Design of periodic laminated composite beams in free vibration

Composite materials are being used in many weight-sensitive applications due to their attractive features of high strength-to-weight and stiffness-to-weight ratios and design flexibility. In harsh dynamic environments, excitation frequencies can lead to resonance at some frequency bands, impacting the integrity and functionality of the whole composite structure. Adding patches to the main structure at periodic locations introduces stopbands, which are frequency bands where vibration amplitudes are highly attenuated, and natural frequencies are absent. Using composite materials in such periodic patches enables more design flexibility that can be used to generate stopbands at desired frequency ranges. This paper presents a design approach for periodic laminated composite beams to obtain the patch length and stacking sequence that realize the desired start and end stopband frequencies. Based on the reverse approach of the wave finite element (WFE) method, the proposed design approach includes solving two nonlinear algebraic equations to find the design point. Then, a search for all possible patch stacking sequences that realize this design point and achieve the target stopband with the least possible error is done. The design approach was validated by demonstrating that it generates the inputs that were used by an analysis code to generate the design code inputs. Various examples are presented with different stopband ranges, fiber-orientation angles and materials of the substrate and patch plies. It is shown that depending on the substrate material, number of plies per patch and desired stopband start and end frequencies, one can obtain several possible stacking sequences that can realize the design. The study focuses on beam bending modes in the 0-2000 Hz frequency range, where classical lamination and Euler-Bernoulli's beam theories are valid.