Volcanic eruptions transfer huge amounts of gas to the atmosphere. In particular, the sulfur released during large silicic explosive eruptions can induce global cooling. A fundamental goal in ...volcanology, therefore, is to assess the potential for eruption of the large volumes of crystal-poor, silicic magma that are stored at shallow depths in the crust, and to obtain theoretical bounds for the amount of volatiles that can be released during these eruptions. It is puzzling that highly evolved, crystal-poor silicic magmas are more likely to generate volcanic rocks than plutonic rocks. This observation suggests that such magmas are more prone to erupting than are their crystal-rich counterparts. Moreover, well studied examples of largely crystal-poor eruptions (for example, Katmai, Taupo and Minoan) often exhibit a release of sulfur that is 10 to 20 times higher than the amount of sulfur estimated to be stored in the melt. Here we argue that these two observations rest on how the magmatic volatile phase (MVP) behaves as it rises buoyantly in zoned magma reservoirs. By investigating the fluid dynamics that controls the transport of the MVP in crystal-rich and crystal-poor magmas, we show how the interplay between capillary stresses and the viscosity contrast between the MVP and the host melt results in a counterintuitive dynamics, whereby the MVP tends to migrate efficiently in crystal-rich parts of a magma reservoir and accumulate in crystal-poor regions. The accumulation of low-density bubbles of MVP in crystal-poor magmas has implications for the eruptive potential of such magmas, and is the likely source of the excess sulfur released during explosive eruptions.
• For the first time, the comprehensive wave propagation analysis of 2D-FG rotating nanobeams with porosity is considered. • General nonlocal theory is used to establish the governing equation which ...exhibits softening and hardening behaviour. • Reddy's beam theory is applied to model the effects of the higher-order transverse shear strains on the wave propagation. • The effects of material variation, porosity, and the length to thickness ratio on the wave propagation are discussed.
This paper studies the wave propagation of two-dimensional functionally graded (2D-FG) porous rotating nano-beams for the first time. The rotating nano-beams are made of two different materials, and the material properties of the nano-beams alter both in the thickness and length directions. The general nonlocal theory (GNT) in conjunction with Reddy's beam model are employed to formulate the size-dependent model. The GNT efficiently models the dispersions of acoustic waves when two independent nonlocal fields are modelled for the longitudinal and transverse acoustic waves. The governing equations of motion for the 2D-FG porous rotating nano-beams are established using Hamilton's principle as a function of the axial force due to centrifugal stiffening and displacement. The analytic solution is applied to obtain the results and solve the governing equations. The effect of the features of different parameters such as functionally graded power indexes, porosity, angular velocity, and material variation on the wave propagation characteristics of the rotating nano-beams are discussed in detail.
•General nonlocal theory with two parameters is used for the porous FG nanobeam.•The nonlocal parameters cause softening and hardening behavior.•Reddy’s beam theory is used to model higher-order ...transverse shear strains.•Material variations in the length and thickness directions are investigated.•The porosity volume fraction and the length to thickness ratio are varied.
A comprehensive vibrational analysis of bi-directional functionally graded (2D-FG) rotating nanobeams with porosities is studied for the first time. The beam is modeled based on general nonlocal theory (GNT) where the beam governing equations are derived depending on two different nonlocal parameters. Unlike Eringen’s conventional form of nonlocal theory, the general nonlocal theory can reveal both hardening and softening behaviors of the material. Here, the attenuation functions are altered in both transverse and longitudinal directions of 2D-FG nanobeam. This feature, which has a significant effect on the vibrational characteristics, has not been considered in previous studies. Moreover, to estimate the effects of the higher-order transverse shear strains on the vibration of the nanobeam, Reddy’s beam theory (RBT), which includes higher-order shear deformation, is employed. The material properties of the 2D-FG rotating nanobeam vary both in the length and thickness directions according to a power law. The generalized differential quadrature method (GDQM) is used to predict the vibration response. Also, the effects of material variation along the length and thickness directions, the rotating velocity of the nanobeam, the porosity volume fraction and the length to thickness ratio of the rotating nanobeam are illustrated and discussed in detail. The investigations performed in this study expose new phenomena for the vibration of nanobeams.
Poisson's ratio is an important mechanical property that explains the deformation patterns of materials. A positive Poisson's ratio is a feature of the majority of materials. Some materials, however, ...display “auxetic” behaviors (i.e. possess negative Poisson's ratios). Indeed, auxetic and non-auxetic materials display different deformation mechanisms. Explaining these differences and their effects on the mechanics of these materials is of a significant importance.
