A non-classical Mindlin plate model is developed using a modified couple stress theory. The equations of motion and boundary conditions are obtained simultaneously through a variational formulation ...based on Hamilton’s principle. The new model contains a material length scale parameter and can capture the size effect, unlike the classical Mindlin plate theory. In addition, the current model considers both stretching and bending of the plate, which differs from the classical Mindlin plate model. It is shown that the newly developed Mindlin plate model recovers the non-classical Timoshenko beam model based on the modified couple stress theory as a special case. Also, the current non-classical plate model reduces to the Mindlin plate model based on classical elasticity when the material length scale parameter is set to be zero. To illustrate the new Mindlin plate model, analytical solutions for the static bending and free vibration problems of a simply supported plate are obtained by directly applying the general forms of the governing equations and boundary conditions of the model. The numerical results show that the deflection and rotations predicted by the new model are smaller than those predicted by the classical Mindlin plate model, while the natural frequency of the plate predicted by the former is higher than that by the latter. It is further seen that the differences between the two sets of predicted values are significantly large when the plate thickness is small, but they are diminishing with increasing plate thickness.
ABSTRACT
High time resolution and accuracy are of critical importance in the studies of timing analysis and time delay localization of gamma-ray bursts (GRBs), soft gamma-ray repeaters (SGRs) and ...pulsars. The Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) consisting of two micro-satellites, GECAM-A and GECAM-B, launched on 2020 December 10, is aimed at monitoring and locating X-ray and GRBs all over the sky. To achieve its scientific goals, GECAM is designed to have the highest time resolution (0.1 $\mu {\rm s}$) among all GRB detectors ever flown. Here, we make a comprehensive time calibration campaign including both on-ground and on-orbit tests to derive not only the relative time accuracy of GECAM satellites and detectors, but also the absolute time accuracy of GECAM-B. Using the on-ground calibration with a $\rm ^{22}Na$ radioactive source, we find that the relative time accuracy between GECAM-A and GECAM-B is about 0.15 $\mu {\rm s}$ (1σ). To measure the relative time accuracy between all detectors of a single GECAM satellite, cosmic-ray events detected on orbit are utilized since they could produce many secondary particles simultaneously record by multiple detectors. We find that the relative time accuracy among all detectors onboard GECAM-B is about 0.12 $\mu {\rm s}$ (1σ). Finally, we use the novel Li-CCF method to perform the absolute time calibration with Crab pulsar and SGR J1935+2154, both of which were jointly observed by GECAM-B and Fermi/GBM, and obtain that the time difference between GECAM-B and Fermi/GBM is 3.06 ± 6.04 $\mu {\rm s}$ (1σ).
H5N1 avian influenza virus (AIV) has emerged as a pathogenic entity for a variety of species, including humans, in recent years. Here we report an outbreak among migratory birds on Lake Qinghaihu, ...China, in May and June 2005, in which more than a thousand birds were affected. Pancreatic necrosis and abnormal neurological symptoms were the major clinical features. Sequencing of the complete genomes of four H5N1 AIV strains revealed them to be reassortants related to a peregrine falcon isolate from Hong Kong and to have known highly pathogenic characteristics. Experimental animal infections reproduced typical highly pathogenic AIV infection symptoms and pathology.
Highlights • Intrathecal injection of DHA prevents and reverses inflammatory pain. • DHA decreases carrageenan-induced microglial activation in the spinal cord. • DHA decreases p38 phosphorylation ...and inflammatory mediators’ production in microglia.
Critical velocities of a two-layer composite tube under a uniform internal pressure moving at a constant velocity are analytically determined. The formulation is based on a Love–Kirchhoff thin shell ...theory that incorporates the rotary inertia and material anisotropy. The composite tube consists of two perfectly bonded axisymmetric circular cylindrical layers of dissimilar materials, which can be orthotropic, transversely isotropic, cubic or isotropic. Closed-form expressions for the critical velocities and radial displacement of the two-layer composite tube are first derived for the general case by including the effects of material anisotropy, rotary inertia and radial stress. The formulas for composite tubes without the rotary inertia effect and/or the radial stress effect and with various types of material symmetry for each layer are then obtained as special cases. In addition, it is shown that the model for single-layer, homogeneous tubes can be recovered from the current model as a special case. To illustrate the new model, a composite tube with an isotropic inner layer and an orthotropic outer layer is analyzed as an example. All four critical velocities of the composite tube are calculated using the newly derived closed-form formulas. Six values of the lowest critical velocity of the two-layer composite tube are computed using three sets of the new formulas, which compare fairly well with existing results.
