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EN
A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances.
2
Content available remote Penny-shaped crack in a piezoceramic cylinder under Mode I loading
EN
The electroelastic response of a penny-shaped crack in a piezoelectric cylinder of finite radius is investigated in this study. Fourier and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. They are then reduced to a Fredholm integral equation of the second kind. Numerical values of the stress intensity factor, energy release rate and energy density factor for piezoelectric ceramics are obtained to show the influence of applied electrical loads.
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