Elastic Half Space under Axisymmetric Surface Loading and Influence of Couple Stresses

2020 ◽  
Vol 897 ◽  
pp. 129-133
Author(s):  
Jintara Lawongkerd ◽  
Toan Minh Le ◽  
Suraparb Keawsawasvong ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Half Space ◽  
Integral Transform ◽  
Couple Stress Theory ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Small Scale ◽  
Internal Length ◽  
Stress Theory ◽  
Axisymmetric Surface ◽  
Small Scale Effect

This paper presents the complete elastic field of a half space under axisymmetric surface loads by taking the influence of material microstructures into account. A well-known couple stress theory is adopted to handle such small scale effect and the resulting governing equations are solved by the method of Hankel integral transform. A selected numerical quadrature is then applied to efficiently evaluate all involved integrals. A set of results is also reported to not only confirm the validity of established solutions but also demonstrate the capability of the selected mathematical model to simulate the size-dependent characteristic of the predicted response when the external and internal length scales are comparable.

Natural vibrations of micro beams with nonrigid supports

2016 ◽  
Vol 23 (19) ◽  
pp. 3233-3246 ◽  
Author(s):  
Diana V Bambill ◽  
Graciela I Guerrero ◽  
Daniel H Felix
Keyword(s):  
Boundary Conditions ◽  
Couple Stress Theory ◽  
Continuum Theory ◽  
Modified Couple Stress Theory ◽  
Free Vibrations ◽  
Small Scale ◽  
Stress Theory ◽  
Edge Conditions ◽  
Micro Systems ◽  
Micro Structures

The present study aims to provide some new information for the design of micro systems. It deals with free vibrations of Bernoulli–Euler micro beams with nonrigid supports. The study is based on the formulation of the modified couple stress theory. This theory is a nonclassical continuum theory that allows one to capture the small-scale size effects in the vibrational behavior of micro structures. More realistic boundary conditions are represented with elastic edge conditions. The effect of Poisson’s ratio on the micro beam characteristics is also analyzed. The present results revealed that the characterization of real boundary conditions is much more important for micro beams than for macro beams, and this is an assessment that cannot be ignored.

Size-dependent in vibration analysis of magnetostrictive sandwich composite micro-plate in magnetic field using modified couple stress theory

2017 ◽  
Vol 21 (2) ◽  
pp. 580-603 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
H Khani Arani ◽  
Z Khoddami Maraghi
Keyword(s):  
Magnetic Field ◽  
Couple Stress Theory ◽  
Composite Fiber ◽  
Modified Couple Stress Theory ◽  
Sandwich Composite ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Stress Theory ◽  
Fiber Angle ◽  
Modified Couple Stress

In the present study, free vibration of magnetostrictive sandwich composite micro plate with magnetostrictive core and composite face sheets are investigated. The modified couple stress theory is taken into account so as to consider the small scale effects. The surrounding elastic medium is simulated as visco-Pasternak foundation to study the effects of both damping and shear effects. Using energy method, Hamilton’s principle and first-order shear deformation theory, the governing equations of motion and related boundary conditions are obtained. Finally, the differential quadrature method is employed to analysis the vibration of magnetostrictive sandwich composite micro plate. In this regard, the dimensionless frequency are plotted to study the effects of small scale parameter, surrounding elastic medium, magnetic field, composite fiber angle, aspect ratio, thickness ratio, and boundary conditions. The results indicate that the magnetic field and composite fiber angle play a key role in the dimensionless frequency of magnetostrictive sandwich composite micro plate. The obtained results in this article can be used to design sensors and actuators, aerospace industry, and control of vibration response of systems.

Axisymmetric contact with friction of a rigid sphere with an elastic half-space

2009 ◽  
Vol 465 (2108) ◽  
pp. 2565-2588 ◽  
Author(s):  
O. I. Zhupanska
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Analytical Treatment ◽  
Normal Contact ◽  
Exact Analytical Solutions ◽  
Single Integral ◽  
Toroidal Coordinates

The problem of normal contact with friction of a rigid sphere with an elastic half-space is considered. An analytical treatment of the problem is presented, with the corresponding boundary-value problem formulated in the toroidal coordinates. A general solution in the form of Papkovich–Neuber functions and the Mehler–Fock integral transform is used to reduce the problem to a single integral equation with respect to the unknown contact pressure in the slip zone. An analysis of contact stresses is carried out, and exact analytical solutions are obtained in limiting cases, including a full stick contact problem and a contact problem for an incompressible half-space.

