Free vibration analysis of fiber-reinforced polymer honeycomb sandwich beams with a refined sandwich beam theory

Free vibration of a fiber-reinforced polymer honeycomb sandwich beam with sinusoidal core configuration is studied based on a refined sandwich beam theory. Using a micro/macromechanics approach for face laminates and a mechanics of material approach for honeycomb core, the equivalent elastic properties of face laminates and honeycomb core are obtained. A free vibration model based on the refined sandwich beam theory is formulated using the Hamilton's variational principle. Analytical solutions for a cantilevered sandwich beam are obtained by the Ritz method. Experimental results conducted on the fiber-reinforced polymer honeycomb sandwich beams with different lengths are applied to validate the proposed analytical solutions. As a comparison and further verification, the analytical solutions based on the Timoshenko beam theory and high-order beam theory are also presented. The analytical solutions in term of natural frequencies are compared with the numerical simulation results as well. Good agreements among various comparisons demonstrate the accuracy and capability of the refined sandwich beam theory and its potentials in design applications and health monitoring of fiber-reinforced polymer honeycomb sandwich beams.