In this study, effects of Poisson's ratio on the mechanics of auxetic and non-auxetic nanobeams are revealed. A parametric study is provided on effects of Poisson's ratio on the static bending and free vibration behaviors of auxetic nanobeams. The general nonlocal theory is employed to model the nonlocal effects. Unlike Eringen's nonlocal theory, the general nonlocal theory uses different attenuation functions for the longitudinal and lateral strains. This theory emphasizes the Poisson's ratio-nonlocal coupling effects on the mechanics of nanomaterials. The obtained results showed that Poisson's ratio is an essential parameter for determining mechanical behaviors of nanobeams. It is demonstrated that auxetic and non-auxetic nanobeams may reflect softening or hardening behaviors depending on the ratio of the nonlocal fields of the beam's longitudinal and lateral strains.
•Poisson's ratio effects on mechanics of nanobeams.•Auxetic beams exhibit nonclassical deformation, bending, and vibration behaviors.•The general nonlocal theory is employed.•The general nonlocal theory outperforms Eringen's nonlocal theory.•The general nonlocal theory reveals the Poisson's ratio-nonlocal coupling effects.
This is the first study on the influence of the surface integrity on the vibration characteristics of microbeams. A new model that represents the real surface texture of beams is developed. This ...model incorporates measures for the surface roughness, surface waviness, altered layer, and surface excess energy. This model outweighs Gurtin-Murdoch surface model by representing beams with real engineering surfaces. The derived model is solved for the free vibration of simple-supported, cantilever, and clamped-clamped microbeams. A parametric study is carried out to demonstrate the variations of the natural frequencies of microbeams due to surface integrity and a beam size decrease. It was revealed that a decrease in the beam size is accompanied with an increase in the surface integrity effects. Moreover, the surface integrity may decrease/increase the beam natural frequency. Surface integrity either softens the beam and hence decreases its natural frequency or inhibits the vibration propagation through the beam and hence increases the beam frequency.
•This is the first study on the influence of surface integrity on vibration characteristics of microbeams.•A new surface integrity beam model.•The surface integrity model outweighs Gurtin-Murdoch surface model.•Free vibration of simple-supported, cantilever, and clamped-clamped microbeams.•The surface integrity may decrease/increase the beam natural frequency.
Current research develops a comprehensive wave propagation analysis of a magneto-electro-thermo-elastic (METE) nano-beam (NB) resting on the visco-elastic medium. To model the size dependency ...effects, modified couple stress (MCS) and Eringen's nonlocal (ENL) theories are employed to analyze and describe the wave propagation behaviors for those nano-beams. These theories were the most used in the literature due to the inclusion of one additional size-dependent length scale parameter. Those theories are compared side by side in this investigation and their impacts/differences on the wave propagation of specific materials are explored. Sinusoidal shear deformation beam model with Hamilton's principle is adopted to develop the governing equations of motion. Then, an analytical solution is executed to extract numerical results for transverse wave propagation in both elastic and METE configurations of the nano-beam. The effects of size-dependent length scale of both theories, thickness of NB, Winkler-Pasternak coefficients, thermal gradient, and magnetic potential and external electric voltage are illustrated and discussed in details. It is concluded that wave frequency decreases with increment of nonlocal parameter for ENL model. On the other hand, a stiffening effect takes place for the wave frequency when the MCS model is considered. Hence, the results indicate that there is a significant difference between ENL and MCS theories in the estimation of the behavior of wave propagation in small-scale structures. One of the main results of this investigation indicates that the MCS theory has similar nonlocal effects as the Eringen's theory for specific conditions.
•Comprehensive wave-propagation analysis on METE nano-beams is presented.•MCST and ENLT are considered as non-classical elasticity to establish the model.•Wave-propagation analysis is considered under elastic foundation and thermal effects.•Effects of nonlocal and length scale parameters are discussed in details.•Selecting the proper theory with correct size effect parameter to describe the wave behavior of small-scale structures.
