1,721,025 research outputs found
An analytical and numerical study of the nonlinear dynamics of a semi-infinite beam on unilateral Winkler soil
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Propagation of detached bubbles in a semi-infinite beam laid on a unilateral elastic support
No full textModelling the response of tensile steel bars by means of incremental energy minimization
No full textHigh-order Absorbing Boundary Conditions and Perfectly Matched Layers for cables and beams laid on elastic supports
No full textNumerical comparison of high-order absorbing boundary conditions and perfectly matched layers for a dispersive one-dimensional medium
No full textHigh-order absorbing boundary conditions (ABC) and perfectly matched layers (PML) are two powerful methods to numerically solve wave problems in unbounded domains. The aim of the proposed study is to analyze and compare the performance of these methods in the one-dimensional problem governed by the dispersive wave equation. The PMLs proposed in literature for time-harmonic dynamics are applied to time-dependent wave problems, and linear, quadratic and cubic polynomial stretching functions are considered. The resulting PMLs exhibit a double absorbing action: (i) they reduce the amplitude of the incident waves and (ii) they delay the wave propagation. Then the ABC proposed by Givoli and Neta and those proposed by Hagstrom, Mar-Or and Givoli are considered. The former are a reformulation of the Higdon high-order non-reflecting boundary conditions, the latter improve the Higdon conditions and extend them to take into account evanescent waves. The accuracy of the PMLs and ABCs, implemented in a finite element code, is first investigated with respect to the frequency of the incident wave, being it progressive or evanescent. Then the response to a wave train characterized by a broad frequency spectrum, resulting from an impulsive force, is studied. A detailed analysis is performed to detect the influence of the parameters of both the ABCs and the PMLs on the absorption of waves. The performances of PMLs and ABCs are compared, and merits and drawbacks of the two methods are pointed out
Dynamics of a semi-infinite beam on unilateral springs: Touch-down points motion and detached bubbles propagation
No full textThe dynamics of a semi-infinite Bernoulli–Euler beam laid on a bed of unilateral elastic springs is governed by a moving-boundary problem, since the positions of the touch-down points, those points which separate the detached beam parts from the laid ones, are unknown. This problem is solved numerically by means of a self-made finite element code and some numerical results are shown and discussed. The nonlinear and non-smooth effects of the touch-down points motion on the beams dynamics are analyzed. The presence of detached bubbles, which appear, propagate and disappear in the beam, is investigated, and new complex motions are highlighted
The nonlinear dynamical problem of a semi-infinite beam on unilateral Winkler soil: analytical vs numerical solutions
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