Search for: All records

Vibrations are ubiquitous in mechanical or biological systems, and they are ruinous in numerous circumstances. We develop a viscoelastic Timoshenko beam model, which naturally captures distinctive power-law responses arising from a broad distribution of time-scales presented in the complex internal structures of viscoelastic materials and so provides a very competitive description of the mechanical responses of viscoelastic beams, thick beams, and beams subject to high-frequency excitations. We, then, prove the well-posedness and regularity of the viscoelastic Timoshenko beam model. We finally investigate the performance of the model, in comparison with the widely used Euler–Bernoulli and Timoshenko beam models, which shows the utility of the new model. 

Abstract Variable-order space-fractional diffusion equations provide very competitive modeling capabilities of challenging phenomena, including anomalously superdiffusive transport of solutes in heterogeneous porous media, long-range spatial interactions and other applications, as well as eliminating the nonphysical boundary layers of the solutions to their constant-order analogues.In this paper, we prove the uniqueness of determining the variable fractional order of the homogeneous Dirichlet boundary-value problem of the one-sided linear variable-order space-fractional diffusion equation with some observed values of the unknown solutions near the boundary of the spatial domain.We base on the analysis to develop a spectral-Galerkin Levenberg–Marquardt method and a finite difference Levenberg–Marquardt method to numerically invert the variable order.We carry out numerical experiments to investigate the numerical performance of these methods.