A second order beam theory

A second order beam theory which takes into account shear curvature, transverse direct stresses and rotatory inertia is presented. The governing differential equation is similar in form to the Timoshenko beam equation but contains two coefficients, one of which depends on cross-sectional warping just as does Cowper's expression while the second, although similar in form, also includes terms dependent on the transverse direct stresses. Comparison is made with exact and other approximate theories for particular cases.     

Application of the Galerkin and Ritz methods to nonconservative problems of elastic stability

Zusammenfassung In dieser Arbeit werden nichtkonservative Probleme der elastischen Stabilität mittels des Galerkin- und des Ritz-Verfahrens behandelt.Zuerst wird bewiesen, dass die Resultate vonLeipholz bezüglich der Konvergenz des Galerkinschen Verfahrens für solche Probleme auf eine grössere Klasse zulässiger Versuchsfunktionen erweitert werden können. Danach wird das Hamiltonsche Prinzip für nichtkonservative mechanische Systeme so formuliert, dass die Ritzsche Methode auf nichtkonservative Probleme der elastischen Stabilität angewendet werden kann, im Gegensatz zur Ansicht, dass eine solche Anwendung nicht möglich ist. Zum Schluss werden einige angenäherte Lösungen des Beckschen Problems angeführt und verglichen, um die Begriffe zu erklären, die am Anfang dieser Arbeit dargestellt wurden.     

Free vibrations of a simply supported,rectangular plate: An exact elasticity solution

An exact, three-dimensional solution for the free vibrations of simply supported, rectangular plates of arbitrary thickness within the linear theory of elastodynamics is given in this paper. The solution, obtained in a semi-inverse fashion as was the solution of the elastostatic problem for such plates, satisfies all of the boundary conditions of the problem in a pointwise manner. It is found that there are two types of modes of oscillation possible which are consistent with the kinematic assumptions made to find the semi-inverse solution. Other modes of oscillation may exist in the three-dimensional theory of elastodynamics for such plates but our kinematic assumptions would not be consistent with such modes. The two types of modes found are analogous to the flexural modes of classical plate theory and the thickness-twist modes, here called breathing modes, of Mindlin plate theory. Some numerical results are given which indicate that the predictions of Mindlin plates are uncannily good approximations to the flexural frequencies given by the present, three-dimensional analysis even for very thick plates. However, the predictions of Mindlin plate theory for the thickness-twist, or breathing, frequencies are not nearly so good. These discrepancies are discussed briefly in an appendix.     

Natural radiative lifetimes and hyperfine structure of the 4s26p2P32,12 levels of gallium

Natural radiative lifetimes and the signs of previously determined hyperfine coupling constants were determined for the $\text{4s}{}^2\text{6p}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext><mtext>,</mtext><mtext>1</mtext><mtext>2</mtext>}}$ levels of gallium. The lifetimes were found to be 167(4) and 172(9) ns, respectively. In addition, the quadrupole moments of ⁶⁹Ga [0.17(3) b] and ⁷¹Ga [0.10(2) b] were deduced, and the isotope shifts in the 639.7 and 641.3 nm Ga lines were determined.