Dynamic stability of weak equations of rectangular plates

The stability analysis method is developed for distributed dynamic problems with relaxed ssumptions imposed on solutions. The problem is motivated by structural vibrations with external time-dependent parametric excitations which are controlled using surfacemounted or embedded actuators and sensors. The strong form of equations involves irregularities which lead to computational difficulties for estimation and control problems. In order to avoid irregular terms resulting from differentiation of force and moment terms, dynamical equations are written in a weak form. The weak form of dynamical equations of linear mechanical structures is obtained using Hamilton's principle. The study of stability of a stochastic weak system is based on examining properties of the Liapunov functional along a weak solution. Solving the problem is not dependent on assumed boundary conditions.