On eigenvalue boundary problems of transversely vibrating sandwich beams

Abstract Flexural vibrations of sandwich beams are analysed as a special eigenvalue boundary problem. To determine the eigenvalues and eigenfunctions an accurate method in closed form is applied. The solution procedure is demonstrated on a sandwich cantilever with unrestrained and riveted free-end boundary conditions. The influences of shear force in the beam core and of a rigid rivet applied at the free-end of the beam on eigenvalues and eigenfunctions are analysed and graphically presented. A special “migratory shift” of the nodes at higher modes of vibration due to shearing strain in the core is observed. It is shown that this phenomenon depends on the rigidity of the core, on cross-section geometry and on the boundary conditions applied.