A size-dependent Reddy-Levinson beam model based on a strain gradient elasticity theory

DOI10.1007/s11012-014-9912-2zbMath1316.74031OpenAlexW2056824799MaRDI QIDQ2510335

Mingchao Liu, Jun-Feng Zhao, Shen-Jie Zhou, Bing-Lei Wang

Publication date: 1 August 2014

Published in: Meccanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11012-014-9912-2

zbMATH Keywords

deflectionrotationnatural frequencymicro-scale Bernoulli-Euler modelmicro-scale Timoshenko model

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45)

Related Items (8)

Strain and velocity gradient theory for higher-order shear deformable beams ⋮ Free and forced vibration nonlinear analysis of a microbeam using finite strain and velocity gradients theory ⋮ A unified beam theory with strain gradient effect and the von Kármán nonlinearity ⋮ Size effects on centrosymmetric anisotropic shear deformable beam structures ⋮ A microstructure- and surface energy-dependent third-order shear deformation beam model ⋮ Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams ⋮ Reconsiderations on boundary conditions of Kirchhoff micro-plate model based on a strain gradient elasticity theory ⋮ Variational approach to dynamic analysis of third-order shear deformable plates within gradient elasticity

Cites Work

• Unnamed Item
• Analysis of wave propagation in micro/nanobeam-like structures: a size-dependent model
• A non-classical third-order shear deformation plate model based on a modified couple stress theory
• Asymptotic fracture modes in strain-gradient elasticity: size effects and characteristic lengths for isotropic materials
• Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory
• Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory
• Nonlinear microbeam model based on strain gradient theory
• Nonlocal theories for bending, buckling and vibration of beams
• The size-dependent natural frequency of Bernoulli-Euler micro-beams
• Static and dynamic analysis of micro beams based on strain gradient elasticity theory
• A nonlinear Timoshenko beam formulation based on the modified couple stress theory
• A non-classical Mindlin plate model based on a modified couple stress theory
• A microstructure-dependent Timoshenko beam model based on a modified couple stress theory
• Experiments and theory in strain gradient elasticity.
• Bending and stability analysis of gradient elastic beams
• Couple stress based strain gradient theory for elasticity
• A micro scale Timoshenko beam model based on strain gradient elasticity theory
• Micro-structure in linear elasticity
• A higher order beam finite element for bending and vibration problems
• A Simple Higher-Order Theory for Laminated Composite Plates
• Generalized Hooke's law for isotropic second gradient materials
• A new rectangular beam theory
• Solid Mechanics
• Bending solutions of Levinson beams and plates in terms of the classical theories

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