Analytical solution of transient in-plane vibration of a thin viscoelastic disc and its multi-precision evaluation

The analytical solution of transient in-plane vibration of a thin viscoelastic disc caused by a radial pressure load is presented. Using the multi-precision implementation of FFT based algorithm, the inverse Laplace transform is carried out and the spatio-temporal distributions of displacement components are obtained. The efficiency and the accuracy of the process of analytical solution evaluation are discussed in detail and the consequences in context of the application of results are mentioned. Finally, the results of numerical simulation are presented. They are used for the verification of the correctness of the derived analytical formulae and their evaluation and for the determination of numerical model capabilities.