The goal of this study was to investigate analytically the buckling phenomena of slender beam structures embedded in an elastic medium. In such cases, there is a possibility that spiral-shaped buckling modes can occur due to the restraining effect of the surrounding medium. As a result of analytical investigations, helical buckling occurs radically. Furthermore the pitch of the helix does not fluctuate as the radius of the helix increases. The interesting mechanical implications of the embedding effect are demonstrated by the theoretical approach established in this study.

A multitude of researchers have utilized a variety of techniques to formulate the stresses and deformations caused by volume misfit inclusions in infinite host media. Few of such techniques can also be extended to derive solutions for inclusions in a half space. In this manuscript we present a novel computational method for determining the elastic fields of two and three-dimensional inclusions of arbitrary shape in an infinite host matrix. The misfit strain is treated by a distribution of prismatic dislocation loops. A systematic numerical assessment illustrates that the discretization can yield excellent agreement with existing analytical solutions for certain particle geometries. This method is then further developed to solve for two-dimensional problems in a half space.

This paper provides a general solution for a crack embedded in multiply confocally elliptical layers in antiplane elasticity. In the problem, the elastic medium is composed of an inclusion, many confocally elliptical layers and the infinite matrix with different elastic properties. In addition, the remote loading is applied at infinity. The complex variable method and the conformal mapping technique are used. On the mapping plane, the complex potentials for the inclusion and many layers are assumed in a particular form with two undetermined coefficients. The continuity conditions for the displacement and traction along the interface between two adjacent layers are formulated and studied. By enforcing those conditions along the interface, the exact relation between two sets of two undetermined coefficients in the complex potentials for j-th layer and j + 1-th layer can be evaluated. From the traction free condition along the crack faces, the correct form of the complex potential for the cracked inclusion is obtained. Finally, many numerical results are provided.

This study adopted the Vector Form Intrinsic Finite Element (VFIFE) method to study the nonlinear vibration of the membrane SAR (Synthetic Aperture Radar) antenna structure. As the dynamic characteristic of the antenna is mainly determined by the support frame, it can be simplified as an axially loaded cantilever beam. The linear and geometrically nonlinear models of the axially loaded cantilever beam are established. The beam is modeled as discrete mass points which are connected by deformable elements through VFIFE method. A statics analysis is first presented to verify the VFIFE method. Then effects of the geometrical nonlinearity and axial load are investigated. It is believed that the presented study is valuable for better understanding the influences of the geometrical nonlinearity and axial load of the cantilever beam on the structural vibration characteristics.

The present study is to investigate the pressure-driven gas flow in microchannel at no-uniform wall temperature. DSMC is employed to generate the flow field details which are then used in analysis of the slip flow characteristics. The major concern is the influences of thermal creep effect on the pressure-driven slip flow. Thermal creep is resulted from tangential wall temperature gradient. In this work, two kinds of thermal boundary condition are considered. One is the linearly varied temperature (LVT) applied to both walls, the other is that has the bottom wall at a thermal condition combined LVT and adiabatic (AD) wall, i.e. LVT-AD-LVT condition. The present DSMC results reveal that the fluid slip is weakened (enhanced) in the case with a negative (positive) wall temperature gradient. Relatively, thermal creep effect on fluid slip over the adiabatic wall is more pronounced in the presence of negative wall temperature gradient. The mass flowrate is a strong function of the wall temperature gradient. However, there is only little difference between the mass flowrates predicted under the two kinds of thermal conditions studied in the present work.

The present study is a theoretical investigation of the laminar flow and convective heat transfer of water/alumina nanofluid inside a horizontal annulus with a streamwise moving inner cylinder. A modified, two-component, four-equation, nonhomogeneous equilibrium model is employed for the alumina/water nanofluid, which fully accounts for the effect of the nanoparticle volume fraction distribution. To determine the effects of thermal boundary conditions on the migration of the nanoparticles, two cases are considered: constant heat flux at the outer wall with an adiabatic inner wall (Case A) and constant heat flux at the inner wall with an adiabatic outer wall (Case B). The numerical results indicate that the thermal boundary conditions at the pipe walls significantly affect the nanoparticle distribution, particularly in cases where the ratio of Brownian motion to thermophoretic diffusivities is small. Moreover, increasing the velocity of the moving inner cylinder reduces the heat transfer rate for Case A. Conversely, in Case B, the movement of the inner cylinder enhances the heat transfer rate, and anomalous heat transfer enhancement occurs when the thermophoretic force is dominant (in larger nanoparticles).

