On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions

The problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated and studied. It is proved a theorem of existence and uniqueness of a weak solution for the problem under consideration.

Non-negative Intensity for Target Strength Identification in Marine Ecosystem Research

In this paper, we propose non-negative intensity (NNI) as an alternative intensity-based technique for target strength identification in marine ecosystem research. NNI identifies local surface regions of a body with positive-only sound power contributions. NNI is employed for sound scattering by fluid-loaded, fluid-filled elastic structures with weak scattering boundary conditions. Three numerical case studies are presented for which fully coupled fluid-structure interaction models based on the finite element method (FEM) and the boundary element method (BEM) are developed. To validate the three-way coupling between the structural and fluid domains, an elastic shell submerged in water and filled with different internal fluids is initially considered. Results for the scattered acoustic intensity obtained numerically are compared with analytical results from the literature. Models representing Antarctic krill of simple and complex geometry are developed. A 3×3 cylinder array representing a simplified aggregation of krill is also presented. Target strength is calculated using both the scattered intensity and NNI for different incident excitation angles. Results for NNI identify the surface regions of an individual organism or group of organisms with the greatest contribution to the scattered sound at the target strength locations.

Determining the dynamic characteristics of elastic shell structures

Building structures are very often operated under the action of dynamic loads, both natural and man-made. The calculation of structures under the influence of static loads has been quite widely studied in detail. When structures are exposed to dynamic loads, additional tests are carried out, where measuring instruments are installed on the structures to register stresses and deformations that occur during dynamic influences. Elastic elements are the responsible functional unit of many measuring instruments. Therefore, the quality of elastic elements ensures the operational stability of the entire structure. This determines the increased attention that is paid to technology and construction to elastic elements. Previously, the work of elastic elements made of homogeneous mono materials with the same physical and geometric properties in all directions and over the entire surface of the element was studied. The elastic element was considered as a shell of rotation with a complex shape of the meridian and various physical and mechanical properties at various points caused by uneven reinforcement. Two types of reinforcement were implied ‒ radial and circular. Elastic shell elements (ESE) operate under conditions of dynamic loading. The equation was derived for determining the dynamic characteristics of inhomogeneous elastic elements. The dependences of the first three natural frequencies of oscillations on the thickness of the shell and the depth of the corrugation and the first two natural frequencies of oscillations on the thickness of the shell have been analyzed. The amplitude-frequency characteristics (AFC) and the phase-frequency characteristics (PFC) of the shell depending on the geometric parameters have been calculated. All these results could significantly improve the quality of the readings of the instruments, which depend on the sensitivity of the shell elastic elements. And it, in turn, depends on the geometric and physical properties of the shell elastic elements.

Compensatory bellows oscillations as a corrugated shell with liquid inside

The paper deals with a relevant problem of shipbuilding, i.e. calculation of free and forced vibrations of pipeline compensatory bellows. These devices are used to reduce the vibration load caused by ship power machines. When analyzing the vibrations of the compensatory bellows, it is necessary to take into account the liquid contained in the bellows. In this work, the design model of the bellows is represented by a corrugated elastic shell as a material surface with five degrees of freedom. A variant of the classical theory of shells, built on the basis of Lagrangian mechanics, is used. The influence of the liquid is taken into account by two models. First, the liquid is considered to be ideal and incompressible and is considered through the attached mass to the shell. The shell is replaced by a cylindrical surface with a radius in the middle line of the corrugation. To account for the influence of the frequency of bellows oscillations on the attached inertia of the liquid in the calculation we also used the acoustic approximation; and derived a formula for a generalized attached mass of the ideal compressible liquid. The equations of the bellows oscillations under the periodic loading are obtained. The problem has been solved by the finite difference method. The values of natural frequencies of free vibrations are obtained for the compensatory bellows from the corrosion-resistant heat-resistant steel. It is shown that by taking account of the liquid, we significantly change the natural frequencies of the bellows. With high-frequency vibrations it is necessary to take into account the compressibility of the liquid. The problem of the forced vibrations of the bellows caused by a displacement of its end face by the harmonic law is solved. The internal forces and moments are determined, as well as occurring stresses by Mises criterion in the bellows. We found the critical value of the end face displacement at a frequency of 50 Hz, at which the bellows goes into a plastic state.

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

We performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. Unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures, i.e. below the experimentally determined critical load at which buckling occurs elastically, often following a significant delay period from the time of load application. While emphasizing the close connections to elastic shell buckling, we rely on viscoelasticity to explain our observations. In particular, we demonstrate that the lower critical load may be determined from the material properties, which is rationalized by a simple analogy to elastic spherical shell buckling. We then introduce a model centred on empirical quantities to show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This allows us to capture how both the deflection at instability and the time delay depend on the applied pressure, material properties and defect geometry. These quantities are straightforward to measure in experiments. Thus, our work not only provides intuition for viscoelastic behaviour from an elastic shell buckling perspective but also offers an accessible pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers.

Applicability and Limitations of Simplified Elastic Shell Theories for Vibration Modelling of Double-Walled Carbon Nanotubes

The applicability and limitations of simplified models of thin elastic circular cylindrical shells for linear vibrations of double-walled carbon nanotubes (DWCNTs) are considered. The simplified models, which are based on the assumptions of membrane and moment approximate thin-shell theories, are compared with the extended Sanders–Koiter shell theory. Actual discrete DWCNTs are modelled by means of couples of concentric equivalent continuous thin, circular cylindrical shells. Van der Waals interaction forces between the layers are taken into account by adopting He’s model. Simply supported and free–free boundary conditions are applied. The Rayleigh–Ritz method is considered to obtain approximate natural frequencies and mode shapes. Different aspect and thickness ratios, and numbers of waves along longitudinal and circumferential directions, are analysed. In the cases of axisymmetric and beam-like modes, it is proven that membrane shell theory, differently from moment shell theory, provides results with excellent agreement with the extended Sanders–Koiter shell theory. On the other hand, in the case of shell-like modes, it is found that both membrane and moment shell theories provide results reporting acceptable agreement with the extended Sanders–Koiter shell theory only for very limited ranges of geometries and wavenumbers. Conversely, for shell-like modes it is found that a newly developed, simplified shell model, based on the combination of membrane and semi-moment theories, provides results in satisfactory agreement with the extended Sanders–Koiter shell theory in all ranges.