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Approximate formulation of the rigid body motions of an elastic rectangle under sliding boundary conditions

Şahin Önur, Erbaş Barış, Wilson Brent

Acta Mechanica et Automatica

2021

Vol. 15, no. 2

82--90

Low-frequency analysis of in-plane motion of an elastic rectangle subject to end loadings together with sliding boundary conditions is considered. A perturbation scheme is employed to analyze the dynamic response of the elastic rectangle revealing nonhomogeneous boundary-value problems for harmonic and biharmonic equations corresponding to leading and next order expansions, respectively. The solution of the biharmonic equation obtained by the separation of variables, a consequence of sliding boundary conditions, gives an asymptotic correction to the rigid body motion of the rectangle. The derived explicit approximate formulae are tested for different kinds of end loadings together with numerical examples demonstrating the comparison against the exact solutions.

Dependence of skill and spread of the ensemble forecasts on the type of perturbation and its relationship with long term norms of precipitation and temperature

Duniec Grzegorz, Mazur Andrzej

Acta Geophysica

2020

Vol. 68, no. 5

1505--1528

A new computing cluster has been operating since 2016 at the Institute of Meteorology and Water Management – National Research Institute. Increasing computing power enabled the implementation of ensemble prediction system forecasts in the operational mode and the use of a new computer for research purposes. As part of the priority project on “Study of Disturbances in the Representation of Modeling Uncertainty in Ensemble Development” and the earlier project entitled “COSMO Towards Ensemble in Km in Our Countries), implemented in the Working Group 7 (Predictability and Ensemble Methods) as part of the COSMO modeling consortium, specifc studies were carried out to test ensemble forecasts. This research concerned the impact of variability of physical felds characterizing the soil surface (a selected parameter determining evaporation from the soil surface and soil surface temperature) using various methods of perturbation. Numerical experiments were completed for the warm period (from June to September) 2013.