A Response-Adjustable Sandwich Beam with Harmonic Distribution Parameters under Stochastic Excitations

This paper demonstrates that a sandwich beam with the continuous harmonic distribution of geometrical and physical parameters can be adjusted to yield the desired response. The facial layer thickness and core layer modulus of the sandwich beam are considered as the harmonic distribution. The frequency responses and response spectral densities of the finite harmonic sandwich beam with supported mass under stochastic support motion excitations are studied for improving the performance. The partial differential equations for the horizontal and vertical coupling motions of the harmonic sandwich beam are derived and converted into the ordinary differential equations for the multi-mode coupling vibration. The modal stiffness, mass and excitation coefficients are functions of the harmonic distribution parameters (HDPs). The vibration responses including resonances and anti-resonances can be adjusted by the harmonic parameter wave numbers and amplitudes. The frequency responses and response spectral densities of the harmonic sandwich beam are obtained. The single and two-mode vibrations are analyzed to demonstrate that the response resonance and anti-resonance can be adjusted via the HDPs of the beam. The substantially improved vibration response characteristics and the influence of the HDPs on the response spectral densities are illustrated with numerical results.