3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials

The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.

Magneto-elastic dynamics and bifurcation of rotating annular plate

In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton＇s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincare′ maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions,and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos.

Rotating Squeezed Vacua as Time Machines

Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticity in the vacuum bounded by them. The geometry resulting from an arbitrarily extended Casimir plates along their axis of rotation is similar to van Stockum spacetime. We observe closed timelike curves (CTC’s) forming in the exterior of the system resulting from frame dragging. The exterior geometry of this system is similar to Kerr geometry, but because of violation of ANEC, the Cauchy horizon lies outside the system unlike Kerr blackholes, giving more emphasis on whether spacetime is multiply connected at the microscopic level.

The Phototropism of Jurassic Petrified Wood in North China Plate

Trees on the side directly exposed to sunlight generally grow faster than on the opposite side, a phenomenon termed plant phototropism. There are in situ vertical trunks of silicified wood in the Xiadelongwan area of Yanqing County, north Beijing, where the first National Geologic Park of Petrified Wood of China has been built since 2002. A few trunks have well-preserved growth rings. One petrified stump from the formation shows a positive phototropism direction of SW230°. As compared with the modern normal growth stumps in Beijing plain area, which have a positive phototropism direction of SW210 °± 5°, the evidence of wood phototropism supports the conclusion of previous palaeomagnetic studies that the North China Plate has rotated clockwise since the Late Jurassic. The known petrified wood stumps in the Yanshan-Liaoning area are mainly found from the strata of 165-136 Ma, which corresponds to the main stage of the Yanshanian Movement.

Geochemistry and Geochronology of Circumferential Dykes of the Franklin LIP: A Rotated Perspective on Plate Reconstruction

In addition to an extrusive volcanic component and associated sills,the Neoproterozoic Franklin Large Igneous Province(LIP)comprises a giant radiating dyke swarm spanning an arc of ca.110?,as well as a less-

Frequency Veering of Rotating Metal Porous Twisted Plate with Cantilever Boundary Using Shell Theory

The frequency veering of a metal porous rotating cantilever twisted plate with twist angle and stagger angle is investigated.Metal porous materials may have the characteristics of gradient or uniform distribution along the thickness direction.Based on the classical shell theory,considering the influence of centrifugal force produced by high-speed rotation,the free vibration equations of a rotating cantilever twisted plate are derived.Through the polynomial function and Rayleigh-Ritz method,the natural frequencies and mode shapes of the metal porous cantilever twisted plate in both static and rotating states are derived.The accuracy of the present theory and calculation results is confirmed by a comparison between them and the results available from the literature and those obtained from Abaqus.The influences of the thickness ratio,porosity,twist angle,stagger angle and rotational velocity on the frequency veering and mode shape shift of the rotating cantilever twisted plate with porous material under three different distributions are analyzed.It should be mentioned that the frequency veering accompanied by mode shape shift occurs in both static and dynamic states.

Discussion on the relationship between the Yanshanian Movement and cratonic destruction in North China

The relationship between the Yanshanian Movement, destruction of the North China Craton(NCC), and subduction of the western Pacific plate is crucial to reconstructing the middle-late Mesozoic tectonic evolution of the eastern Asian continent and margin. The Yanshanian Movement was a globally important change in crustal tectonics during the Middle-Late Jurassic.Previous research has systematically studied the formation and evolution of the Yanshanian Movement, focusing on the timing and location of tectonic movements, and the sedimentary and volcanic strata. However, the question of whether the tectonic activity occurred globally, and the characteristics of the Yanshanian Movement remain debated. The main argument is that if a tectonic movement can only be characterized by a regional or local disconformity, and if the tectonic movement occurred in an intracontinental setting, with extensive deformation but with no disconformity despite volcanic eruptions and magmatic intrusions, accompanied by changes in crustal structure and composition, should it be defined as a tectonic event or process? This question requires further analysis. The main aim of this study is to distinguish whether the Yanshanian Movement is a local feature of the eastern Asian continent, or a global tectonic event related to subduction of the Pacific Plate. In this paper, based on previous research, we discuss the spatial and temporal evolution of the Yanshanian Movement, the controlling tectonic mechanisms, and its relationship to the reactivation and destruction of the NCC and the subduction of the western Paleo-Pacific slab.We emphasize that the Yanshanian Movement in the Middle-Late Jurassic is distinct from the lithospheric thinning responsible for Early Cretaceous extension and magmatism related to the destruction of the NCC. The various tectonic stages were constrained by different dynamics and tectonic settings, or by different tectonic events and processes. Therefore, it is possible that the deformation and reactivation of the NCC contributed to its destruction, in addition to lithospheric thinning. Finally, we discuss whether the Yanshanian Movement was associated with the destruction of the NCC.