Vibration Analysis of a Three-Layered FGM Cylindrical Shell Including the Effect Of Ring Support

In this work, we study vibrations of three-layered cylindrical shells with one ring support along its length. Nature of material of the central layer is a functionally graded material (FGM) type. The considered FGM is of stainless steel and nickel. The internal and external layers are presumed to be made of isotropic material i.e., aluminum. The functionally graded material composition of the center layer is assorted by three volume fraction laws (VFL) which are represented by mathematical expressions of polynomial, exponential and trigonometric functions. The implementation of Rayleigh-Ritz method has been done under the Sanders’ shell theory to obtain the shell frequency equation. Natural frequencies (NFs) are attained for the present model problem under six boundary conditions. Use of characteristic beam functions is made for the estimation of the dependence of axial modals. The impact of layer material variations with ring support is considered for many ring positions. Also the effect of volume fraction laws is investigated upon vibration characteristics. This investigation is performed for various physical parameters. Numerous comparisons of values of shell frequencies have been done with available models of such types of results to verify accuracy of the present formulation and demonstrate its numerical efficiency.

Justification of the Calculation Method for Arch Support with Rock Grouting

This paper proposes a new method for calculating arch support with grouted space behind the support. The analysis of existing installations and methods for the calculation of frame supports was made. It has been established that the existing methods of frame parts calculation do not take into account the presence of grouted space behind the support. It is proposed to take into account the presence of the grouted layer in the space behind the support when it interacts with the rock mass. The formation of partially disturbed rock adjacent to the grouted layer is taken into account in the behaviour of rocks. In this method, the arch support is replaced with a ring support. The finite element method establishes the reduced dimensions of the ring support and its module of linear deformations, corresponding to these values of the arch support when its bearing capacity is lost. The scheme for calculating arch support ultimately boils down to considering the interaction of the support, the grouted layer, the zone of partially destroyed rocks and the rest of the mass of intact rocks in the hydrostatic field of rock pressure.

Optimal location of ring support for heavy Mindlin plates under axisymmetric loading

Bending of an annular thick plate resting on a ring support is analyzed under the action of power-law axisymmetric loading. A single governing differential equation for the Mindlin plate theory is derived. By solving associated boundary value problem, the optimal support location is determined to achieve minimizing the maximum deflection of a moderately thick circular or annular plate. The minimum sag of a heavy solid circular plate with or without the center support under self-weight is also analyzed. In addition to applied loading and the restraint of plate's rims, the optimal location of the ring support is also related to Poisson's ratio and the ratio of inner-to-outer radius. Auxetic plates with negative Poisson's ratio require larger ring support's radius, and conventional plates require smaller ring support's radius. Usually, the optimal support location is closer to the outer rim and far to the inner rim for a plate of self-weight. The obtained results are useful in safety design of circular or annular plates under complicated loading.