Computational Analysis of Curved Beams - In and Out-of-Plane Vibrations

Abstract

In the present work are shown results obtained from a computational model for the dynamic analysis of planed curved beams with constant cross-section and curve radius, based on the exact solution of the differential equilibrium equations of a beam element. This model allows the estimation of the forced harmonic motion, both in-plane and out-of-plane of curvature on a free-free support condition. The input data of the model is the geometry section of the beam, material properties, type of motion, consideration of the shear stiffness, and rotatory inertia effects. The output result is possible either in a frequency response of a fixed parameter curved beam or a plot representation of the natural frequencies curves for an opening angle range, from an approximated straight beam to a closed opened ring. Each of those curves is defined as family of modes and performed on present work. The objective of this work is to clarify the general behaviour of curved beams with the mentioned conditions by using an accurate model showing results as a reference for the scientific community. The model was validated by testing and comparing results with three beam specimens previously studied in other publications. The biggest aim is also to present new results and hypothesis, contesting other authors regarding the natural frequencies of curved beams.