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**Study of non-uniform viscoelastic nanoplates vibration based on nonlocal first-order shear deformation theory.**
*(English)*
Zbl 1364.74058

Summary: In this paper, vibration features of variable thickness rectangular viscoelastic nanoplates are studied. In order to consider the small-scale and the transverse shear deformation effects, governing differential equations and relevant boundary conditions are adopted based on the nonlocal elasticity theory in relation to first-order shear deformation theory of plates. The numerical solution for the nanoplate vibration frequencies is proposed applying the differential quadrature method, as a simple, effective and precise numerical tool. The present formulation and solution method are validated showing their fast convergence rate and comparison of results, in limited cases, using the available literature. Excellent agreement between the obtained and available results is observed. The effects of structural damping coefficient, boundary conditions, aspect ratio, nonlocal and variable thickness parameters on viscoelastic nanoplates vibration behaviour are studied in detail.

### MSC:

74K20 | Plates |

74H45 | Vibrations in dynamical problems in solid mechanics |

74M25 | Micromechanics of solids |

### Keywords:

free vibration; viscoelastic nanoplates; non-uniform geometry; nonlocal first-order shear deformation theory
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\textit{M. Mohammadsalehi} et al., Meccanica 52, No. 4--5, 1063--1077 (2017; Zbl 1364.74058)

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### References:

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