Size effect of vibration characteristics of Bernoulli-Euler microbeam

Key words:  Bernoulli-Euler microbeam  couple stress theory  bending stiffness  natural frequency  scale effect

Abstract:

Based on the modified couple stress theory, the couple stress theoretical expressions of the basic variables such as deformation energy, bending stiffness, external force work and kinetic energy of Bernoulli-Euler microbeam with arbitrary cross-section shape were derived. Then the couple stress theoretical dynamic differential equation of Bernoulli-Euler microbeam was established according to Hamilton principle. The scale effect of bending stiffness of Bernoulli-Euler microbeam with arbitrary section shape was assessed using the couple stress theoretical expression of the bending stiffness. And the influences of Poisson 's coefficient and section shape on the bending stiffness and its scale effect of Bernoulli-Euler microbeam were analyzed. Based on the couple stress theoretical dynamic differential equation, the natural frequency of Bernoulli-Euler simply supported beam was obtained. The scale effect of the natural frequency of Bernoulli-Euler beams with arbitrary cross-section shape was assessed. And the influences of Poisson’s coefficient and cross-section shape on the natural frequency and its scale effect of Bernoulli-Euler beams were analyzed. The results show that the developed dynamic model, which consists of the couple stress theoretical expressions of the aforementioned basic variables and the couple stress theoretical dynamic differential equation, can effectively describe the scale effect of the dynamic characteristics of the Bernoulli-Euler microbeam.