A detailed variational formulation is provided for a simplified strain gradient elasticity theory by using the principle of minimum total potential energy. This leads to the simultaneous ...determination of the equilibrium equations and the complete boundary conditions of the theory for the first time. To supplement the stress-based formulation, the coordinate-invariant displacement form of the simplified strain gradient elasticity theory is also derived anew. In view of the lack of a consistent and complete formulation, derivation details are included for the tutorial purpose. It is shown that both the stress and displacement forms of the simplified strain gradient elasticity theory obtained reduce to their counterparts in classical elasticity when the strain gradient effect (a measure of the underlying material microstructure) is not considered. As a direct application of the newly obtained displacement form of the theory, the problem of a pressurized thick-walled cylinder is analytically solved. The solution contains a material length scale parameter and can account for microstructural effects, which is qualitatively different from Lamé’s solution in classical elasticity. In the absence of the strain gradient effect, this strain gradient elasticity solution reduces to Lamé’s solution. The numerical results reveal that microstructural effects can be large and Lamé’s solution may not be accurate for materials exhibiting significant microstructure dependence.
A new model for anisotropic magneto-electro-elastic Mindlin plates is developed by using an extended modified couple stress theory. The equations of motion and complete boundary conditions are ...simultaneously obtained by a variational formulation based on Hamilton’s principle. The new anisotropic magneto-electro-elastic plate model includes the models for orthotropic and transversely isotropic magneto-electro-elastic Mindlin plates and the model for isotropic Mindlin plates, all incorporating the microstructure effect, as special cases. To illustrate the new model, the static bending and free vibration problems of a simply supported transversely isotropic magneto-electro-elastic plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection, rotation, electric potential, and magnetic potential of the simply supported plate predicted by the current non-classical model are always smaller than those predicted by the classical elasticity-based model, and the differences are significant when the plate thickness is very small but is diminishing as the thickness increases. For the free vibration problem, it is found that the natural frequency predicted by the new plate model is higher than that predicted by the classical model, and the difference is quite large for very thin plates.
Closed-form expressions for critical velocities and middle-surface displacements of anisotropic tubes subjected to a uniform internal pressure moving at a constant speed are derived using a ...first-order shear deformation (FSD) model for axisymmetric orthotropic cylindrical shells. The FSD shell model is first formulated employing a variational method based on Hamilton’s principle, which incorporates both the transverse shear and rotary inertia effects. The general 3-D constitutive relations for orthotropic elastic materials are utilized to describe the tube anisotropy, which enables a unified treatment of orthotropic, transversely isotropic, cubic and isotropic tubes representing various composite and metallic cylindrical shells. Closed-form formulas for four critical velocities of the anisotropic tube are derived for the general case with the transverse shear, rotary inertia and radial stress effects, which divide the range of the pressure velocity into four segments. For each of these segments, closed-form expressions for the mid-surface radial displacement are obtained. By suppressing the transverse shear, rotary inertia or radial stress effect, the general formulas are reduced to those for special cases. In particular, when the transverse shear, rotary inertia and radial stress effects are all neglected, the newly derived critical velocity formulas for orthotropic and isotropic tubes recover the two existing ones for thin tubes. To quantitatively illustrate the new model, a numerical example is provided for an isotropic tube, where eight values of the lowest critical velocity are directly determined using newly derived formulas and compared with an existing value computationally obtained by others.
Control of the radiative properties of functional molecules near metals is a key issue in nano-optics, and is particularly important in the fields of energy transfer and light manipulation at the ...nanoscale and the development of plasmonic devices. Despite the various vibronic transitions (S1 (vvariant prime) arrow right S0 (v)) available for frequency tuning of fluorescence, the molecular emissions near metals reported to date have been subject to Kasha's rule, with radiative decay from the lowest excited state (S1 (0)) (refs 6-10). Here, we show resonant hot electroluminescence arising directly from higher vibronic levels of the singlet excited state (S1 (vvariant prime > 0)) for porphyrin molecules confined inside a nanocavity in a scanning tunnelling microscope, by spectrally tuning the frequency of plasmons. We also demonstrate the generation of unexpected upconversion electroluminescence. These observations suggest that the local nanocavity plasmons behave like a strong coherent optical source with tunable energy, and can be used to actively control the radiative channels of molecular emitters by means of intense resonance enhancement of both excitation and emission.
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