A balanced cavitation bubble is released near the rigid wall in the sound field generated by the incidence plane wave and its reflecting wave. With the modified boundary integral equation, the dynamics of bubble is solved considering the compressibility of fluid in this paper. Also the Bernoulli equation as the boundary condition for cavitation bubble in sound field is deduced using Euler equation. Since the arbitrary incidence angle of acoustic wave, the three-dimensional model is utilized. The bubble will expand or contract at first according to the initial phase of acting acoustic pressure on bubble surface. And during the contraction phase, the liquid jet with high speed will be generated pointing to rigid wall but be deflected to the incidence direction of acoustic wave. The oblique degree of jet will be affected by the incidence angle and initial distance between bubble center and rigid wall. The oscillation amplitude of bubble will be affected by the incidence amplitude and incidence frequency, but be limited by the rigid wall. Since the compressibility of fluid, the perturbation will propagate to the far-field. Thus the oscillation amplitude of bubble will be reduced.

The combined effects of Joule and Newtonian heating in magnetohydrodynamic (MHD) flow of Jeffrey fluid over a stretching cylinder with heat source/sink are addressed. Suitable transformations are considered to reduce the non-linear boundary layer partial differential equations into the ordinary differential equations. Convergent series solutions of the resulting dimensionless problems are obtained. Effects of emerging physical parameters on the velocity and temperature profiles are examined. Comparison between viscous and Jeffrey fluids for different cases of flat plate and cylinder is made. Numerical values of skin friction coefficient and local Nusselt number are tabulated and analyzed for different values of emerging parameters.

The purpose of this study was to investigate the influence of a diaphragm material on the performance of a microspeaker. The finite element method was adopted to analyze the mode shapes and the displacement of the diaphragm under a force load. The Rayleigh integral was then calculated to determine the radiated sound pressure and frequency response of a loudspeaker. The location of the voice coil was also investigated. Locating the voice coil at approximately 53% to 76% of coil-radius/diaphragm-radius ratio yielded a favorable mode shape distribution and performance for the loudspeaker. In addition, two loudspeaker designs, Models A and B, were analyzed to determine the effects of the diaphragm material. The numerical results of Models A and B, indicated that the mode shape is a crucial factor when considering the materials used in a loudspeaker diaphragm. The property of a material at the inflection point of a mode shape obviously affects the modal frequency. According to this observation, the most crucial first and second axial symmetric modes in a loudspeaker design can be adjusted and the performance can be improved.

This paper introduces a unique, efficient, and exact formulation for solving a single-degree-of-freedom system with nonlinear stiffness under a harmonic loading. This formulation is one kind of the piecewise exact method, and its benefit lies in providing the closed-form exact solution in each displacement segment. Since the exact solution is given in each segment, the continuity between two segments can be confirmed. Consequently, no instability errors affect the analysis. To determine the exact solutions in these segments, this research develops a technique that shifts the equilibrium points of the piecewise linear segments, which are discretized from a nonlinear stiffness curve, to new equilibrium points in order to satisfy the typical linear exact solution. Thus, positive- and negative-stiffness linear segments can be solved with this technique. This formulation saves roughly 60% of the calculation time (error < 10−10) as compared to the numerical approximation.

The most common method of vibration control is the use of the dynamic absorbers. Two types of absorbers can be found: Linear and nonlinear. The use of linear absorbers allows reducing vibration but only at the resonance frequency, whereas nonlinear absorbers attenuate vibration on a wide band of frequency. In this paper, a nonlinear two degrees of freedom (DOF) model is developed. A cubic nonlinearity induced by a gap is considered. The objective of the paper is to characterize nonlinear vibration of the system by applying explicit formulation (EF). An experimental study is performed to validate the numerical results. The jump phenomenon is the principal nonlinear dynamic phenomenon observed on both numerical and experimental investigations.