Limitations in application of basic frequency simplest lower estimators in investigation of natural vibrations of circular plates with variable thickness and clamped edges

In this paper, we discussed the effects of application the Bernstein-Keropian simplest lower estimators for calculation of basic natural vibration frequencies of variable-thickness circular plates. Following a thorough analysis, we showed a significant role of the operators of the 4th order Euler equations of motion describing vibrations of circular plates with exponentially variable thickness. The dependence of solutions on values of the variable thickness power index of the plate and Poisson's ratio of the plate material was investigated. The variable power thickness diaphragm model was verified by FEM which confirmed the usefulness of the simplest estimator for following materials: titanium, steel, zinc. Comparison of the results obtained after applying the simplest lower estimators for the basic frequency with the results of exact solutions for particular cases found in the literature, confirmed high accuracy of the applied method.