A Physically Consistent Model for Forced Torsional Vibrations of Automotive Driveshafts

The aim of this research was to design a physically consistent model for the forced torsional vibrations of automotive driveshafts that considered aspects of the following phenomena: excitation due to the transmission of the combustion engine through the gearbox, excitation due to the road geometry, the quasi-isometry of the automotive driveshaft, the effect of nonuniformity of the inertial moment with respect to the longitudinal axis of the tulip–tripod joint and of the bowl–balls–inner race joint, the torsional rigidity, and the torsional damping of each joint. To resolve the equations of motion describing the forced torsional nonlinear parametric vibrations of automotive driveshafts, a variational approach that involves Hamilton’s principle was used, which considers the isometric nonuniformity, where it is known that the joints of automotive driveshafts are quasi-isometric in terms of the twist angle, even if, in general, they are considered CVJs (constant velocity joints). This effect realizes the link between the terms for the torsional vibrations between the elements of the driveshaft: tripode–tulip, midshaft, and bowl–balls–inner race joint elements. The induced torsional loads (as gearbox torsional moments that enter the driveshaft through the tulip axis) can be of harmonic type, while the reactive torsional loads (as reactive torsional moments that enter the driveshaft through the bowl axis) are impulsive. These effects induce the resulting nonlinear dynamic behavior. Also considered was the effect of nonuniformity on the axial moment of inertia of the tripod–tulip element as well as on the axial moment of inertia of the bowl–balls–inner race joint element, that vary with the twist angle of each element. This effect induces parametric dynamic behavior. Moreover, the torsional rigidity was taken into consideration, as was the torsional damping for each joint of the driveshaft: tripod–joint and bowl–balls–inner race joint. This approach was used to obtain a system of equations of nonlinear partial derivatives that describes the torsional vibrations of the driveshaft as nonlinear parametric dynamic behavior. This model was used to compute variation in the natural frequencies of torsion in the global tulip (a given imposed geometry) using the angle between the tulip–midshaft for an automotive driveshaft designed for heavy-duty SUVs as well as the characteristic amplitude frequency in the region of principal parametric resonance together the method of harmonic balance for the steady-state forced torsional nonlinear vibration of the driveshaft. This model of dynamic behavior for the driveshaft can be used during the early stages of design as well in predicting the durability of automotive driveshafts. In addition, it is important that this model be added in the design algorithm for predicting the comfort elements of the automotive environment to adequately account for this kind of dynamic behavior that induces excitations in the car structure.

The irreducible mass of Christodoulou–Ruffini–Hawking mass formula

We reveal three new discoveries in black hole physics previously unexplored in the Hawking era. These results are based on the remarkable 1971 discovery of the irreducible mass of the black hole by Christodoulou and Ruffini, and subsequently confirmed by Hawking. (1) The Horizon Mass Theorem states that the mass at the event horizon of any black hole — neutral, charged, or rotating — is always twice its irreducible mass observed at infinity. (2) The External Energy Theorem asserts that the rotational energy of a Kerr black hole exists completely outside the horizon. This is due to the fact that the irreducible mass does not contain rotational energy. (3) The Moment of Inertia Theorem shows that every black hole has a moment of inertia. When the rotation stops, the irreducible mass of a Kerr black hole becomes the moment of inertia of a Schwarzschild black hole. This is recognized as the rotational equivalent of the rest mass of a moving body in relativity. Thus after 50 years, the irreducible mass has gained a new and profound significance. No longer is it a limiting value in rotation, it determines black hole dynamics and structure. What is believed to be a black hole is a mechanical body with an extended structure. Astrophysical black holes are likely to be massive compact objects from which light cannot escape.

Serviceability of Post-fire RC Rafters with Openings of Different Sizes and Shapes

This study deals with the serviceability of reinforced concrete solid and perforated rafters with openings of different shapes and sizes based on an experimental study that includes 12 post-fire non-prismatic reinforced concrete beams (solid and perforated). Three groups were formed based on heating temperature (room temperature, 400 °C, and 700 °C), each group consisting of four rafters (solid, rafters with 6 and 8 trapezoidal openings, and rafter with eight circular openings) under static loading. A developed unified calculation technique for deflection and crack widths under static loading at the service stage has been provided, which comprises non-prismatic beams with or without opening exposed to flexure concentrated force. Two approaches were used to compute the deflection: The first attempt was conducted by using the moment of inertia for solid non-prismatic beam and reduced for those with openings by the ratio of residual rafter self-weight. The second was performed by using the moment of inertia of transformed cracked sections depending on the segmental rafter method. The crack width was determined using the ACI code's equation. The analytical and experimental results were evaluated and found to be in good agreement.

