Dynamic stability of a viscoelastic beam with frequency-dependent modulus

This study presents the dynamic stability of a simply supported, viscoelastic beam subjected to an axially harmonic load. The complex modulus of viscoelastic material is considered to depend on the frequency of parametric loading. Applying Galerkin’s method, the governing equation of motion is simplified to the complex form of the Mathieu equation with frequency-dependent coefficients. Then, the boundary of dynamic stability is determined by coupling the numerical binary search procedure and the complex incremental harmonic balance (IHB) method, which are developed in this study. This algorithm is easily, simply and conveniently used to perform computer numerical analysis. The results indicate that the loss factor presents the damping capacity of viscoelastic material. The numerical results reveal that the frequency influences the dynamic stability.