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Stability Analysis of Continuous Systems with Imperfect Boundary Conditions in a Weak Formulation

Tylikowski A.

Machine Dynamics Problems

2008

Vol. 32, No. 3

107-116

Dynamics of continuous systems have been considered in a weak (variational) form. Dynamics equation of beam subjected to the axial stochastic force in the weak formulation has been derived. The weak form of dynamics equations of linear mechanical structures is obtained using variational calculus. The almost sure stochastic stability of beam equilibrium, without the previous discretization, has been analysed by means of direct Lyapunov method. The stability analysis method is developed for distributed dynamic problems with relaxed assumptions imposed on solutions. Sufficient stability conditions have been established for the imperfect boundary conditions and two limit cases: the simply supported beam and the clamped beam are obtained.

Method of analytical regularization based on the static part inversion in wave scattering by imperfect thin screens

Nosich A.I.

Journal of Telecommunications and Information Technology

2001

nr 3

72-79

The paper is focussed on the development of the method of analytical regularization (MAR) in electromagnetic wave scattering and absorption by imperfect scatterers shaped as thin screens.