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Monday, July 8 • 12:20 - 12:40
IN-PLANE FREE VIBRATIONS OF CURVED TIMOSHENKO BEAMS WITH RAYLEIGH-RITZ METHOD

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Curved beams are frequently used structural elements in traditional and emerging fields of civil and mechanical engineering with usual requirements of vibration and deformation analyses utilizing the beam theory and numerical methods. There are challenges in such analyses due to complex equations with the curved beam segment and numerical methods in case the analytical solutions are no longer available. In this study, curved Timoshenko beams with commonly encountered arc types are studied with the Rayleigh-Ritz method using polynomial functions as the deformation for calculations of strain and kinetic energies, and accurate frequencies and mode shapes are obtained from convergent and verified solutions. It is the objective of this study that the method will be extended to a short, curved, and periodic beam for its free vibrations for in-depth understanding of such unusual but widely encountered structures from recent technological advances. It is found that for the sinusoidal-shaped beams, we need the deformation in since series up to the 25th order, showing a large size equation for the eigenvalue extraction. It is worth to try other types of deformation functions to improve the computing efficiency for curved beams. Eventually, the study will be merged with current methods for analyses of beams of various types for unified approach and results with further extension to composite structures of combinations of periodic beams with shorter unit cells from the 3D-printing technology showing up with wide applications today. Additional considerations of higher-order theories and couplings of modes can also be included for more practical and robust analyses of beam elements.

Moderators
avatar for Simon Jones

Simon Jones

Associate Professor, Rose-Hulman Institute of Technology
Professional interests include undergraduate engineering education, finite element modeling, ground-borne vibrations, vibrations of musical instruments, and dynamics of toys.
GM

Guilhem Michon

Professor, ISAE-SUPAERO

Authors

Monday July 8, 2019 12:20 - 12:40 EDT
St-Laurent 7
  T07 Struct. dyn. & nonlin. vib., RS03 Struct ac & vibr