Analysis of periodic laminated fiber-reinforced composite beams in free vibration

The dynamic behavior of solid structures is an important aspect that must be considered in the design phase to ensure that the designed structure will have desired response under external excitation. Periodic structures offer various design possibilities that can tailor the dynamic behavior of the structure to match the desired response under a given applied excitation. The use of laminated fiber-reinforced composite materials in periodic structures further increases the design degrees of freedom by introducing new design parameters, such as the number of plies in each periodic patch and their fiber-orientation angles. In this article, the classical lamination theory is integrated with the forward approach of the wave finite element method to analyze periodic fiber-reinforced composite beams in flexural vibration. Since Euler–Bernoulli’s beam theory is used, the proposed approach is much simpler and computationally efficient than using laminated shell finite elements. The article shows the effects of the number of periodic cells, the segment length ratio, the number of plies in each periodic patch, and their fiber-orientation on the first stop band of the beam. The results reported can guide the design of such structures to attenuate vibration amplitudes at specific target frequency bands and avoid undesired dynamic responses. Results have been validated in the 0–2000 Hz frequency range by comparison with finite element laminated shell models.