Timoshenko beam and plate non-stationary vibrations

The problems of Timoshenko beams and plates lateral vibrations under the influence of unsteady loads are considered. Both beam and plate is supposed to be unlimited. In case of the plate the problem has been simply studied. The approach to the solution was based on dominant function method and principle of superposition. Integral models of solutions with cores as dominant functions were built which could be analytically found with the help of the Fourier and Laplace integral transforms. Two original analytical methods for Fourier and Laplace transforms were offered and realized. The examples of calculations were given.

Generating Functions for Some Hypergeometric Functions of Four Variables via Laplace Integral Representations

Generating functions plays an essential role in the investigation of several useful properties of the sequences which they generate. In this paper, we establish certain generating relations, involving some quadruple hypergeometric functions introduced by Bin-Saad and Younis. Some interesting special cases of our main results are also considered.

The Rheological Analytical Solution and Parameter Inversion of Soft Soil Foundation

In soft soil engineering projects, the building loads are always required to be symmetrically distributed on the surface of the foundation to prevent uneven settlement. Even if the buildings and soft clay are controlled by engineers, it can still lead to the rheology of the foundation. The analytical solution based on the Laplace integral transformation method has positive significance for providing a simple and highly efficient way to solve engineering problems, especially in the long-term uneven settlement deformation prediction of buildings on soft soil foundations. This paper proposes an analytical solution to analyze the deformation of soft soil foundations. The methodology is based on calculus theory, Laplace integral transformation, and viscoelastic theory. It combines an analytical solution with finite theory to solve the construction sequences and loading processes. In addition, an improved quantum genetic algorithm is put forward to inverse the parameters of soft soil foundations. The analytical solution based on Laplace integral transformation is validated through an engineering case. The results clearly illustrate the accuracy of the method.

On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions

Recently, the applications and importance of integral transforms (or operators) with special functions and polynomials have received more attention in various fields like fractional analysis, survival analysis, physics, statistics, and engendering. In this article, we aim to introduce a number of Laplace and inverse Laplace integral transforms of functions involving the generalized and reverse generalized Bessel matrix polynomials. In addition, the current outcomes are yielded to more outcomes in the modern theory of integral transforms.

Integrated Semigroups on Fréchet Spaces II: F_sBSV ([a,b],F)-space, FsLip_0,w([0,+∞),F)-space, Isometric Theorem and Application

In this article we will study the Riemann Stieltjes Laplace integral of vectorial functions in Fréchet spaces. Particularly we will prove a isometric theorem and a generation theorem for integrated semigroups on Fréchet spaces.