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Content available Stability of nonlinear Volterra equations
Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear time-varying Volterra difference equations. Furthermore, an explicit stability bound for equations subject to nonlinear time-varying perturbations is given. Finally, the obtained results are used to study uniform attraction of equilibrium of discrete-time bidirectional associative memory (BAM) neural networks. Some illustrative examples are given.
Content available remote Vibrations of point-supported rectangular thin plate subjected to a moving force
In this paper, the dynamic behaviour of a rectangular thin plate simply supported on all edges and point supported within its region is investigated. The problem is solved by replacing this type of structure with a simply supported plate subjected to a given moving load and redundant forces situated in positions of intermediate point supports. Redundant forces are obtained by solving Volterra integral equations of the first order, which are compatibility equations corresponding to each redundant. Solutions for a simply supported plate loaded with a moving point force and concentrated time-varying force are given. Difficulties of solving Volterra integral equations analytically are bypassed by applying a simple numerical procedure. Finally, a numerical example of a plate with two point supports is presented in order to show the effectiveness of the presented method.
Content available remote Linear and Non-linear Creep models for a multi-layered concrete composite
One- and two-dimensional linear and nonlinear creep models for predicting the time-dependent behavior of a concrete composite under compression are proposed. These models use the analytical and iterative solutions of the Volterra integral equation. The analytical approach is based on the age-adjusted effective modulus method, and the nonlinear technique applies an iterative approach to the system of non-linear equations, implying a generalization of the principle of superposition. Both models are validated in this study. It has been recently found that negative values of the aging coefficient can emerge in early age multi-layered composites when the stress redistribution between the layers is governed by the combination of considerably different creep strains and aging of the layers. In the plane-strain state, the two-dimensional creep analysis of multi-layered composites yields the same vertical stress-time history as that in a one-dimensional case if the Poisson ratios of the layers are equal. This is valid even though the average value of the vertical stress used to calculate the Volterra integral term is dependent on the Poisson ratio of the layers. In particular, the evolution of vertical stress with time is dependent only on the vertical strain and compatibility conditions in a direction parallel to the lamination. A fracture mechanics approach is also introduced to predict the gradual degradation of long-term strength for a multi-layered composite under a sustained compressive load. The results show that the stress redistribution near the crack-tip under the final period of a high level of sustained loading may lead to an additional required compressive stress for complete failure of the composite. Long-term failure primarily begins with the less deformable (stiffer) layers because the more-deformable layers can relieve the initial stresses. Thus, the long-term strength of the composite can exceed its instantaneous strength for early age composites or for composites composed of layers that possess considerably different creep and aging properties.
Aim of this work is to extend the results of Clément, Da Prato and Prüss [5] on the fractional white noise perturbation with Hurst parameter H ∈ (0,1). We will obtain similar results and it will turn out that the regularity of the solution u(t) increases with Hurst parameter H.
Content available remote Global solutions for Volterra ordinary and retarded integral equations
Using a generalization of Darbo's fixed point theorem, we obtain the existence of global solutions for nonlinear Volterra-type integral equations in Banach spaces. The involved functions are supposed to be continuous only with respect to some variables, integrability or essential boundedness conditions being also imposed. Our result improves the similar result given in [10] (where uniform continuity was required), as well as those referred by the authors of the cited paper. Finally, following the same ideas, the existence of continuous solutions is proved for a Volterra-type retarded integral equation, under less restrictive assumptions than in the others related results in literature.
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