A theoretical analysis of the free axial vibration of non-local rods with fractional continuum mechanics
From MaRDI portal
Publication:497599
DOI10.1007/s11012-015-0157-5zbMath1325.74088OpenAlexW2067290298WikidataQ59403045 ScholiaQ59403045MaRDI QIDQ497599
J. Fernández-Sáez, R. Zaera, Wojciech Sumelka
Publication date: 24 September 2015
Published in: Meccanica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11012-015-0157-5
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) PDEs in connection with mechanics of deformable solids (35Q74) Fractional partial differential equations (35R11)
Related Items
Formulation of non-local space-fractional plate model and validation for composite micro-plates ⋮ Energy preserving low-thrust guidance for orbit transfers in KS variables ⋮ Application of the generalized Hooke's law for viscoelastic materials (GHVMs) in nanoscale mass sensing applications of viscoelastic nanoplates: a theoretical study ⋮ Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects ⋮ INVERSE PROBLEM FOR THE TIME-FRACTIONAL EULER-BERNOULLI BEAM EQUATION ⋮ Surface energy effect on nonlinear free axial vibration and internal resonances of nanoscale rods ⋮ A new iterative technique for a fractional model of nonlinear Zakharov-Kuznetsov equations via Sumudu transform ⋮ Study of non-uniform viscoelastic nanoplates vibration based on nonlocal first-order shear deformation theory
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Application of fractional continuum mechanics to rate independent plasticity
- Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method
- Nonlocal theories for bending, buckling and vibration of beams
- Atomistic viewpoint of the applicability of microcontinuum theories
- Fractional Noether's theorem in the Riesz-Caputo sense
- Wave propagation in nonlocal elastic continua modelled by a fractional calculus approach
- Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes
- Long-range cohesive interactions of non-local continuum faced by fractional calculus
- Non-local continuum mechanics and fractional calculus
- Variational formulation of a modified couple stress theory and its application to a simple shear problem
- A novel atomistic approach to determine strain-gradient elasticity constants: tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir)relevance for nanotechnologies
- Generalized wave equation in nonlocal elasticity
- Elastic materials with couple-stresses
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Experiments and theory in strain gradient elasticity.
- Nonlocal elasticity theory for radial vibration of nanoscale spherical shells
- Couple stress based strain gradient theory for elasticity
- Fractional sequential mechanics - models with symmetric fractional derivative.
- A fractional model of continuum mechanics
- Nonlocal elasticity: an approach based on fractional calculus
- Theories of elasticity with couple-stress
- Multipolar continuum mechanics
- Approximations of fractional integrals and Caputo fractional derivatives
- Elasticity theory of materials with long range cohesive forces
- On first strain-gradient theories in linear elasticity
- Nonlocal polar elastic continua
- On nonlocal elasticity
- Effects of couple-stresses in linear elasticity
- Micro-structure in linear elasticity
- Fractional mechanical model for the dynamics of non-local continuum
- Continuous limit of discrete systems with long-range interaction
- Free transverse vibrations of nano-to-micron scale beams
- Non-local elastic plate theories
- Axisymmetric free vibration of closed thin spherical nanoshells with bending effects
- Fractional variational calculus in terms of Riesz fractional derivatives
