In this paper, vibration analysis of the 2 D-FG nanoplate is studied based on a novel higher-order shear deformation theory (HSDT). The proposed HSDT is a composition of trigonometric, exponential and polynomial functions which is one of the most accurate HSDTs. The mechanical properties of the nanoplate change along with the length and thickness directions, according to arbitrary functions. To model the displacement field, the impacts of both transverse shear and thickness stretching are considered. To consider the small-scale impact, nonlocal elasticity theory is applied. To obtain the equations of motion, Hamilton’s principle is applied. Navier method is used for a closed-form solution of the 2 D-FG nanoplates with simply-supported boundary conditions. The impact of different parameters including the small-scale parameter are studied on the natural frequency of the system. The results illustrate that when size effect parameter is smaller/greater than 0.5 nm, the impacts of the FG parameters on the frequency of the system increase/reduce.

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In this paper, a structure for a piezoelectric beam vibrator driven by a groove cam is analysed. The vibrator takes the simplified form of a piezoelectric beam model, where one end of the beam is clamped and the other end is simply supported, and is thus named the clamped/simply supported piezoelectric beam model (CSPBM). Mathematical models of the damped forced vibration and electromechanical energy conversion processes of the CSPBM are established based on the harmonic displacement excitation of the simply supported end. Factors that affect the energy generated by the CSPBM are analyzed theoretically and are simulated separately using both the MATLAB software and ANSYS software. Theoretical analysis results indicate that there is an optimal value of the ratio of the base plate thickness to the beam thickness (α) at which the energy generated by the CSPBM is maximum. In addition, the optimal α value of a unimorph beam is about 0.3 and is irrelevant to the material parameters of the beam. The voltage and energy generated by the CSPBM are measured on an experimental bench and the results show that the maximum generated voltage increases with increasing the first natural frequency when the α value of piezoelectric beam and the amplitude of displacement excitation are constant. In addition, the theoretical results of the generated voltage are coincident with experimental results, which confirms the validity of the theoretical model. The vibrator driven by a groove cam provides a practical form of the piezoelectric beam excited by the displacement.