Experimental and Computational Analysis of Periodic Laminated Fiber-Reinforced Composite Beams

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 with varying geometries and materials have been examined under analytical, numerical and experimental ways when looking into current literature. There has been a confirmation of attenuation of wave propagation in periodic structures compared to non-periodic ones. The inclusion of laminated fiber-reinforced composite materials to periodic structures are yet to be heavily researched. Laminated fiber-reinforced composite materials, in general, give an additional design characteristic, which is the stacking sequence of the plies. The ability to create materials that work for a design instead of designing based on available materials makes them a powerful solution to future problems. In this work, a commercial finite element analysis software (FEA), SOLIDWORKS, was used to analyze the natural frequencies of periodic beams with periodic laminated fiber-reinforced composite patched. Then with the use of composite lamination theory and wave finite element (WFE) method, an in-house code was developed to plot bending frequencies, and solve for "stop bands". Along with the in-house code, an attempt to make a simplified rectangular twist element using a stiffness factor relative to a circular shaft was done to enable analyzing twisting modes of vibration. Finally, experimental studies were done to show the effectiveness of periodic wave guides. Using a surface model, SOLIDWORKS allows composite materials to be defined and studied. The natural frequencies agreed with isotropic cantilever beam bending frequencies and composite beam analytical theory. When sweeping angle of the periodic ply, and viewing the change in frequencies, it was shown, for a laminated fiber-reinforced periodic cantilever beam, that the angle of the plies affects the natural frequencies less as number of plies increase. A sensitivity analysis was done investigating the effects of periodic beam parameters on stopbands, using the in-house MATLAB code and a laminated fiber-reinforced composite material. Using formulas for effective stiffnesses for symmetric laminated composites, a beam element was defined. The element was seen to have agreeance with analytical solutions within 2.75% for the first five bending modes. Number of plies (NP), periodic segment ratio (PSR), periodic ply angle (PPA), and number of cells (NC) were swept to show how each affects the location and width of the stopbands. Experimental modal testing was conducted to verify the presence of the stop bands utilizing periodic fiber-reinforced composite patches. An aluminum beam was outfitted with carbon fiber-reinforced composite patches and compared to numerical results. With the use of an accelerometer, shaker and clamp system, a cantilever support was created and bending modes of vibration were plotted. A trend that resembles the computational results was seen, and a stop band was found in a similar frequency range as in the computational results.