Intrinsic mechanisms of vibrational mode jumping in sandwich panels

Abstract

This paper focuses on the mode jumping and natural frequency loci veering properties of the sandwich panel with three dimensional (3D) Kagome truss core under two different boundary conditions. The first-order shear deformation theory is employed to formulate the equations of motion and the general elastic boundary conditions are taken into account, which are simulated by a series of rotational and translational springs. The Rayleigh-Ritz method is deployed to derive the mode shape functions for the sandwich panel, where displacements and rotations of the structure are expressed as combination of the admissible functions composed of Fourier series and supplemental by Legendre polynomials. By solving the characteristic equations, the mode shapes and natural frequencies of the 3D-Kagome truss core sandwich panel are determined. Specifically, the present approach can provide a unified solution scheme to address the vibration issues of the moderately thick plates subjected to arbitrary boundary conditions including classical ones and with elastic constraints, which can be conveniently achieved by adjusting the stiffnesses of the constraint springs. From the obtained results, the most noteworthy ones are modal shifting or mode jumping and frequency loci veering, which are observed for the first time in the vibration modes of the tuned periodic panel, comparing with those in buckling modes of the beams or plates, vibration modes of mistuned periodic structures and mistuned rotor systems. Modal assurance criteria (MAC) are applied to check the spatial coincidence and correlation of the modal vectors before and after the mode jumping. Finally, the accuracy of the theoretical results are verified by vibration experiments and ABAQUS simulations.