On vibrations of nonlocal rods: boundary conditions, exact solutions and their asymptotics

DOI10.1016/J.IJENGSCI.2017.06.025zbMath1423.74521OpenAlexW2673616273MaRDI QIDQ1624967

Xiao-Jian Xu, Mu-Lian Zheng, Xuan-Cang Wang

Publication date: 28 November 2018

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ijengsci.2017.06.025

zbMATH Keywords

vibrationboundary conditionweighted residual methodnonlocal strain gradient theory

Mathematics Subject Classification ID

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

Related Items (30)

A size-dependent differential quadrature element model for vibration analysis of FG CNT reinforced composite microrods based on the higher order Love-Bishop rod model and the nonlocal strain gradient theory ⋮ On the mechanics of Kirchhoff and Mindlin plates incorporating surface energy ⋮ On non-linear flexure of beams based on non-local elasticity theory ⋮ On vibrations of porous nanotubes ⋮ Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams ⋮ Ambient vibration energy harvesters: a review on nonlinear techniques for performance enhancement ⋮ On wave propagation of porous nanotubes ⋮ Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams ⋮ Nonlinear mechanics of nanotubes conveying fluid ⋮ Two-phase nonlocal integral models with a bi-Helmholtz averaging kernel for nanorods ⋮ A fractional nonlocal time-space viscoelasticity theory and its applications in structural dynamics ⋮ A review on the mechanics of functionally graded nanoscale and microscale structures ⋮ Computational vibration and buckling analysis of microtubule bundles based on nonlocal strain gradient theory ⋮ Analyzing the bond behavior of fiber-reinforced polymer (FRP) bars embedded in engineered cementitious composites (ECCs) with the nonlocal continuum rod model ⋮ Integral and differential approaches to Eringen's nonlocal elasticity models accounting for boundary effects with applications to beams in bending ⋮ Nonlocalized thermal behavior of rotating micromachined beams under dynamic and thermodynamic loads ⋮ Global dynamics of fluid conveying nanotubes ⋮ On nonlinear bending behavior of FG porous curved nanotubes ⋮ Viscoelastic dynamics of axially FG microbeams ⋮ A size-dependent elastic theory for magneto-electro-elastic materials ⋮ Buckling analyses of three characteristic-lengths featured size-dependent gradient-beam with variational consistent higher order boundary conditions ⋮ Application of hetero junction CNTs as mass nanosensor using nonlocal strain gradient theory: an analytical solution ⋮ On size-dependent mechanics of nanoplates ⋮ A unified size-dependent plate model based on nonlocal strain gradient theory including surface effects ⋮ Analytical solutions for buckling of size-dependent Timoshenko beams ⋮ Variational nonlocal gradient elasticity for nano-beams ⋮ On the resonance of functionally graded nanoplates using bi-Helmholtz nonlocal strain gradient theory ⋮ On the dynamics of small-sized structures ⋮ On the statics and dynamics of granular-microstructured rods with higher order effects ⋮ Nonlocal strain gradient elastic beam models with two-step differential approach and decoupling of standard and extra boundary conditions. I

Cites Work

• Unnamed Item
• A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment
• A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation
• On a Moser-Steffensen type method for nonlinear systems of equations
• Non-local continuum modeling of carbon nanotubes: physical interpretation of non-local kernels using atomistic simulations
• Elastic materials with couple-stresses
• Experiments and theory in strain gradient elasticity.
• A unified integro-differential nonlocal model
• Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory
• Bending of Euler-Bernoulli beams using Eringen's integral formulation: a paradox resolved
• Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach
• Exact solution of Eringen's nonlocal integral model for bending of Euler-Bernoulli and Timoshenko beams
• Exact solution of Eringen's nonlocal integral model for vibration and buckling of Euler-Bernoulli beam
• Comment on the paper ``Exact solution of Eringen's nonlocal integral model for bending of Euler-Bernoulli and Timoshenko beams
• A generalized nonlocal elasticity solution for the propagation of longitudinal stress waves in bars
• Couple stress based strain gradient theory for elasticity
• Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method
• Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem
• Nonlocal theoretical approaches and atomistic simulations for longitudinal free vibration of nanorods/nanotubes and verification of different nonlocal models
• Application of nonlocal beam models for carbon nanotubes
• Theories of elasticity with couple-stress
• On first strain-gradient theories in linear elasticity
• Effects of couple-stresses in linear elasticity

This page was built for publication: On vibrations of nonlocal rods: boundary conditions, exact solutions and their asymptotics