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This paper proposes a refined formulation of linearized problems of internal nonuniformly scaled flat buckling modes of a rigid lamina consisting of fibers and fiber bundles with allowance for their interaction with the surrounding matrix. Fibers are the structural elements of fibrous composites and in a prebuckling (unperturbed) state under the action of shear stresses and tensile (compression) stresses in the transverse direction. The problems are formulated using equations constructed by reducing the version of geometrically nonlinear equations of the elasticity theory to one-dimensional equations of the theory of rectilinear rods. These equations are based on the use of the refined Timoshenko shear model with allowance for tension-compression strains in the transverse direction for the rigid lamina and the transverse-soft layer model with immobile boundary planes in a perturbed state for the epoxy layers. It is shown that loading samples with a structure is accompanied by constant changes in the composite structure due to implementation and alternation of the internal buckling modes with a varying wave formation parameter. This particularly allows explaining the changing of the effective shear modulus of the fibrous composite with increasing shear strains. [ABSTRACT FROM AUTHOR]

The propagation of a stationary acoustic wave through an infinite thin plate stiffened on two sides by a system of absolutely rigid, crossed ribs and located between two absolutely rigid barriers. It is assumed that the plate and the ribs evenly distributed along rectangular Cartesian axes are connected through elastic spacers (supports) without slip. The dynamic deformation of the plate is described by the linearized Kirchhoff-Love equations of the classical theory of plates, the dynamic deformation of the spacers is described by two-dimensional and one-dimensional relations based on linear approximations of displacements of points of the coating and spacers along the thickness and taking into account only transverse compression and transverse shear, and the motion of acoustic media by the well-known wave equations. The solution of the problem is obtained using the Ritz method. The constructed solution was used to investigate how the physico-mechanical and geometric parameters of the mechanical system and the frequency of acoustic waves incident on the plate influence the sound-insulating parameters and the stress-strain state of the plate. [ABSTRACT FROM AUTHOR]