Non-linear principal resonance of an orthotropic and magnetoelastic rectangular plate

Based on the von Karman plate theory of large deflection, we have derived a non-linear partial differential equation for the vibration of a thin orthotropic plate under the combined action of a transverse magnetic field and a transverse harmonic mechanical load. The influence of the magnetic field is due to the magnetic Lorentz force induced by the eddy current. By employing the Bubnov-Galerkin method, the non-linear partial differential equation is transformed into a third-order non-linear ordinary differential equation. The amplitude-frequency equations are further derived by means of the multiple-scale method. As numerical examples for an orthotropic plate made of silver, the influence of the magnetic field, orthotropic material property, plate thickness, and the mechanical load on the principal resonance behavior is investigated. The higher-order effect and stability of the solution are also discussed.     

Erratum to: Experimental Investigation on Mechanical Behavior of Coarse Marble Under Six Different Loading Paths

A series of triaxial compression experiments were preformed for the coarse marble samples under different loading paths by the rock mechanics servo-controlled testing system. Based on the experimental results of complete stress-strain curves, the influence of loading path on the strength and deformation failure behavior of coarse marble is made a detailed analysis. Three loading paths (Paths I–III) are put forward to confirm the strength parameters (cohesion and internal friction angle) of coarse marble in accordance with linear Mohr-Coulomb criterion. Compared among the strength parameters, two loading paths (i.e. Path II by stepping up the confining pressure and Path III by reducing the confining pressure after peak strength) are suggested to confirm the triaxial strengths of rock under different confining pressures by only one sample, which is very applicable for a kind of rock that has obvious plastic and ductile deformation behavior (e.g. marble, chalk, mudstone, etc.). In order to investigate re-fracture mechanical behavior of rock material, three loading paths (Paths IV–VI) are also put forward for flawed coarse marble. The peak strength and deformation failure mode of flawed coarse marble are found depending on the loading paths (Paths IV–VI). Under lower confining pressures, the peak strength and Young’s modulus of damage sample (compressed until post-peak stress under higher confining pressure) are all lower compared with that of flawed sample; moreover mechanical parameter of damage sample is lower for the larger compressed post-peak plastic deformation of coarse marble. However under higher confining pressures (e.g. σ ₃ = 30 MPa), the axial supporting capacity and elastic modulus of damage coarse marble (compressed until post-peak stress under lower confining pressure) is not related to the loading path, while the deformation modulus and peak strain of damage sample depend on the difference of initial confining pressure and post-peak plastic deformation. The friction among crystal grains determines the strength behavior of flawed coarse marble under various loading paths. In the end, the effect of loading path on failure mode of intact and flawed coarse marble is also investigated. The present research provides increased understanding of the fundamental nature of rock failure under different loading paths.     

Energy density and release rate study of an elliptic-arc interface crack in piezoelectric solid under anti-plane shear

The anti-plane problem of an elliptical inhomogeneity with an interfacial crack in piezoelectric materials is investigated. The system is subjected to arbitrary singularity loads (point charge and anti-plane concentrated force) and remote anti-plane mechanical and in-plane electrical loads. Using the complex variable method, the explicit series form solutions for the complex potentials in the matrix and the inclusion regions are derived. The electroelastic field intensity factors, the corresponding energy release rates and the generalized strain energy density at the cracks tips are then provided. The influence of the aspect ratio of the ellipse, the crack geometry and the electromechanical coupling coefficient on the energy release rate and the strain energy density is discussed and shown in graphs. The results indicate that the energy release rate increases with increment of the aspect ratio of the ellipse and the influence of electromechanical coupling coefficient on the energy release rate is significant. The strain energy density decreases with increment of the aspect radio of the ellipse and it is always positive for the cases discussed. The energy release rate, however, can be negative when both mechanical and fields are applied.     

Laminar heat transfer characteristics of internally finned tube with sinusoidal wavy fin

Comparative numerical study of laminar heat transfer characteristics of annular tubes with sinusoidal wavy fins has been conducted both experimentally and numerically with Re = 299–1,475. The uniform heat flux is imposed on the tube outside wall surface. Two tube materials (copper and stainless steel) are considered. It is found that the fluid temperature profile is not linear but convex along the flow direction due to the axial heat conduction in tube wall, and the effects of axial heat conduction on the heat transfer decreases with an increase in Reynolds number or decrease in tube wall thermal conductivity. The axial distributions of local Nusselt number could reach periodically fully developed after 3–5 cycles. The convectional data reduction method based on the traditional method should be improved for tube with high thermal conductivity or low Reynolds numbers, Otherwise, the heat transfer performance of internally finned tube may be underestimated.     

Application of hybrid and moment methods to the measurement of moisture diffusion coefficients of building materials

This work proposes two simple dynamic methods that provide an accurate method for measurement of diffusion coefficients in building materials. Experimental measurements of moisture diffusion coefficients covered three commonly used building materials and they were carried out for a range of the relevant parameters, as temperature and relative humidity. The diffusion coefficients obtained by the two dynamic methods show a deviation comparatively to the steady-sate cup method; however, this variance is in accordance with the results presented in literature.     

Comparison of Fe and Ni opacity calculations for a better understanding of pulsating stellar envelopes

Opacity is an important ingredient of the evolution of stars. The calculation of opacity coefficients is complicated by the fact that the plasma contains partially ionized heavy ions that contribute to opacity dominated by H and He. Up to now, the astrophysical community has greatly benefited from the work of the contributions of Los Alamos [1], Livermore [2], [2a] and [2b] and the Opacity Project (OP) [3]. However unexplained differences of up to 50% in the radiative forces and Rosseland mean values for Fe have been noticed for conditions corresponding to stellar envelopes. Such uncertainty has a real impact on the understanding of pulsating stellar envelopes, on the excitation of modes, and on the identification of the mode frequencies. Temperature and density conditions equivalent to those found in stars can now be produced in laboratory experiments for various atomic species. Recently the photo-absorption spectra of nickel and iron plasmas have been measured during the LULI 2010 campaign, for temperatures between 15 and 40 eV and densities of ∼3 mg/cm³. A large theoretical collaboration, the “OPAC”, has been formed to prepare these experiments. We present here the set of opacity calculations performed by eight different groups for conditions relevant to the LULI 2010 experiment and to astrophysical stellar envelope conditions.     

Convolution theorems associated with some integral operators and convolutions

In this article, various convolution theorems involving certain weight functions and convolution products are derived. The convolution theorems we obtain are more general, convenient, and efficient than the complicated convolution theorem of the Hartley transform. Further results involving new variants of generalizations of Fourier and Hartley transforms are also discussed.     

Exact tail asymptotics for fluid models driven by an M/M/c queue

Queueing Systems - In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the M / M / c queue, which is...     

App-based scaffolds for writing two-column proofs

This paper presents apps designed to assist students in understanding and developing proofs in geometric theorems. These technologies focus on triangle congruence, triangle similarity and properties of parallelograms. Focus group discussions and initial testing of the apps revealed that the apps offered a more engaging medium for learning proving and were capable of facilitating proof-writing skills in geometry.     

Interlaboratory Study of Digital Volume Correlation Error Due to X-Ray Computed Tomography Equipment and Scan Parameters: an Update from the DVC Challenge

Experimental Mechanics - The quality of Digital Volume Correlation (DVC) full-field displacement measurements depends directly on the characteristics of the X-ray Computed Tomography (XCT)...