We investigate the bending behavior of functionally graded (FG) nanobeams with internal porosity and subjected to a hygro-thermo-mechanical loading. The Eringen's Nonlocal Theory (ENT) is here applied for the numerical study, while considering a uniform porosity within the nanobeam. The mechanical and thermal properties of FG materials are assumed to vary throughout the thickness. The equations of motion are derived from the Hamilton's law and solved with the Navier's procedure. A key point of the work is to explore the effect of the material length-scale, power-law index, porosity volume fraction, temperature rise, and moisture concentration on the global deflection of nanobeams, as useful for practical applications.

Structural response of porous FG nanobeams under hygro-thermo-mechanical loadings

Size-dependent forced vibration of non-uniform bi-directional functionally graded beams embedded in variable elastic environment carrying a moving harmonic mass

The instability of nanobeams rested on two-parameter elastic foundations is studied through the Bernoulli–Euler beam theory and the stress-driven nonlocal elasticity model. The size-dependency is i...

Size-dependent buckling analysis of nanobeams resting on two-parameter elastic foundation through stress-driven nonlocal elasticity model

Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory

The nonlinear vibration of cantilever nickel microbeams with thickness in micron level is investigated through experiment and theory. A non-contact dynamic vibration measurement system is built to test the fundamental linear frequency and the nonlinear amplitude-frequency curves near the primary resonance . Experimental result reveals the nonlinear amplitude-frequency curves exhibit a marked weak softening-type behavior as well as hysteresis behavior . To elucidate the experimental observations, a modified couple stress-based Euler-Bernoulli beam model incorporating geometric and inertial nonlinearities is established. The derived partial differential equation of motion is converted into a set of ordinary differential equations (ODEs) by employing the Galerkin method. And then, the multi-dimensional Lindstedt-Poincare (L-P) method is applied to solve these ODEs. By comparing these analytical and experimental results, a good agreement is observed. Besides, a p -version Ritz method is combined with the iteration algorithm to reveal the close similarity of the beam and plate models and to further demonstrate the size-dependency in the nonlinear regime. Meanwhile the size-dependency in nonlinear regime is demonstrated. The effects of different order nonlinear terms , length scale parameter and damping coefficients on the system are investigated. It is illustrated that the period-doubling bifurcation occurs when imposing sufficiently large excitations, and it turns into chaos with increasing the excitations continuously.

Experimental investigation and theoretical modelling on nonlinear dynamics of cantilevered microbeams

In this paper, we present the non-local nonlinear finite element formulations for the case of nonuniform rotating laminated nano cantilever beams using the Timoshenko beam theory. The surface stress effects are also taken into consideration. Non-local stress resultants are obtained by employing Eringen's nonlocal differential model. Geometric nonlinearity is taken into account by using the Green Lagrange strain tensor. Numerical solutions of nonlinear bending and free vibration are presented. Parametric studies have been carried out to understand the effect of non-local parameter and surface stresses on bending and vibration behavior of cantilever beams. Also, the effects of angular velocity and hub radius on the vibration behavior of the cantilever beam are studied.

K. Preethi

Papers

Nonlocal nonlinear bending and free vibration analysis of a rotating laminated nano cantilever beam