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The model of Timoshenko's shell theory of shells was used to analyze the dynamic characteristics of conical shells of variable thickness on a Pasternak elastic bed under nonstationary loading. Based on the Hamilton–Ostrogradsky variational principle, the equations of motion of a conical shell of variable thickness on a Pasternak elastic bed were derived. This system of hyperbolic differential equations is solved by the finite difference method. The numerical algorithm for solving the obtained equations is based on applying the integral-interpolation method for constructing difference schemes in the spatial coordinate and an explicit finite difference scheme for integration in the time coordinate. The influence of geometric dimensions, taper angle, and elastic media on the natural frequencies and other dynamic characteristics of a conical shell of variable thickness under the action of a pulsed load is analyzed using specific examples. New mechanical effects are revealed. [ABSTRACT FROM AUTHOR]

The paper deals with the dynamics of asymmetric three-layer hemispherical shells with the discretely symmetric lightweight, rib-reinforced filler under pulsed loads. Since the distances between the ribs are much larger than the dimensions of the rib cross-sections, the theory of independent static and kinematic hypotheses for each layer is applied. In asymmetric shells, the load-bearing layers are made of different materials and have various thicknesses. The equations of motion of asymmetric three-layer spherical shells and natural boundary conditions are obtained using the Hamilton– Ostrogradsky variational principle for the Timoshenko-type shell and rod theory model. This makes it possible to develop an adequate finite element model for asymmetric three-layer shells composed of several materials and obtain numerical results on the dynamic behavior of an asymmetric three-layer elastic structure using the finite element method. The influence of physical and mechanical parameters of asymmetric layers of hemispherical shells on the stress-strain state under axisymmetric internal pulse loading is investigated. New mechanical effects are revealed. [ABSTRACT FROM AUTHOR]

The dynamics of asymmetric three-layer spherical shells with a ribbed discrete-symmetric lightweight core under nonstationary loading is studied. The elements of the elastic structure are analyzed using the Timoshenko model of the theory of shells and rods and independent static and kinematic hypotheses for each layer. The equations of motion of the shells under axisymmetric impulsive loading are derived using the Hamilton–Ostrogradsky variational principle. A finite-element shell model that relates the potential strain energy in the body and the potential of the applied forces is developed. The numerical results on the dynamics of the asymmetric three-layer elastic structure with face layers made of dissimilar materials are obtained using the finite-element method. The effect of the geometrical and mechanical parameters of the asymmetric layers of the shell on its dynamic behavior under axisymmetric internal nonstationary loading is studied. New mechanical effects are revealed. [ABSTRACT FROM AUTHOR]

The dynamics of spherical sandwich shells with a discretely symmetric light core reinforced with ribs under nonstationary loads is studied. To analyze the shell members of the elastic structure, the Tymoshenko theory of shells and rods and independent static and kinematic hypotheses for each layer are used. The equation of motion of spherical sandwich shells with a discrete-symmetric light core reinforced with ribs under axisymmetric impulsive loading is derived using the Hamilton–Ostrogradsky variational principle. Numerical results of on the vibrations of the elastic sandwich are obtained by the finite-element method. The effect of the geometrical, physical, and mechanical parameters of the symmetric layers of the shell on its dynamic behavior under axisymmetric internal impulsive loading is analyzed, and new mechanical effects are discovered. [ABSTRACT FROM AUTHOR]

The dynamics of sandwich conical shells under nonstationary loading is studied. The equations of motion of sandwich conical shells with a discrete symmetric lightweight ribbed core under axisymmetric impulsive loading are derived. In analyzing elements of an elastic shell, the Timoshenko theory of shells and rods is combined with independent static and kinematic hypotheses for each layer. The load-bearing layers in non-symmetric shells are made of dissimilar materials. The equation of motion for a non-symmetric sandwich conical shell with a discretely inhomogeneous core is derived using the Hamilton–Ostrogradsky variational principle. The numerical results on the vibrations of a sandwich elastic shell are obtained using the finite-element method. The influence of the physical and mechanical parameters of symmetric and non-symmetric layers on the stress–strain state of shells under the axisymmetric internal impulsive loading is studied. New mechanical effects are established. [ABSTRACT FROM AUTHOR]

A method for determining the nature of vibrations and stress–strain state of ribbed orthotropic conical shells with asymmetric layers interacting with masses under dynamic loads is developed using the theory of shells and the Tymoshenko hypotheses. The equations of vibrations of a shell formulated for the displacements of points of the midsurface are obtained using the Hamilton principle. To solve the system of equations of motion of the shell, trigonometric series in spatial coordinates and an explicit finite-difference scheme with respect to time are used. The accuracy of calculations by the finite-difference method depending on the number of time steps is estimated for a layered cylindrical shell as an example. The stress–strain state of a conical orthotropic shell with symmetric and asymmetric layers, longitudinal ribs, and masses under a short-term axisymmetric external load distributed over a portion of the shell and moving from the minor base to the major base is analyzed. [ABSTRACT FROM AUTHOR]

The stress–strain state of asymmetric three-layer cylindrical shells under nonstationary loads is considered. The sandwich structure is asymmetric due to the bearing layers that are made of different materials. The equation of motion of the asymmetric cylindrical sandwich shell with a light core reinforced with ribs is derived using independent static and kinematic hypotheses for each layer. The Tymoshenko model of the theory of shells and rods is used in the analysis of the members of the elastic structure. Numerical results on the stress–strain state and the nature of vibrations of the asymmetric elastic sandwich structure with bearing layers made of different materials are obtained using the finite-element method. The effect of the physical and mechanical parameters of layers and geometry of the shell on its stress–strain state under axisymmetric impulsive loads is studied in a wide range. [ABSTRACT FROM AUTHOR]