Response surface methodology and Taguchi design for rotating Euler–Bernoulli beam Available to Purchase

This paper aims at the optimization of rotating Euler–Bernoulli beam using response surface methodology (RSM) and the Taguchi design.

The free vibration problem is solved using the meshless local Petrov–Galerkin method where orthogonal polynomials are used. In RSM, non-dimensional rotating speed $(ΩmR4EI)$ and non-dimensional stiffness $(EImΩ2R4)$ are varied to solve the optimization problem for the rotating beam. The approximate equations are obtained for first natural frequency to fifth natural frequency. RSM is combined with analysis of variance (ANOVA) where central composite design (CCD) is applied. In Taguchi design, radius (R), non-dimensional rotating speed (s) and flexural rigidity (EI) are used as inputs while optimizing the first-five natural frequencies. Here Ω is the rotational speed, m is the mass per unit length, R is the rotating radius and EI represents the flexural rigidity.

Here, high coefficients of determination (R²) are obtained for the first five natural frequencies, confirming the accuracy of the developed models. Contour and three-dimensional response plots are generated for both RSM and Taguchi analyses, with orthogonal arrays employed in the latter. Cubic regression equations are formulated for all five modes and show excellent agreement with conventional MATLAB results. Signal-to-noise ratio analysis reveals rotational speed as the dominant parameter, followed by flexural rigidity, while the beam radius has minimal influence.

This study presents a combined MLPG–RSM–Taguchi framework for optimizing the first five natural frequencies of a rotating Euler–Bernoulli beam and provides an efficient framework for improving the dynamic performance of rotating beam systems.