TWO KINDS OF SCALE EFFECTS OF VIBRATION CHARACTERISTICS OF NANO-PLATE¹⁾

In this paper, the lateral free vibration of nano plates is studied based on the nonlocal strain gradient theory. The expression of the nonlocal stress is obtained via the iterative method and the vibration governing equation of the nano-plate is derived based on the Hamilton variational principle. Under the simply supported boundary conditions, the expression of the natural frequency of the plate is obtained by using the double triangle series method. The influences of the nonlocal parameters, the material characteristic parameters and the geometrical dimensions on the natural frequencies of the nano plate are studied. Numerical results show that the nonlocal effect weakens the equivalent stiffness of the nano-plate and thus the natural frequency of the plate is reduced. The effect on the material characteristic parameter is just the opposite. The two kinds of effects have a significant bearing on the frequency of the vibration only in the nanoscale. The change of the geometrical size also has an important effect on the vibration frequency.