Transverse vibration of a class of orthotropic plates

This study determines the eigenvalues, eigenvectors, and nodal patterns of a class of orthotropic plates whose geometry is governed by the equation (x/a)α + (y/b)β = 1, where the parameters a, b, a, and a permit the plate geometry to vary over a range which includes the rhombus, circle, ellipse, square, and rectangle. Variable thickness, inplane forces, and mixed or discontinuous boundary conditions are also considered. The following assumptions have been employed: i). plate is thin with respect to other dimensions, ii). deflections are small, iii). rotary inertia and shear are neglected. The method of analysis employed is the Rayleigh-Ritz energy technique using xy-polynomials as the approximated deflection. Eigenvalues and eigenvectors were computed by the method of reductions, and the evaluation of double integrals was achieved by the numerical procedure of Gauss-Legendre quadratures. The validity of the analysis was checked by comparison with known solutions for rectangular orthotropic plates, and isotropic plates with variable thickness, in-plane forces, and mixed or discontinuous boundary conditions. It was found that the calculated frequencies and nodal patterns were in good agreement with existing data

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements