The vibration and stability analyses are presented for axially compressed three-layered truncated conical shells with a functionally graded (FG) middle layer surrounded by elastic media. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to simple power law and exponential distributions in terms of the volume fractions of the constituents. Five sets of the material mixture are considered. The Pasternak model is used to describe the reaction of the elastic medium on the truncated conical shell. The fundamental relations, the modified Donnell-type dynamic stability and compatibility equations for the three-layered truncated conical shell with an FGM middle layer are derived. The governing equations are solved by using the Galerkin method and obtained expressions for dimensionless frequency parameters and dimensionless critical axial loads for three-layered truncated conical shells with the FG middle layer with and without an elastic foundation. The numerical results reveal that variations of the shell thickness-to-FGM thickness ratio, lengths-to-radius ratio, Winkler foundation stiffness, shear subgrade modulus of the foundation, material mixture and compositional profiles of the FG middle layer have significant effects on the values of dimensionless critical axial load and dimensionless frequency parameter. The results are verified by comparing the obtained values with those in the existing literature.

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In this study, the dynamic stability problem of a cylindrical shell composed of non-homogeneous orthotropic materials with Young's moduli and density varying continuously in the thickness direction under the effect of an axial compressive load varying with a parabolic function of time is considered. At first, the fundamental relations and the modified Donnell type dynamic stability equations of a non-homogeneous orthotropic cylindrical shell are set up. Applying the Galerkin method, first, and then the Ritz-type variational method, the closed-form solutions have been derived for the dynamic critical axial load and dynamic factor. Finally, carrying out some computations, the effects of the non-homogeneity of the orthotropy ratio and the axial loading parameter on the critical parameters have been studied. Comparing results with those in the literature validates the present analysis.

Rheological measurements of a concentrated suspension can be used to describe the flow of concrete. The rheological constants (yield value and plastic viscosity) of the mortar can be determined with a co-axial viscosimeter, and this technique is applied in this study. If the efficiencies of the mortar phase with respect to the cohesion, fluidity, bleeding and the friction of the concrete with the pipe are taken into consideration, this approach can be recognized as beneficial and helpful. Rheological tests on mortars were carried out with a Mettler RM 180 Rheomat co-axial viscosimeter. The angular deformation rate (γ ) and shearing stresses (τ ) were determined, andγ -τ diagrams were drawn. All the mortars showed a tixotropic behavior conforming to the Bingham model. A linear regression of these parameters gave the yield value (τ o ) and the plastic viscosity (η pl ) of the mortars.