Abstract
This study investigates the wettability and confinement size effects on vibration and stability of water conveying nanotubes. We present an accurate assessment of nanotube stability by ...considering the exact mechanics of the fluid that is confined in the nanotube. Information on the stability of nanotubes in relation to the fluid viscosity, the driving force of the fluid flow, the surface wettability of the nanotube, and the nanotube size is missing in the literature. For the first time, we explore the surface wettability dependence of the nanotube natural frequencies and stability. By means of hybrid continuum-molecular mechanics (HCMM), we determined water viscosity variations inside the nanotube. Nanotubes with different surface wettability varying from super-hydrophobic to super-hydrophilic nanotubes were studied. We demonstrated a multiphase structure of nanoconfined water in nanotubes. Water was seen as vapor at the interface with the nanotube, ice shell in the middle, and liquid water in the nanotube core. The average velocity of water flow in the nanotube was obtained strongly depend on the surface wettability and the confinement size. In addition, we report the natural frequencies of the nanotube as functions of the applied pressure and the nanotube size. Mode divergence and flutter instabilities were observed, and the activation of these instabilities strongly depended on the nanotube surface wettability and size. This work gives important insights into understanding the stability of nanotubes conveying fluids depending on the operating pressures and the wettability and size of confinement. We revealed that hydrophilic nanotubes are generally more stable than hydrophobic nanotubes when conveying fluids.
In this paper, we investigate the surface roughness-dependence of buckling of beam-nanostructures. A new variational formulation of buckling of Euler-Bernoulli rough beams is developed based on the ...Hamilton's principle. The equation of motion of the beam is obtained with a coupling term that depends on the beam surface roughness. Exact solutions are derived for the buckling configurations and the pre-buckling and postbuckling vibrations of simply supported structures. The derived solutions are used to comprehensively explain influence of surface roughness on buckling characteristics of micro/nano-beams. We reveal that the buckling configurations and postbuckling mode shapes are distorted due to surface roughness. Thus, the beam with a rough surface may exhibit a localized buckling configuration where the buckling energy is confined over a small portion of the beam. In addition, the postbuckling mode shape of simply supported beams with rough surfaces is applied load-dependent. We report a value of the applied axial load at which the postbuckling mode shape is completely distorted, and the beam exhibits a mode shape that is identical to its buckling configuration but with a different amplitude. For the first time, we reveal a postbuckling mode inversion due to surface roughness. We demonstrate that the postbuckling mode shape starts to exhibit an inverted form of its original shape at high load values. The findings presented in this study highlight new insights into buckling characteristics of micro/nano-beams.
The present research focuses on the analysis of wave propagation on a rotating viscoelastic nanobeam supported on the viscoelastic foundation which is subject to thermal gradient effects. A ...comprehensive and accurate model of a viscoelastic nanobeam is constructed by using a novel nonclassical mechanical model. Based on the general nonlocal theory (GNT), Kelvin-Voigt model, and Timoshenko beam theory, the motion equations for the nanobeam are obtained. Through the GNT, material hardening and softening behaviors are simultaneously taken into account during wave propagation. An analytical solution is utilized to generate the results for torsional (TO), longitudinal (LA), and transverse (TA) types of wave dispersion. Moreover, the effects of nonlocal parameters, Kelvin-Voigt damping, foundation damping, Winkler-Pasternak coefficients, rotating speed, and thermal gradient are illustrated and discussed in detail.
Energy harvesting at micro- and nanoscales has recently seen a renewed interest that the flexoelectric effect can counter the inability of piezoelectric energy harvesters to generate enough energy at ...small scales. Almost all small-scale energy harvesters use uniform rectangular geometries, whereas at the macroscale energy harvesters use a wide array of geometries including tapered rectangular geometries. The incorporation of non-uniform effects into a piezoelectric system considering the flexoelectric effect should give insight into how these systems can benefit from different geometries. A non-uniform flexoelectric Euler–Bernoulli cantilever energy harvester is modeled using classical continuum theories and is examined at the microscale. The non-uniformity of the energy harvester is governed by linear and nonlinear tapering effects, with the nonlinearities represented by high-order polynomials. The system is assumed to be linear, only undergoing harmonic base excitation. The varied tapering ratios and powers of the geometric tapering, considering that only the thickness and the width of the beam are tapered, are compared with uniform systems. The results show that non-uniform beams exhibit more harvested power than their uniform counterparts and also increase the range of resonant frequencies where significant power can be generated. Nonlinear tapering increases the amount of power that could be harvested compared to linear tapering; however, the nonlinearity of the tapering effects is limited to cubic and quadratic forms. It is demonstrated that higher-order tapering effects reduce the amount of harvested power compared to the linear taper counterpart. Non-uniform beams prove to be more effective than their rectangular counterparts within a linear system, whereas optimal resistive loads decrease as the tapering effects increase.
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