Vibration analysis of FG piezoelectric-elastic annular nanoplates: rotational-thermal effects with geometric imperfection

This study analyzes the vibrational characteristics of functionally graded piezoelectric-elastic (FGPE) annular nanoplates under rotational and thermal loads. The material system consists of piezoelectric (BaTiO3) and non-piezoelectric elastic (CoFe2O4) phases. The thermo-electro-elastic properties of the nanoplate vary continuously along its thickness according to a power-law distribution. The analysis employs the nonlocal strain gradient theory (NSGT), the governing equations are derived using Hamilton’s principle and solved via the Runge-Kutta method. Results demonstrate that: The natural frequency exhibits complex behavior influenced by rotational speed, initially decreasing, then increasing, and subsequently fluctuating. Increasing the functionally graded index or porosity volume fraction reduces the natural frequency by softening material stiffness and weakening piezoelectric coupling efficiency. The electric potential enhances frequency at low rotational speeds but induces complex fluctuations beyond a critical speed. Temperature changes cause a non-monotonic frequency response, initially decreasing, then increasing, and finally decreasing again. Clearly, initial geometric imperfection significantly alter the vibration characteristics, with frequency decreasing at low speeds, increasing beyond a critical rotational speed, and decreasing again at higher speeds, highlighting the importance of accounting for geometric imperfections in nanoscale structural design.