Tension-Stiffening Effect Consideration for Modeling Deflection of Cracked Reinforced UHPC Beams

Tension-stiffening effects can significantly influence the flexural performance of cracked reinforced concrete specimens. Such effect is amplified for fiber-reinforced concrete, given the fact that fibers can bridge the cracks. The objective of this study was to develop a model to predict the deflection of cracked reinforced ultra-high performance concrete (R-UHPC) beam elements. The modeling approach characterized the average bending moment of inertia by combining the existing model used for conventional reinforced concrete and the analytical model of stress distribution of UHPC along the cross-section. The finite element analysis (FEA) was employed to evaluate the flexural deflection based on the average bending moment of inertia. The calculated load-deflection relationships have been compared to experimental results. The results indicated that the relative errors of deflection between predicted and experimental results can be controlled within 15%, compared to values ranging from 5% to 50% calculated by neglecting the tensile properties of cracked UHPC and values ranging from 5% to 30% calculated by effective inertia of bending moment of ACI code. Therefore, the developed model can be used in practice because it can secure the accuracy of deflection prediction of the R-UHPC beams. Such a simplified model also has higher sustainability compared to FEA using solid elements since it is easier and time-saving to be established and calculated.

Inferring the gravitational binding energy and moment of inertia of PSR J0030+0451 and PSR J0740+6620 from new universal relations

The Neutron Star Interior Composition Explorer (NICER) recently simultaneously measured the gravitational mass (Mg) and radius (R) of PSR J0030+0451 and PSR J0740+6620, respectively. Inspired by the groundbreaking observations, we establish two high accuracy universal relations (with the relative error at 1% level) related to Mg and R to infer the gravitational binding energy (Eg) and moment of inertia (I) of the two pulsars. By combining these universal relations with the data of (Mg, R) released by NICER collaboration, the gravitational binding energy and moment of inertia of PSR J0030+0451 can be constrained within |Eg| = 0.21+0.03−0.03M⊙ and I = 1.95+0.70−0.50×1045g cm2at 68% credible level, respectively. The gravitational binding energy and moment of inertia of PSR J0740+6620 can be constrained within |Eg| = 0.47+0.09−0.12M⊙ and I = 4.65+1.16−0.82 × 1045g cm2at 68% credible level, respectively.

Deformability of discs in turbulence

The aim of this study is to investigate experimentally the transition from a rigid regime to a deformed regime for flexible discs freely advected in turbulent flows. For a given disc, the amplitude of the deformation is expected to increase when its bending modulus decreases or when the turbulent kinetic energy increases. To quantify this qualitative argument, experiments are performed where the deformation of flexible discs is measured using three cameras. The amplitude of the deformation has been characterised by the eigenvalues of the moment of inertia tensor. Experimental results exhibit a transition from a rigid regime to a deformed regime that depends on the size, the density and the flexibility of the disc and the turbulent kinetic energy. The modelling of this transition is a generalisation and an extension of the previous models used to characterise the deformation of flexible fibres in turbulent flows.

The Maximum Flywheel Load: A Novel Index to Monitor Loading Intensity of Flywheel Devices

Background: The main aim of this study was (1) to find an index to monitor the loading intensity of flywheel resistance training, and (2) to study the differences in the relative intensity workload spectrum between the FW-load and ISO-load. Methods: twenty-one males participated in the study. Subjects executed an incremental loading test in the squat exercise using a Smith machine (ISO-load) or a flywheel device (FW-load). We studied different association models between speed, power, acceleration, and force, and each moment of inertia was used to find an index for FW-load. In addition, we tested the differences between relative workloads among load conditions using a two-way repeated-measures test. Results: the highest r2 was observed using a logarithmic fitting model between the mean angular acceleration and moment of inertia. The intersection with the x-axis resulted in an index (maximum flywheel load, MFL) that represents a theoretical individual maximal load that can be used. The ISO-load showed greater speed, acceleration, and power outcomes at any relative workload (%MFL vs. % maximum repetition). However, from 45% of the relative workload, FW-load showed higher vertical forces. Conclusions: MFL can be easily computed using a logarithmic model between the mean angular acceleration and moment of inertia to characterize the maximum theoretical loading intensity in the flywheel squat.

Comprehensive exploration of chemical space using trisubstituted carboranes

A total of 42 trisubstituted carboranes categorised into five scaffolds were systematically designed and synthesized by exploiting the different reactivities of the twelve vertices of o-, m-, and p-carboranes to cover all directions in chemical space. Significant inhibitors of hypoxia inducible factor transcriptional activitay were mainly observed among scaffold V compounds (e.g., Vi–m, and Vo), whereas anti-rabies virus activity was observed among scaffold V (Va–h), scaffold II (IIb–g), and scaffold IV (IVb) compounds. The pharmacophore model predicted from compounds with scaffold V, which exhibited significant anti-rabies virus activity, agreed well with compounds IIb–g with scaffold II and compound IVb with scaffold IV. Normalized principal moment of inertia analysis indicated that carboranes with scaffolds I–V cover all regions in the chemical space. Furthermore, the first compounds shown to stimulate the proliferation of the rabies virus were found among scaffold V carboranes.