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Wind and Structures
  Volume 27, Number 6, December 2018 , pages 431-438

Vibration analysis of inhomogeneous nonlocal beams via a modified couple stress theory incorporating surface effects
Farzad Ebrahimi and Hamed Safarpour

    This paper presents a free vibration analysis of size-dependent functionally graded (FG) nanobeams with all surface effects considerations on the basis of modified couple stress theory. The material properties of FG nanobeam are assumed to vary according to power law distribution. Based on the Euler–Bernoulli beam theory, the modeled nanobeam and its equations of motion are derived using Hamilton\'s principle. An analytical method is used to discretize the model and the equation of motion. The model is validated by comparing the benchmark results with the obtained results. Results show that the vibration behavior of a nanobeam is significantly influenced by surface density, surface tension and surface elasticity. Also, it is shown that by increasing the beam size, influence of surface effect reduces to zero, and the natural frequency tends to its classical value.
Key Words
    surface effects; vibration analysis; modified couple stress theory; functionally graded material; nanobeam
Farzad Ebrahimi and Hamed Safarpour: Mechanical Engineering department, faculty of engineering, Imam Khomeini International University, Qazvin, Iran

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