Response of beams resting on viscoelastically damped foundation to moving oscillators

The response of beams resting on viscoelastically damped foundation under moving SDoF oscillators is scrutinized through a novel state-space formulation, in which a number of internal variables is introduced with the aim of representing the frequency-dependent behaviour of the viscoelastic foundation. A suitable single-step scheme is provided for the numerical integration of the equations of motion, and the Dimensional Analysis is applied in order to define the dimensionless combinations of the design parameters that rule the responses of beam and moving oscillator. The effects of boundary conditions, span length and number of modes of the beam, along with those of the mechanical properties of oscillator and foundation, are investigated in a new dimensionless form, and some interesting trends are highlighted. The inaccuracy associated with the use of effective values of stiffness and damping for the viscoelastic foundation, as usual in the present state-of-practice, is also quantified

An earthquake response spectrum method for linear light secondary substructures

YesEarthquake response spectrum is the most popular tool in the seismic analysis and design of structures. In the case of combined primary-secondary (P-S) systems, the response of the supporting P substructure is generally evaluated without considering the S substructure, which in turn is only required to bear displacements and/or forces imposed by the P substructure (¿cascade¿ approach). In doing so, however, dynamic interaction between the P and S components is neglected, and the seismic-induced response of the S substructure may be heavily underestimated or overestimated. In this paper, a novel CQC (Complete Quadratic Combination) rule is proposed for the seismic response of linear light S substructures attached to linear P substructures. The proposed technique overcomes the drawbacks of the cascade approach by including the effects of dynamic interaction and different damping in the substructures directly in the cross-correlation coefficients. The computational effort is reduced by using the eigenproperties of the decoupled substructures and only one earthquake response spectrum for a reference value of the damping ratio

Peak response of non-linear oscillators under stationary white noise

The use of the Advanced Censored Closure (ACC) technique, recently proposed by the authors for predicting the peak response of linear structures vibrating under random processes, is extended to the case of non-linear oscillators driven by stationary white noise. The proposed approach requires the knowledge of mean upcrossing rate and spectral bandwidth of the response process, which in this paper are estimated through the Stochastic Averaging method. Numerical applications to oscillators with non-linear stiffness and damping are included, and the results are compared with those given by Monte Carlo Simulation and by other approximate formulations available in the literature

iResum: a new paradigm for resumming gravitational wave amplitudes

We introduce a new, resummed, analytical form of the post-Newtonian (PN), factorized, multipolar amplitude corrections $f_{\ell m}$ of the effective-one-body (EOB) gravitational waveform of spinning, nonprecessing, circularized, coalescing black hole binaries (BBHs). This stems from the following two-step paradigm: (i) the factorization of the orbital (spin-independent) terms in $f_{\ell m}$; (ii) the resummation of the residual spin (or orbital) factors. We find that resumming the residual spin factor by taking its inverse resummed (iResum) is an efficient way to obtain amplitudes that are more accurate in the strong-field, fast-velocity regime. The performance of the method is illustrated on the $\ell=2$ and $m=(1,2)$ waveform multipoles, both for a test-mass orbiting around a Kerr black hole and for comparable-mass BBHs. In the first case, the iResum $f_{\ell m}$'s are much closer to the corresponding "exact" functions (obtained solving numerically the Teukolsky equation) up to the light-ring, than the nonresummed ones, especially when the black-hole spin is nearly extremal. The iResum paradigm is also more efficient than including higher post-Newtonian terms (up to 20PN order): the resummed 5PN information yields per se a rather good numerical/analytical agreement at the last-stable-orbit, and a well-controlled behavior up to the light-ring. For comparable mass binaries (including the highest PN-order information available, 3.5PN), comparing EOB with Numerical Relativity (NR) data shows that the analytical/numerical fractional disagreement at merger, without NR-calibration of the EOB waveform, is generically reduced by iResum, from a $40\%$ of the usual approach to just a few percents. This suggests that EOBNR waveform models for coalescing BBHs may be improved using iResum amplitudes.Comment: 6 pages, 7 figures. Improved discussion for the comparable-mass cas

QCD×\timesQED evolution of TMDs

We consider for the first time the QED corrections to the evolution of (un)polarized quark and gluon transverse-momentum-dependent distribution and fragmentation functions (TMDs in general). By extending their operator definition to QCD$\times$QED, we provide the mixed new anomalous dimensions up to ${\cal O}(\alpha_s\alpha)$ and the pure QED ones up to ${\cal O}(\alpha^2)$. These new corrections are universal for all TMDs up to the flavor of the considered parton, i.e., the full flavor universality of TMD evolution found in pure QCD is broken in QCD$\times$QED by the presence of the electric charge. In addition, we provide the leading-order QED corrections to the matching coefficients of the unpolarized quark TMD parton distribution function onto its integrated counterparts at ${\cal O}(\alpha_s^0\alpha)$.Comment: 9 pages, 3 figures. v2: minor corrections, accepted for publication in Phys. Lett.

On the non-local heat kernel expansion

We propose a novel derivation of the non-local heat kernel expansion, first studied by Barvinsky, Vilkovisky and Avramidi, based on simple diagrammatic equations satisfied by the heat kernel. For Laplace-type differential operators we obtain the explicit form of the non-local heat kernel form factors to second order in the curvature. Our method can be generalized easily to the derivation of the non-local heat kernel expansion of a wide class of differential operators.Comment: 23 pages, 1 figure, 31 diagrams; references added; to appear in JM