An Analysis of in-Plane Free Vibrations of Combinedcurved and Periodic Beams with Rayleigh-Ritzmethod

The curved and periodic beams are frequently used nowadays as essential structural and functional elements with many processes to produce including the popular 3D printing technology.As part of the effort in the analysis of curved and periodic beams, we have studied some special cases of beams with both Euler-Bernoulli and Timoshenko theories.The Rayleigh-Ritz method is used along with extra constraints at each joint, and the analysis now have the combinations of beams considered. By allowing the constraints to be realistic with the actual joint, the accurate frequencies of the combined beam structures are obtained.By further extension of the analytical procedure of curved and periodic beams, we can use the Rayleigh-Ritz method for the analysis of structures of combined beam elements for the evaluation of dynamic properties to satisfy design and application requirements.