Analysis and control of vibrations of honeycomb plates by parametric stiffness modulations

Abstract

This paper addresses an active control of the resonant vibrations of a sandwich plate with the honeycomb composition of a core ply performed by a parametric stiffness modulation. The controlled vibrations are those of the dominantly flexural type excited by a transverse force acting at a low resonant frequency. The stiffness modulation is introduced by some fairly small changes in an orientation of plates composing cell elements of a core ply. It is performed at a comparatively high frequency identified by the resonance of a mode of the dominantly shear type. The method of direct partition of motions is used that predicts an existence of the modal interaction between the low-frequency and the high-frequency motions. It is shown that such a parametric control can provide a significant favourable shift of the first eigenfrequency of a controlled beam (the one subjected to the stiffness modulation) from its nominal value for an uncontrolled beam. Asymptotic results are checked by direct time-marching integration. The energy of the `micro-motions' is calculated and it is compared with the energies of flexural vibrations of a plate with and without control. Heavy fluid loading conditions are accounted for as well as material losses in a structure. It is demonstrated that although heavy fluid loading reduces the resonant frequencies of forced vibrations, the suggested mechanism of control remains valid in these cases.

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.…”

“…In such a formulation, parameters of a sandwich plate composition, which control these eigenfrequencies should include (besides the physical parameters of thickness, stiffness and density) the parameters of ''vibrational rheology'', see references [3][4]7]. These parameters specify ''hidden'' motions, which produce stiffness modulation.…”

“…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.…”

Using high-frequency vibrations and non-linear inclusions to create metamaterials with adjustable effective properties

“…Such materials are known as dynamic materials [2,17]. In [19,18] HF parametric excitation has been applied to control the effective material properties. In [7] by assuming the existence of a HF standing wave in a continuous non-linear systems, the effective material properties for the LF motion (slow motion) are derived analytically.…”

“…Compared to the approaches in [19,18], where distributed actuation and control are used, the advantage of the approach in [7] is the use of a single excitation source for generating the HF field. However, in contrast to the parametric case, where the stiffness change depends on the frequency of the excitation, for the externally excited non-linear system it does not depend on the frequency of the excitation, and is proportional to the response amplitude and the strength of the non-linearity.…”