The active control of vibrations of composite beams by parametric stiffness modulation

Forced and Free Vibrations of Rectangular Sandwich Plates With Parametric Stiffness Modulation

“…Graphs shown in Figures 2-4 are typical for sandwich plates having other realistic geometry and stiffness parameters. Similar to the cases considered in the references [3,4], it is important to notice that eigenfrequencies of the third (dominantly shear) spectrum are much higher than the relevant eigenfrequencies from the first (dominantly flexural) spectrum. This makes it possible to control low-frequency resonant flexural vibrations by the parametric stiffness modulation performed at a comparatively high frequency of resonant shear vibrations.…”

“…A theory of sandwich plate formulated by Skvortsov [11], which has been used to analyze vibrations of sandwich beams (or plates in cylindrical bending) in references [3,[12][13] is adotped. In the framework of this theory, the deformation of a sandwich plate element is governed by three independent variables: a displacement of the mid-surface of the whole element w (which is the same for all plies), a shear angle W x about the y axis and a shear angle W y about the x axis.…”

“…Derivation of the governing equations of such a plate is easily performed by the use of Hamilton principle and the energy functional is taken as (see reference [3] for a case of cylindrical bending) Figure 1. The element of a sandwich plate.…”

“…In particular, the concept of ''dynamic materials'' as a special type of smart materials designed to suppress vibrations has been suggested and elaborated in recent papers [2][3][4][5][6]. This concept is in effect based on the ideas of ''vibrational rheology'' suggested in reference [7].…”

“…In recent papers [2][3][4] it has been shown that parametric control introduced as the modulation of the stiffness parameters of a structure in response to specific excitation conditions effectively prevents vibrations with large amplitudes. Due to such a parametric control very small stiffness modulation at a certain frequency extinguishes the resonant behaviour of a structure in given excitation conditions.…”