Size-Dependent Dynamic Behavior and Instability Analysis of Nano-Scale Rotational Varactor in the Presence of Casimir Attraction

2016 ◽  
Vol 08 (02) ◽  
pp. 1650018 ◽  
Author(s):  
Hamid M. Sedighi ◽  
Meisam Moory-Shirbani ◽  
Mohammad Shishesaz ◽  
Ali Koochi ◽  
Mohamadreza Abadyan
Keyword(s):  
Dynamic Behavior ◽  
Casimir Force ◽  
Scale Parameter ◽  
Dynamic Instability ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Small Scale ◽  
Stress Theory ◽  
Size Dependent ◽  
Casimir Attraction

When the size of structures approaches to the sub-micron scale, physical responses of such systems become size-dependent, hence, classic theories may not be able to predict the behavior of the miniature structures. In the present article, the modified couple stress theory (MCST) is employed to account for the effect of the size-dependency on the dynamic instability of torsional nano-electromechanical systems (NEMS) varactor. By incorporating the Coulomb, Casimir and damping forces, the dimensionless governing equations are derived. The influences of Casimir force, applied voltage and length scale parameter on the dynamic behavior and stability of fixed points are investigated by plotting the phase portrait and bifurcation diagrams. It is found that the Casimir force reduces the instability threshold of the systems and the small-scale parameter enhances the torsional stability. The pull-in instability phenomenon shows the saddle-node bifurcation for torsional nano-varactor.

Rayleigh wave equations with couple stress: modeling and dispersion characteristic

Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Yanqi Wu ◽  
Jianwei Ma
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Scale Effect ◽  
Linear Elasticity ◽  
Rayleigh Waves ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Stress Theory ◽  
Homogeneous Half Space

In elastostatics, the scale effect is a phenomenon in which the elastic parameters of a medium vary with specimen size when the specimen is sufficiently small. Linear elasticity cannot explain the scale effect because it assumes that the medium is a continuum and does not consider microscopic rotational interactions within the medium. In elastodynamics, wave propagation equations are usually based on linear elasticity. Thus, nonlinear elasticity must be introduced to study the scale effect on wave propagation. In this work, we introduce one of the generalized continuum theories—couple stress theory—into solid earth geophysics to build a more practical model of underground medium. The first-order velocity-stress wave equation is derived to simulate the propagation of Rayleigh waves. Body and Rayleigh waves are compared using elastic theory and couple stress theory in homogeneous half- space and layered space. The results show that couple stress causes the dispersion of surface waves and shear waves even in homogeneous half-space. The effect is enhanced by increasing the source frequency and characteristic length, despite its insufficiently clear physical meaning. Rayleigh waves are more sensitive to couple stress effect than body waves. Based on the phase-shifting method, it was determined that Rayleigh waves exhibit different dispersion characteristics in couple stress theory than in conventional elastic theory. For the fundamental mode, the dispersion curves tend to move to a lower frequency with an increase in characteristic length l. For the higher modes, the dispersion curves energy is stronger with a greater characteristic length l.

Effects of microstructure and liquid loading on velocity dispersion of leaky Rayleigh waves at liquid–solid interface

2018 ◽  
Vol 96 (1) ◽  
pp. 11-17 ◽  
Author(s):  
Vikas Sharma ◽  
Satish Kumar
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Liquid Layer ◽  
Rayleigh Waves ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Liquid Loading ◽  
Stress Theory ◽  
Leaky Rayleigh Waves

Inner atomic interactions at the micro scale produce new effects that cannot be accounted for by the classical theory of elasticity. To study the impact of the microstructures of the material, generalized continuum theories involving additional microstructural material parameters are preferred. One such microcontinuum theory involving an additional material parameter called internal characteristic length (l) is a consistent couple stress theory. The study of leaky Rayleigh waves generated at the interface of solid half-space with liquid layer is of great importance for quick scanning and imaging of large civil engineering structures. The problem of leaky Rayleigh waves propagating in elastic half-space under liquid loading has been studied in the context of this consistent couple stress theory. Dispersion equations are obtained by developing the mathematical model of the problem. Phase velocity of leaky Rayleigh waves is studied for three different values of characteristic length parameter (l), which is of the order of internal cell size of the material. Effects of thickness of liquid layer are also studied on the phase velocity profiles.

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