Vibration analysis of two-dimensional micromorphic structures using quadrilateral and triangular elements

PurposeThe paper aims to presents a numerical analysis of free vibration of micromorphic structures subjected to various boundary conditions.Design/methodology/approachTo accomplish this objective, first, a two-dimensional (2D) micromorphic formulation is presented and the matrix representation of this formulation is given. Then, two size-dependent quadrilateral and triangular elements are developed within the commercial finite element software ABAQUS. User element subroutine (UEL) is used to implement the micromorphic elements. These non-classical elements are capable of capturing the micro-structure effects by considering the micro-motion of materials. The effects of the side length-to-length scale parameter ratio and boundary conditions on the vibration behavior of 2D micro-structures are discussed in detail. The reliability of the present finite element method (FEM) is confirmed by the convergence studies and the obtained results are validated with the results available in the literature. Also, the results of micromorphic theory (MMT) are compared with those of micropolar and classical elasticity theories.FindingsThe study found that the size effect becomes very significant when the side length of micro-structures is close to the length scale parameter.Originality/value The study is to analyze the free vibrations of 2D micro-structures based on MMT; to develop a 2D formulation for micromorphic continua within ABAQUS; to propose quadrilateral and triangular micromorphic elements using UEL and to investigate size effects on the vibrational behavior of micro-structures with various geometries.

Heterogeneous diffusion with stochastic resetting

We study a heterogeneous diffusion process with position-dependent diffusion coefficient and Poissonian stochastic resetting. We find exact results for the mean squared displacement and the probability density function. The nonequilibrium steady state reached in the long time limit is studied. We also analyze the transition to the non-equilibrium steady state by finding the large deviation function. We found that similarly to the case of the normal diffusion process where the diffusion length grows like $t^{1⁄2}$ while the length scale ξ(t) of the inner core region of the nonequilibrium steady state grows linearly with time t, in the heterogeneous diffusion process with diffusion length increasing like $t^{p⁄2}$ the length scale ξ(t) grows like $t^{p}$. The obtained results are verified by numerical solutions of the corresponding Langevin equation.

Stable channel flow with spanwise heterogeneous surface temperature

Recent studies have demonstrated that large secondary motions are excited by surface roughness with dominant spanwise length scales of the order of the flow's outer length scale. Inspired by this, we explore the effect of spanwise heterogeneous surface temperature in weakly to strongly stratified closed channel flow (at $Ri_\tau =120$ , 960; $Re_\tau = 180$ , 550) with direct numerical simulations. The configuration consists of equally sized strips of high and low temperature at the lower and upper boundaries, while an overall stable stratification is induced by imposing an average temperature difference between the top and bottom. We consider the influence of the width of the strips ( ${\rm \pi} /8 \leq \lambda /h \leq 4{\rm \pi} $ ), Reynolds number, stability and upper boundary condition on the mean flow structure, skin friction and heat transfer. Results indicate that secondary flows are excited, with alternating high- and low-momentum pathways and vortices, similar to the patterns induced by spanwise heterogeneous surface roughness. We find that the impact of the surface heterogeneity on the outer layer depends strongly on the spanwise heterogeneity length scale of the surface temperature. Comparison to stable channel flow with uniform temperature reveals that the heterogeneous surface temperature increases the global friction coefficient and reduces the global Nusselt number in most cases. However, for the high-Reynolds cases with $\lambda /h \geq {\rm \pi} /2$ , we find a reduction of the friction coefficient. At stronger stability, the vertical extent of the vortices is reduced and the impact of the heterogeneous temperature on momentum and heat transfer is smaller.

Wave propagation analysis of magnetic nanotubes conveying nanoflow

According to the nonlocal strain gradient theory, wave propagation in magnetic nanotubes conveying magnetic nanoflow under longitudinal magnetic field is inspected. The nonlocal strain gradient Timoshenko beam model is coupled with magnetic nanoflow considering slip boundary condition to model fluid structure interaction. By applying Hamilton’s principle, the size-dependent governing equations of motion have been obtained. Calculation of the wave frequency as well as phase velocity has been carried out based on the harmonic solution. The influences of strain gradient length scale, nonlocal parameter, Knudsen number, longitudinal magnetic field and magnetic nanoflow on nanotubes’ wave propagation behavior have been examined. According to analytical results, the magnetic intensity related to the longitudinal magnetic field contributes significantly to increasing nanotubes’ wave frequency as well as phase velocity. Besides, the magnetic nanotubes conveying magnetic nanoflow predict the highest phase velocity and wave frequency. Also, the wave frequency decrease when the nonlocal parameter increases or the strain gradient length scale decreases. Moreover, an increase in fluid velocity reduces the wave frequency and phase velocity. Article highlights The nonlocal strain gradient Timoshenko beam model is considered. Wave propagation in magnetic nanotubes conveying magnetic nanoflow is studied. Longitudinal magnetic field and magnetic nanoflow with considering slip boundary condition is inspected. Wave frequency decrease when the nonlocal parameter increases or the strain gradient length scale decreases. Increase in fluid velocity reduces the wave frequency and phase velocity.

Bayesian inference and Markov chain Monte Carlo based estimation of a geoscience model parameter

The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few meters depending on the length scale of the critically stressed fault. This makes it incredibly important to construct an inversion framework that provides good estimates of the critical slip distance purely based on the observed acceleration at the seismogram. The framework is based on Bayesian inference and Markov chain Monte Carlo. The synthetic data is generated by adding noise to the acceleration output of spring-slider-damper idealization of the rate and state model as the forward model.

Microfluidics as a tool to assess and induce emulsion destabilization

Microfluidic technology enables a judicious control of the process parameters on a small length-scale, which in turn allows speeding up the destabilization of emulsion droplets interface in microfluidic devices. In...