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Abstract In this paper, we explain why beyond a certain critical frequency the extreme ends of a beam under flexural oscillations remain sometimes plane and in other cases become warped. We have seen this to be the case when the flexural oscillations of a beam are studied experimentally. Using the plane stress elastodynamic theory as well as a more precise calculation based on a 3D finite element method, we show for the first time that when the transverse displacement has a derivative equal to zero near the beam extremes, the ends can indeed become warped. In addition it is shown, from an energetic point of view, that warped modes result from a constructive spatial interference of the two components of flexural oscillations while flat modes result from a destructive interference of these two components. [ABSTRACT FROM AUTHOR]

In this work, we demonstrate, analytically and numerically, that degenerate states of a beam with free ends, with anti-symmetrical transverse mode shape and occurring in the first-degeneracy points above the cutoff frequency, tend asymptotically to the thickness-shear mode in the infinitely long beam limit, which has not been previously reported. We compare our numerical results, obtained using a Timoshenko–Ehrenfest beam theory of second order, with those obtained with the Finite Element method and plane stress elastodynamics theory, obtaining an excellent agreement. We show that anti-symmetric states within the vicinity of these first-degeneracy states are very similar and closely resemble the so-called thickness-shear mode but for a finite beam with free ends under flexural vibrations. • Mode shapes of degenerate states are studied in Timoshenko–Ehrenfest beams. • First-degeneracy asymmetric states turn out very similar to the thickness-shear mode. • Instead, it is shown that transverse oscillations of the cutoff states are non-negligible. • Results for a beam with free ends are corroborated with the Finite Element method. • It is demonstrated that analogs to the thickness-shear mode exist for finite beams. [ABSTRACT FROM AUTHOR]

Abstract: A comparison in the quantity of force was carried out among the Interamerican Metrology System (SIM) national laboratories in order to estimate the level of agreement for the realization of the quantity and the uncertainty associated to its measurement. This comparison was carried out up to 10kN. The equipment used consisted on two force transducers (load cells); both with the same measuring range (10kN). With the purpose of obtaining maximum accuracy on the transducers, the comparison range was selected from 4kN up to 10kN. This comparison (SIM comparison number SIM 7.7) has an overlap with the force steps used in the CIPM key comparison CCM.F-K1.a and CCM.F-K1.b. The results obtained, as well as the reference values selected for the comparison are included in this document. Two different methods were used to analyze the level of agreement and to state the conformity declaration. [Copyright &y& Elsevier]