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Free vibration of tapered beams and plates based on unified beam theory

In this paper, accurate frequency solutions of tapered vibrating beams and plates using a simple and efficient displacement based unified beam theory in lieu of computationally expensive and rather complex two-dimensional plate theories are presented. The results are given in the form of Euler-Bernoulli/Timoshenko to quasi three-dimensional (3D) solutions. Lower frequency bending and axial modes, as well as torsional and biaxial bending modes corresponding to higher frequency values, are predicted which are in very good agreement with 3D finite element results as well as the published literature. The effects of different parameters like taper ratio, thickness and beam/plate-aspect ratios on the vibration frequencies of tapered structures are studied. It can be seen that due to taper, bending vibration modes become asymmetric along the longitudinal axis of the structure. Further, it can also be noticed that the vibration behavior of thicker beams and plates is characterized by the appearance of a significant number of axial modes at lower frequency values as compared to that of relatively thinner beams/plates.