Application of Volterra Integral Equations in Dynamics of Multispan Uniform Continuous Beams Subjected to a Moving Load

Abstract

The dynamic behavior of multispan uniform continuous beam arbitrarily supported on its edges subjected to various types of moving noninertial loads is studied. Problem is solved by replacing a multispan structure with a single-span beam loaded with a given moving load and redundant forces situated in the positions of the intermediate supports. Redundant forces are obtained by solving Volterra integral equations of the first or the second order (depending on the stiffness of the intermediate supports) which are consistent deformation equations corresponding to each redundant. Solutions for the beam arbitrarily supported on its edges (pinned or fixed) due to a moving concentrated force and moving distributed load are given. The difficulty of solving Volterra integral equations analytically is bypassed by proposing a simple numerical procedure. Numerical examples of two- and three-span beam have been included in order to show the efficiency of the presented method.

Zastosowanie Metody Różnic Skończonych W Dynamice Cienkich Płyt Mostowych Poddanych Działaniu Obciążeń Ruchomych

“…W ciągu wielu lat problem ten był analizowany przez wielu autorów rozpatrujących różne typy konstrukcji, zarówno pła-skich jak i przestrzennych, a także różne modele obciążeń ruchomych [1][2][3][4][5][6][7].…”

Regularization and uniqueness of solutions of Volterra linear integral equations of the third kind

“…Various questions for integral equations have been investigated in many papers [1]. In particular, Volterra integral equations were used to calculate dynamics of multi span uniform continuous beams subjected to a moving load [1], for population growth of a species within a closed system [2], and for duality theory solutions [3].…”

“…Various questions for integral equations have been investigated in many papers [1]. In particular, Volterra integral equations were used to calculate dynamics of multi span uniform continuous beams subjected to a moving load [1], for population growth of a species within a closed system [2], and for duality theory solutions [3]. Recently the Volterra integral equations have been studied and reported for the oscillation of equations with positive and negative nonlinearities [4], Volterra integral equations and evolution equations with an integral condition [5], and on time scales -the long time behavior of solutions [6].…”

“…Evidence. In equation ( 2), we make a replacement 𝜐(𝑡, 𝜀) = 𝑢(𝑡) + 𝜉(𝑡, 𝜀), (16) where 𝑢(𝑡) is the solution of equation (1). Substituting ( 16) in ( 2…”

A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

“…Integral equations involving Volterra operators occur in diverse applications in various disciplines of engineering [55,59] and finance and economics [3,37], as well as the natural sciences [9,20,28,30,31,35,44,58]. Beyond linear Volterra integral equations of first and second kinds, which respectively take the forms…”