University of Padova
Beatrice Pomaro has completed her Ph.D in 2011 from University of Padova and is at present Research Fellow at the same Department. She is leading research on two main fields: dynamic stability of structural elements and coupled thermo-hydro-mechanical modeling of cementitious materials.
The vibration of plate structures is one of the typical dynamic problems encountered in various fields of engineering and technology, such as aerospace, automotive, marine as well as civil applications. When the constraints loose their stiffness or their intrinsic viscosity occurs in time, they start behaving like spring-dumper systems and the dynamic response of the structural elements is supposed to vary, if compared with the system perfectly constrained, as already envisaged in [1, 2] for one-dimensional structural elements. The phenomenon of dynamic stability is investigated in this study for plate elements with visco-elastic supports, both translational and rotational, variously arranged, in order to understand the influence of viscoelasticity of the constraints on the response of rectangular plates under periodic axially distributed loads. Starting from the generic form of the solution of the partial differential equation for free vibrations of thin plates, a closed solution for the natural frequencies is provided in function of the degree of elasticity and viscosity of the constraints, so that the case of perfect supports turns to be a particular case of this more general solution. The free vibrations of the system at varying constraint conditions (both perfect, for comparison against known solutions, and visco-elastic) are obtained this way. Consequently the solution to the Mathieu-Hill equation at the basis of the problem, as found in , is applied to define the first region of instability and discuss the resulting unstable regions in function of the load condition, the geometric aspect and the slenderness of the plate.