Investigation of the oscillatory dynamics of the plate with the control layer of material

The emerging concept of active constrained layer control of vibrating structures involved the application of a viscoelastic layer constrained by a piezoelectric constrained layer. Attempts have been made to optimize the performance of the constrained layer treatments by selecting the optimal thickness, length, elasticity of the viscoelastic core [1, 2, 3]. This paper deals with the control of dynamics of an elastic structural plate by application of a layer of material the parameters of which can be varied by selecting the thickness of the layer. Another problem occurring in such a type of applications is the appropriate interpretation of the results of simulation. Comparisons between the vibrations of the core and the controlling surface are very important from the point of design of controlling elements, though conventional visualization techniques can produce rather poor results in that sense. Therefore there exist a definite need for developing more appropriate visualization techniques capable of detection small variations from a predefined regime of dynamic motion. The plate as a structural element by taking into account the layer of material on its surface is analyzed. This serves as a model of the transporting element with the interacting transported material. The simplified model of the transported material consists of the distributed springs with masses performing vertical motion and without mutual interaction. This is a modification of the Winkler type elastic layer known in applied elasticity [5]. The finite element with four degrees of freedom per node (the deflection and the two rotations of the plate and the deflection of the layer) is developed for the analysis of the described systems. The eigenmodes are calculated and each of them provides the two surfaces: the first one describing bending of the core plate, another – the motion of the control layer.