: an exact solution

Abstract

Present disquisition proposes an analytical solution method for exploring the vibration characteristics of a cantilever functionally graded nanobeam with a concentrated mass exposed to thermal loading for the first time. Thermo-mechanical properties of FGM nanobeam are supposed to change through the thickness direction of beam based on the rule of power-law (P-FGM). The small-scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. Linear temperature rise (LTR) through thickness direction is studied. Existence of centralized mass in the free end of nanobeam influences the mechanical and physical properties. Timoshenko beam theory is employed to derive the nonlocal governing equations and boundary conditions of FGM beam attached with a tip mass under temperature field via Hamilton’s principle. An exact solution procedure is exploited to achieve the non-dimensional frequency of FG nanobeam exposed to temperature field with a tip mass. A parametric study is led to assess the efficacy of temperature changes, tip mass, small scale, beam thickness, power-law exponent, slenderness and thermal loading on the natural frequencies of FG cantilever nanobeam with a point mass at the free end. It is concluded that these parameters play remarkable roles on the dynamic behavior of FG nanobeam subjected to LTR with a tip mass. The results for simpler states are confirmed with known data in the literature. Presented numerical results can serve as benchmarks for future thermo-mechanical analyses of FG nanobeam with tip mass.