Study on the Parameter Equation of Coal and Gas Outburst Hole

Studying the parameters of a coal and gas hole (CGOH), such as the hole shape, hole size and volume, coal quantity of CGOH, coal throw distance, calculated hole density, and gas pressure, is helpful in revealing the coal and gas outburst mechanism. In this study, we found that there were close mathematical relationships between these parameters. A nonlinear composite function relationship (CGOH parameter equation) was observed between the coal quantity, CGOH volume, and throw distance. The correctness of these relationships was verified using the Origin software. The stagnation point and inflection point of the parameter curve were obtained through the derivation of the parameter equation, and the transformation path from coal and gas outburst to coal and gas extrusion or dumping was clarified. At the same time, the equations of gas pressure, coal quantity, and throw distance are derived.

Optical bistability in two-dimensional nonlinear composites of coated cylinders with nonlinear core and graded shell

The intrinsic optical bistability of the nonlinear composite consisting of coated cylinders with nonlinear core and graded Drude shell is investigated with self-consistent mean-field approximation. We derive the nonlinear equation of near field for such graded composite in the quasistatic limit. We demonstrate that the bistability threshold and the bistable width are highly dependent on the core radius, the incident frequency, and the graded coefficient of the coated cylinder inclusion. It is found that the optical bistability appears only when the core radius and the incident frequency satisfy some specific conditions. Therefore, the optical bistability for nonlinear composite materials may be optimized by the suitable adjustment of the physical and geometrical parameters. Our results may be helpful for the design of the nonlinear device with appropriate bistability.

Flexural vibrations of geometrically nonlinear composite beams with interlayer slip

This paper addresses moderately large vibrations of immovably supported three-layer composite beams. The layers of these structural members are elastically bonded, and as such, subjected to interlayer slip when excited. To capture the moderately large response, in the structural model a nonlinear axial strain-displacement relation is implemented. The Euler–Bernoulli kinematic assumptions are applied layerwise, and a linear interlaminar slip law is utilized. Accuracy and efficiency of the resulting nonlinear beam theory is validated by selective comparative plane stress finite element calculations. The outcomes of application examples demonstrate the grave effect of interlayer slip on the geometrically nonlinear dynamic response characteristic of layered beams.