Conceptual Design of Oblong Ring Vibrators

Abstract

An oblong ring-type structure is composed by two straight segments (length L) and two semicircular segments (radius R). It can be used to generate traveling waves, being applied to build linear piezoelectric motors and linear conveyor systems. The traveling waves to such applications occur at specific frequencies, generated by simultaneous symmetric and antisymmetric flexural vibration modes which, in general, have distinct natural frequencies. However, for specific designs, they may coincide or be very close. This may be achieved by finding the appropriate L/R ratio. For preliminary design, an analytical model is very desirable, due to its computational efficiency and the absence of a computational automatic identification of symmetric and antisymmetric flexural vibration modes among numerical solutions. Therefore, the objective of this work is to propose an analytical and practical model to determine classes of vibration modes of interest for producing traveling waves in oblong ring-type structures, being employed for conceptual design such that the L/R ratio is determined in an efficient way. The oblong ring is considered as a beam-like structure composed by straight and curved segments, employing Timoshenko and Euler–Bernoulli kinematic assumptions. A design method is proposed by solving sequentially and systematically distinct geometric proposals of oblong ring-type designs and, for each one, evaluating the candidates to produce the flexural traveling waves. Later, the strong-candidates are analyzed by finite element models to test the quality of the design with less assumptions. We show that the methodology provides convenient results as a design method for oblong ring-type structures.