The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the GeoClaw software and demonstrate well-balanced methods that exactly ma...

Torsional vibrations of composite poroelastic dissipative spherical shell are investigated in the framework of Biot’s extension theory.Here composite poroelastic spherical shell consists of two spherical shells, one is placed on other, and both are made of different poroelastic materials. Consideration of the stress-free boundaries of outer surface and the perfect bonding between two shells lea...

Low natural frequencies and vibration modes of the structure, consisting a closed circular cylindrical shell with end cap, having shape shallow spherical segment, are examined in paper using numerical asymptotic methods. There three types vibrations structure. Natural first type close to shell, second - those third cantilever beam load at end. In part research approximate values for found by As...

The aim of this paper is to determine the critical buckling load for simply supported thin shallow spherical shells made of functionally graded material (FGM) subjected to uniform external pressure. A metal-ceramic functionally graded (FG) shell with a power law distribution for volume fraction is considered, where its properties vary gradually through the shell thickness direction from pure me...

The large-amplitude vibrational behavior of a shallow spherical-cap shell is investigated theoretically using simple arguments. The results of this approximate analysis are expressed in the form of appealingly simple nondimensional quantities. It is shown that the frequency of the fundamental mode of such ashell falls by as much as 50% as the vibration amplitude is increased to approximately th...

Using numerical and asymptotic methods, the lowest natural frequencies vibration modes of a structure consisting closed circular cylindrical shell with an end cap attached to it, having shape shallow spherical segment, are studied in paper. Three types vibrations described. Eigenfrequencies first type, close shell, were previous works. In this paper, we study forms second type (cylindrical shel...

The invasive zebra mussel (Dreissena polymorpha) has quickly colonized shallow-water habitats in the North American Great Lakes since the 1980s but the quagga mussel (Dreissena bugensis) is becoming dominant in both shallow and deep-water habitats. While quagga mussel shell morphology differs between shallow and deep habitats, functional causes and consequences of such difference are unknown. W...

We consider the problem of local controllability from the origin for a coupled nonlinear shell via boundary controls.