RESONANCE PARAMETRIC VIBRATIONS OF A CYLINDRICAL SANDWICH SHELL

Abstract

This paper considers cylindrical composite sandwich shells that consist of two thin outer layers and one thick honeycomb filler. The outer layers are made of a composite orthotropic material, for example, carbon-reinforced plastic. The honeycomb filler is made of an orthotropic plastic, for example, PLA, using additive technologies.   

To obtain a mathematical model of nonlinear structural vibrations, the honeycomb core is homogenized into a uniform orthotropic solid layer using a finite-element simulation in ANSYS.  Parametric vibrations of the cylindrical shell under the action of a longitudinal load are considered. Each layer of the structure is described by a higher-order shear theory, which uses five generalized displacements (three displacements projections onto the axes and two rotation angles of the middle surface normal). The displacement projections are continuous at the layer interfaces.  The assumed mode method is used to obtain a system of nonlinear ordinary differential equations in the generalized coordinates. The method uses the kinetic and the potential energy of the structure.

The shooting technique and the parameter continuation method are used jointly to analyze nonlinear vibrations, their stability and bifurcations. The multipliers are calculated to estimate the vibration stability. The stability and bifurcations of periodic oscillations are shown in the frequency responses, which describe the structure dynamics in the principal parametric resonances. As shown by the numerical analysis, standing waves are observed in the cylindrical shell. As a result of the bifurcations, the standing waves are transformed into travelling ones, which are described by a loop in the frequency response.

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