Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations

A convenient and universal residue calculus method is proposed to study the stochastic response behaviors of an axially moving viscoelastic beam with random noise excitations and fractional order constitutive relationship, where the random excitation can be decomposed as a nonstationary stochastic process, Mittag-Leffler internal noise, and external stationary noise excitation. Then, based on the Laplace transform approach, we derived the mean value function, variance function and covariance function through the Green＇s function technique and the residue calculus method, and obtained theoretical results. In some special case of fractional order derivative α , the Monte Carlo approach and error function results were applied to check the effectiveness of the analytical results, and good agreement was found. Finally in a general-purpose case, we also confirmed the analytical conclusion via the direct Monte Carlo simulation.

General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off

According to the limit equilibrium state of soils behind rigid walls and the pseudo-static approach,a general closed-form solution to seismic and static active earth pressure on the walls,which considers shear and tension failure of the retained soil,is put forward using a variational calculus method.The application point of the active resultant force specified in the proposed method is explained with a clear physical meaning related to possible movement modes of the walls.In respect of the derived nine dependent equations reflecting the functional characteristics of the earth pressure,the proposed method can be performed easily via an implicit strategy.There are 13 basic factors related to the retained soils,walls,and external loads to be involved in the proposed method.The tension crack segment of the slip surface is obviously influenced by these parameters,apart from vertical seismic coefficient and geometric bounds of the surcharge,but the shear slip segment maintains an approximately planar shape almost uninfluenced by these parameters.Noticeably,the proposed method quantitatively reflects that the resultant of the active earth pressure is always within a limited range under different possible movements of the same wall.

Conformable Fractional Nikiforov–Uvarov Method

We introduce conformable fractional Nikiforov–Uvarov(NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schr¨odinger equation(SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods–Saxon potential, and Hulthen potential.