Abstract
A new tractable formulation of a zig-zag beam theory is developed. The zig-zag theory is presented in an elegant way, which makes it easy to follow and understand and can readily be employed. The presented theory is used to investigate the free vibration of soft core sandwich beams. The state space approach is then used to find analytical solutions for the natural frequencies and mode shapes of sandwich beams with arbitrary boundary conditions. The presented analysis and solutions are verified by comparison with experimental, analytical and numerical results available in the literature. The comparisons show that the zig-zag theory provides accurate predictions of the natural frequencies for sandwich beams with soft core. Furthermore, the analytical solutions for the natural frequencies can be used as benchmarks for approximate solutions such as Rayleigh-Ritz, finite element methods and other numerical methods. (C) 2016 Elsevier Ltd. All rights reserved.