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Recent researches on nonlocal elasticity theory in the vibration of carbon nanotubes using beam models: a review. (English) Zbl 1375.74012

Summary: Understanding dynamic behavior of carbon nanotubes has been of interest to researchers because of its practical applications. Recent studies show that nonlocal elasticity theory gives better results in the vibration of carbon nanotubes. The necessity of nonlocal elasticity theory, calibration of nonlocal parameter and application of nonlocal elasticity theory in various studies related to vibration of carbon nanotubes are discussed. This review emphasizes the application of nonlocal elasticity theory in the vibration of carbon nanotubes considering various types of complicating effects, nonlinearity, functionally graded material and different beam theories.

MSC:

74B20 Nonlinear elasticity
74H45 Vibrations in dynamical problems in solid mechanics
82D80 Statistical mechanics of nanostructures and nanoparticles
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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