A problem of non – linear deformation of five–layer conical shells with allowance for discrete ribs

A problem of non – linear deformation of multiplayer conical shells with allowance for discrete ribs under non – stationary loading is considered. The system of non – linear differential equations is based on the Timoshenko type theory of rods and shells. The Reissner’s variational principle is used for deductions of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance distcrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers. As a numerical example, the problem of dynamic deformation of a five-layer conical shell with rigidly clamped ends under the action of an internal distributed load was considered.

Towards a combined perfectly matching layer and infinite element formulation for unbounded elastic wave problems

This paper presents a framework for implementing a novel perfectly matching layer and infinite element (PML+IE) combination boundary condition for unbounded elastic wave problems in the time domain. To achieve this, traditional hexahedral finite elements are used to model wave propagation in the inner domain and IE test functions are implemented in the exterior domain. Two alternative implementations of the PML formulation are studied: the case with constant stretching in all three dimensions and the case with spatially dependent stretching along a single direction. The absorbing ability of the PML+IE formulation is demonstrated by the favourable comparison with the reflection coefficient for a plane wave incident on the boundary achieved using a finite-element-only approach where stress free boundary conditions are implemented at the domain edge. Values for the PML stretching function parameters are selected based on the minimisation of the reflected wave amplitude and it is shown that the same reduction in reflection amplitude can be achieved using the PML+IE approach with approximately half of the number of elements required in the finite-element-only approach.

Use of the pass-through method to solve sound radiation problems of a spherical electro-elastic source of zero order

In the article was solved the problem of radiation of a sound by the electroacoustic transducer which is executed in the form of a thin spherical cover, using a pass-through method. The outer and inner surfaces of the shell are completely electroded. The application of this method provides an opportunity to avoid inaccuracies that arise during the traditional formulation of boundary conditions for acoustic mechanical fields, the use of equivalent substitution schemes and the absence of boundary conditions for the electric field in general. Given methodology eliminates these shortcomings by applying conjugation conditions, taking into account the types of electroding of the surfaces of piezoceramic transducers, the introduction of boundary conditions for current and voltage. The results of the solution demonstrate the high capabilities of this pass-through method, in terms of taking into account the peculiarities of determining the characteristics of these fields, values and dependences of the main complex characteristics of the electroelastic transducer, and auxiliary material constants of the piezoelectric material. The proposed approach is relevant, because it allows to increase the reliability of modeling the operating conditions of acoustic transducers in the context of wave problems of acoustics. Aim is to enhance the range of performances and build algorithms solving problems of stationary mode hydroelectroelasticity sound radiation. The expected results are presented in terms of improving approaches to studying the features of the oscillatory process of the active elements of sound-emitting systems and the accompanying effects of the transformation of interconnected fields involved in the formation of the acoustic signal in the liquid

Mach Wave and Acoustical Wave Structure in Nonequilibrium Gas-Particle Flows

In this Element, the gas-particle flow problem is formulated with momentum and thermal slip that introduces two relaxation times. Starting from acoustical propagation in a medium in equilibrium, the relaxation-wave equation in airfoil coordinates is derived though a Galilean transformation for uniform flow. Steady planar small perturbation supersonic flow is studied in detail according to Whitham's higher-order waves. The signals owing to wall boundary conditions are damped along the frozen-Mach wave, and are both damped and diffusive along an effective-intermediate Mach wave and diffusive along the equilibrium Mach wave where the bulk of the disturbance propagates. The surface pressure coefficient is obtained exactly for small-disturbance theory, but it is considerably simplified for the small particle-to-gas mass loading approximation, equivalent to a simple-wave approximation. Other relaxation-wave problems are discussed. Martian dust-storm properties in terms of gas-particle flow parameters are estimated.