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With the Hamilton-Jacobi equation, we obtain the energy-momentum relation of a charged particle as it is absorbed by the Gauss-Bonnet AdS black hole. On the basis of the energy-momentum relation at the event horizon, we investigate the first law, second law, and weak cosmic censorship conjecture in both the normal phase space and extended phase space. Our results show that the first law, second law as well as the weak cosmic censorship conjecture are valid in the normal phase space for all the initial states are black holes. However, in the extended phase space, the second law is violated for the extremal and near-extremal black holes, and the weak cosmic censorship conjecture is violable for the near-extremal black hole, though the first law is still valid. In addition, in both the the normal and extended phase spaces, we find the absorbed particle changes the configuration of the near-extremal black hole, while don't change that of the extremal black hole. *

In this paper, we explore three simple models of accretions on a global monopole black hole in f(R) theory, and numerically study the corresponding observational appearances as seen by an observer located at the asymptotic infinity and the certain region out of black hole. For the thin-disk accretion, the results here show that the brighter lensing ring and the darker photon ring that around black hole shadow, always make a small contribution and a negligible contribution to total observed intensity respectively. While, the direct emission of disk contributes a dominant part, and the size of shadow always depends on the disk’s location. For the static and infalling spherical accretions, it turns out that the radiuses of the shadows and photon spheres are always same for both accretions, which implies that the boundary of shadow represents the signature of the spacetime geometry in this case. However, we also find that the brightness of shadow in infalling accretion is darker than that in static case since the Doppler effect is taken into account. In addition, the effect of the global monopole parameter $$\eta $$ η and f(R) parameter $$\psi _0$$ ψ 0 on observational appearances of black hole are clearly emphasized throughout of this paper. Finally, we conclude that black hole shadows and the related rings with some different observable features can be used for us to distinguish black holes from different gravity theories and set the upper limits to the f(R) parameter $$\psi _0$$ ψ 0 .

Due to bending-torsion coupled vibrations of the L-shaped beams and numerous uncertainties associated with the bolted joints, modeling structures with L-shaped beams and bolted joints is a challenging task. With the recent development of the modeling techniques for L-shaped beams by the authors (He and Zhu, 2009, “Modeling of Fillets in Thin-Walled Beams Using Shell/Plate and Beam Finite Elements,” ASME J. Vibr. Acoust., 131(5), p. 051002), this work focuses on developing new finite element (FE) models for bolted joints in these structures. While the complicated behavior of a single bolted connection can be analyzed using commercial FE software, it is computationally expensive and inefficient to directly simulate the global dynamic response of an assembled structure with bolted joints, and it is necessary to develop relatively simple and accurate models for bolted joints. Three new approaches, two model updating approaches and a predictive modeling approach, are developed in this work to capture the stiffness and mass effects of bolted joints on the global dynamic response of assembled structures. The unknown parameters of the models in the model updating approaches are determined by comparing the calculated and measured natural frequencies. In the predictive modeling approach, the effective area of a bolted connection is determined using contact FE models and an analytical beam model; its associated stiffnesses can also be determined. The models developed for the bolted joints have relatively small sizes and can be easily embedded into a FE model of an assembled structure. For the structures studied, including a three-bay space frame structure with L-shaped beams and bolted joints, and some of its components, the errors between the calculated and measured natural frequencies are within 2% for at least the first 13 elastic modes, and the associated modal assurance criterion values are all over 94%.

In this paper, under the illumination of thin disk accretion, we have employed the ray-tracing method to carefully investigate shadows and rings of the Kehagias-Sfetsos(KS) black hole in deformed Hořava-Lifshitz(HL) gravity. The results show that the event horizon r+, the radius r_p and impact parameter bp of photon sphere are all decreased with the increase of the HL parameter ω, but the effective potential increases. And, it also turns out that the trajectories of light rays emitted from the north pole direction are defined as the direct emission, lensing ring and photon ring of KS black hole, on the basis of orbits n = ϕ/2π. As black hole surrounded by thin disk accretion, we show that the corresponding transfer functions have their values increased with the parameter ω. More importantly, we also find that the direct emissions always dominate the total observed intensity, while lensing rings as a thin ring make a very small contribution and photon ring as a extremely narrow ring make a negligible contribution, for all three toy-model functions. In view of this, the results finally imply that shadows and rings as the observational appearance of KS black hole exhibit some obvious interesting features, which might be regarded as an effective way to distinguish black holes in HL gravity from the Schwarzschild black hole.

Considering the cosmological constant as the pressure, we mainly study the laws of thermodynamics and weak cosmic censorship conjecture in the Reissner-Nordström-AdS black hole surrounded by quintessence dark energy under charged particle absorbtion. The first law of thermodynamics is found to be valid as a particle is absorbed by the black hole. The second law however is found to be violated for the extremal and near-extremal black holes since the entropy of these black hole decrease. Moreover, we find that the extremal black hole do not change it configuration in the extended phase space, implying that the weak cosmic censorship conjecture is valid. Remarkably, the near-extremal black hole can be overcharged beyond the extremal condition under charged particle absorption. That is, the cosmic censorship conjecture could be violated for the near-extremal black hole in the extended phase space. To make a comparison, we also discuss the first law, second law as well as the weak cosmic censorship conjecture in the normal phase space, and find that all of them are valid in this case.