Sensitivity Analysis of Dynamic Characteristics of Composite Beams with Viscoelastic Layers

In this paper, a beam consisting of elastic layers and a viscoelastic layer located between them is considered. The Euler-Bernoulli theory is used to describe the elastic layer and the Timoshenko theory is used to describe the viscoelastic layer. The fractional Zener model is used to express the viscoelastic material properties. The equation of motion of the considered system in the frequency domain is derived using the finite element method, the virtual work principle and the Laplace transform. Eigenproblem is solved by means of the continuation method. The sensitivity analysis is carried out by means of the direct method and allows for determination of sensitivities of eigenvalue and its corresponding eigenvector with respect to the chosen design parameter. Formulae, which enable the calculation of the sensitivities of natural frequencies and non-dimensional damping ratios, are also derived. In order to illustrate the presented method, the numerical example is calculated.