1,720,968 research outputs found
Periodic traveling waves in a taut cable on a bilinear elastic substrate
No full textThe wave propagation problem in a second-order nonlinear PDE, with specific reference to a mechanical system consisting of a taut cable, or string, resting on a piecewise linear foundation is investigated, without and with a distribute transversal load. The piecewise nature of the problem offers a sufficiently simple kind of nonlinearity as to permit a closed form solution both for the wave phase velocity and the wave form. We show that the solution depends only on the ratio between the two soil stiffnesses, and that no waves propagate if one side of the substrate is rigid. Some numerical simulations, based on a finite difference method, are performed to confirm the analytical findings. The stability of the proposed waves is discussed theoretically and numerically, also by using return maps in phase space. (C) 2022 Elsevier Inc. All rights reserved
An impact model of a ball bouncing on a flexible beam
No full textIn this work we investigate a model for the description of the impact of a ball with a flexible beam. The coupling of the kinematic parameters of the ball (the velocity components) with the vibration modes of the beam are taken into account by using the Hertz theory of impact. We solve the model equations numerically in a few physically relevant cases and illustrate the variation of the modal coefficients of the beam and of the velocity components of the ball during the impact. The restitution coefficient, the size of the deformation region and the impact duration are also reported as functions of the impact velocity and of the impact location
Influenza delle condizioni al contorno nella valutazione dei parametri di dispersione-diffusione ed assorbimento da prove di laboratorio in colonna filtrante
No full textModelling of pollutant transport experiments: A numerical study of the diffusion equation
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Promoting a meaningful learning of double integrals through routes of digital tasks
Full text linkWithin a wider project aimed at innovating the teaching of mathematics for
freshmen, in this study we describe the design and the implementation of two routes of
digital tasks aimed at fostering students’ approach to double integrals. The tasks are
built on a formative assessment frame and classical works on problem solving. They
provide facilitative and response-specific feedback and the possibility to request differ-
ent hints. In this way, students may be guided to the development of well-connected
knowledge, operative and decision-making skills. We investigated the effects of the inter-
action with the digital tasks on the learning of engineering freshmen, by comparing the
behaviours of students who worked with the digital tasks (experimental group, N=19)
and students who did not (control group, N=19). We detected that students in the ex-
perimental group showed more flexibility of thinking and obtained better results in the
final exam than students in the control group. The results confirmed the effectiveness
of the experimental educational path and offered us interesting indications for further
studies
WAVE PROPAGATION ON A STRING RESTING ON A GENERAL NONLINEAR SUBSTRATE
No full textTraveling waves propagating on a taut cable resting on an elastic substrate are in-vestigated by an equivalent mechanical model based on the classical Klein-Gordon equation. The formulation is devised for an elastic response of generally arbitrary shape, and permits one to compute the propagation wave velocity without solving the equation of motion, thus providing a unified the-oretical framework for a large class of response functions, linear or nonlinear, smooth or nonsmooth. The general solution is then applied to the cases of a general polynomial substrate, a bilinear sub-strate, a bilinear substrate with a cubic correction, and a negative linear stiffness substrate, all of them falling within the realm of nonsmooth systems when a piecewise continuous stiffness is chosen; in the second one, we recover results present in the literature and obtained by employing a method based on matching conditions, which are spared in the approach used in this paper. Finally, the application to the sine-Gordon equation is considered
Pauli principle and the Monte Carlo method for charge transport in graphene
Full text linkAn attempt to include the Pauli principle in the Monte Carlo method by also acting on the free-flight step and not only at the end of each collision is investigated. The charge transport in suspended monolayer graphene is considered as a test case. The results are compared with those obtained with the standard ensemble Monte Carlo technique and with the updated direct simulation Monte Carlo algorithm which is able to correctly handle with Pauli's principle. The physical aspects of the investigated approach are analyzed as well
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