On the dynamics of small-sized structures. (English) Zbl 1476.74060
Summary: In this study, free vibration analyses of small-scaled trusses and frames are firstly carried out based on nonlocal elasticity of Eringen. Nonlocal matrix motion formulation is derived by using linear algebraic equations. Finite element method based weighted residual is utilized to solve the resulting equations. Various numerical studies are presented for nondimensional natural frequencies of different truss and frame models. A detailed parametric study is performed to investigate the influences of nonlocal parameter, geometric properties, direction angle, mode numbers, and length-to-diameter ratio on the natural frequencies of micro/nano trusses and frames. It is revealed that there is a significant relationship between the size-dependent dynamic response of these structures and the geometrical and structural properties of them.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74B05 | Classical linear elasticity |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Keywords:
nonlocal elasticity; nano/micro truss; nano/micro frame; nonlocal elasticity; size-dependency; nonlocal matrices; dynamic analysisReferences:
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