Time domain analysis of the weighted distributed order rheological model

This paper presents the fundamental solution and relevant properties of the weighted distributed order rheological model in the time domain. Based on the construction of distributed order damper and the idea of distributed order element networks, this paper studies the weighted distributed order operator of the rheological model, a generalization of distributed order linear rheological model. The inverse Laplace transform on weighted distributed order operators of rheological model has been obtained by cutting the complex plane and computing the complex path integral along the Hankel path, which leads to the asymptotic property and boundary discussions. The relaxation response to weighted distributed order rheological model is analyzed, and it is closely related to many physical phenomena. A number of novel characteristics of weighted distributed order rheological model, such as power-law decay and intermediate phenomenon, have been discovered as well. And meanwhile several illustrated examples play important role in validating these results.