Liapunov functionals application to dynamic stability analysis of continuous systems

Using the appropriate energy-like Liapunov functional sufficient conditions for the uniform stability of undeflected form of structures are derived. The structures are described by partial differential equations and integro-partial differential equations with time and space-time-dependent coefficients. Stability domains obtained by applying the linearized equations of motion are compared with those employing the typical nonlinearity e.g. Kármán nonlinear effects and Brazier's nonlinearity. A relation between the stability of nonlinear equations and linearized ones is analyzed. An influence of geometrical, and material parameters as well as constant components of axial and in-plane forces for different classes of parametric excitation on stability regions is shown.