Dynamic stability of a three-layer beam – Generalization of the sandwich structures theory

The work is devoted to the mathematical modeling of a three-layer beam. A generalization of the "broken-line" hypothesis describing the displacement field is proposed and used to analyze the problem of dynamic stability. Based on Hamilton's principle, equations of motion are obtained. Then this system of two differential equations is approximately solved. In this way, the fundamental natural frequency and two unstable regions are obtained.