Techniques for vibration analysis of hybrid beam and ring structures with variable thickness

Free vibration analysis of hybrid nonlocal Euler-Bernoulli beams and non-uniform rings needs solving sixth-order differential equations with variable coefficients. In this paper, techniques are proposed to solve this problem. Discrete singular convolution beam/ring elements and weak form quadrature beam/ring elements are developed. Explicit formulas are derived and presented. The efficiency of the proposed techniques is compared to the existing advanced methods such as the differential quadrature element method and the local adaptive differential quadrature method. Selected cases of hybrid nonlbcal Euler-Bernoulli beams and non-uniform rings with variable thickness are investigated. Comparisons reveal that among these methods, the proposed quadrature element method is the most efficient one. In addition, the discrete singular convolution element method with the harmonic kernel is the best efficient technique for obtaining high mode frequencies. (C) 2018 Elsevier Ltd. All rights reserved.