The stability of linear potential gyroscopic systems when the potential energy has a maximum

1997 ◽  
Vol 61 (3) ◽  
pp. 371-375 ◽  
Author(s):  
R.M. Bulatovič
2018 ◽  
Vol 6 (3) ◽  
pp. 20-28
Author(s):  
Faisal Al Tabatabaie ◽  
Dhabia Sabeeh Al Waily

The use of cutoffs underneath the hydraulic structures is considered a safe solution to ensure the stability of hydraulic structure against uplift pressure and piping phenomenon in addition to the sliding and overturning forces of the water. These cutoffs are used at critical sections underneath the floor of hydraulic structure to substitute with their depths the horizontal lengths of the creep line of the hydraulic structure base. In this paper, the experimental method- by using electrical analogue model- was carried out to plot the flow net and study the efficiency of the front and rear faces of the cutoffs for dissipating the potential energy of the percolating water underneath the floor of hydraulic structure. An electrical analogue model which was used in this study consists of twenty five models with different depths of upstream and downstream cutoffs. After plotting the flow net for all models, it is concluded that the efficiency of the inner sides are less than that of the outer sides which were investigated before in this topic of this work that both faces reduction values in the uplift pressure are considered the same, where the efficiency of the outer face of upstream cutoff is (70.35) % and for the inner face is (29.64)%, while for the downstream cutoff the efficiency for the outer face is (76.21)% and for the inner face is (23.79)% .


Author(s):  
Hongbin Fang ◽  
Tse-Shao Chang ◽  
K. W. Wang

Multi-stable structures and materials have attracted extensive research interests because they can provide a wide spectrum of adaptive properties and functionalities. Recently, origami has been identified as an important source for achieving multi-stability and has been exploited for developing unconventional mechanical metamaterials and metastructures. Once the crease pattern and the constituent materials have been specified for an origami structure, its multi-stability profile becomes unchangeable. On the other hand, a controllable profile would be desirable to endow the origami structures and origami metamaterials with further adaptability and versatility. This research investigates how to integrate magnets with origami to fundamentally alter the stability profiles. By embedding magnets into the origami facets or vertices, the magnetic potential energy would modify the original elastic potential energy landscape both quantitatively and qualitatively. Taking the stacked Miura-ori structures as examples, we show that different magnet assignments could either enrich the original bistable profile into a tri-stable or quad-stable profile, or simplify it into a mono-stable profile. Simultaneously, such magnet-induced evolutions of stability profile would trigger essential changes of the structure’s mechanical properties, which are promising to be used for developing multi-functional devices or metamaterials/metastructures. In this paper, in addition to the analyses, proof-of-concept design and prototype are presented. The results of this research would open up a new path for designing origami structures and metamaterials with controllable stability profiles that can be harnessed for many novel applications.


2019 ◽  
Vol 25 (4) ◽  
pp. 961-967
Author(s):  
Yan-Ping Zhao ◽  
Lin Li ◽  
Ming Jin

In this paper, stability of the neutral equilibrium and initial post-buckling of a column with a rotational end restraint is analyzed based on Koiter initial post-buckling theory. The potential energy functional is written in terms of the angle. By the generalized Fourier series of the disturbance angle, it is proved that the second-order variation of the potential energy is semi-positive definite at the neutral equilibrium. The stability of the neutral equilibrium is determined by the sign of the fourth-order variation for the buckling mode. For all values of the stiffness of the rotational end restraint, the neutral equilibrium is stable and the bifurcation equilibrium is upward in the initial post-buckling.


2019 ◽  
Vol 82 ◽  
pp. 365-371
Author(s):  
K. Augustson ◽  
S. Mathis ◽  
A. Strugarek

This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. One such instability is the purely magnetic Tayler instability, which can occur for poloidal, toroidal, and mixed poloidal-toroidal axisymmetric magnetic field configurations. However, most of the magnetic field configurations observed at the surface of massive stars are non-axisymmetric. Thus, extending earlier studies in spherical geometry, we introduce a formulation for the global change in the potential energy contained in a convectively-stable region for both axisymmetric and non-axisymmetric magnetic fields.


Author(s):  
Rama Dhar Misra

On the assumption that the potential energy of the three cubic lattices of the Bravais type consists of two terms, an attractive one proportional to r−m and a repulsive one proportional to r−n, n > m, stability conditions are expressed in the form that two functions of the number n should be monotonically increasing. These functions have been calculated numerically for n = 4 to 15, and are represented as curves with the abscissa n. The result is that the face-centred lattice is completely stable, that the body-centred lattice is unstable for large exponents in the law of force, and that the simple lattice is always unstable,—in complete agreement with the results of Part I.


2017 ◽  
Vol 203 ◽  
pp. 47-60 ◽  
Author(s):  
Kevin E. Riley ◽  
Khanh-An Tran

Halogen bonds involving cationic halogen bond donors and anionic halogen bond acceptors have recently been recognized as being important in stabilizing the crystal structures of many salts. Theoretical characterization of these types of interactions, most importantly in terms of their directionality, has been limited. Here we generate high-quality symmetry adapted perturbation theory potential energy curves of a H3N–CC–Br+⋯Cl− model system in order to characterize halogen bonds involving charged species, in terms of contributions from electrostatics, exchange, induction, and dispersion, with special emphasis on analyzing contributions that are most responsible for the directionality of these interactions. It is found that, as in the case of neutral halogen bonds, exchange forces are important contributors to the directionality of charged halogen bonds, however, it is also found that induction effects, which contribute little to the stability and directionality of neutral halogen bonds, play a large role in the directionality of halogen bonds involving charged species. Potential energy curves based on the ωB97X-D/def2-TZVP/C-PCM method, which includes an implicit solvation model in order to mimic the effects of the crystal medium, are produced for both the H3N–CC–Br+⋯Cl− model system and for the 4-bromoanilinium⋯Cl− dimer, which is based on the real 4-bromoanilinium chloride salt, whose crystal structure has been determined experimentally. It is found that, within a crystal-like medium, charged halogen bond are significantly weaker than in the gas phase, having optimum interaction energies up to approximately −20 kcal mol−1.


Author(s):  
Fengxia Wang ◽  
Albert C. J. Luo

The stability of period-1 motions of a rotating blade with geometric nonlinearity is studied. The roles of cubic stiffening geometric term are considered in the study of nonlinear periodic motions and its stability and bifurcations of a rotating blade. The nonlinear model of a rotating blade is reduced to the ordinary differential equations through the Galerkin method, and the gyroscopic systems with parametric excitations are obtained. The generalized harmonic balance method is employed to determine the period-1 solutions and the corresponding stability and bifurcations.


Author(s):  
H. W. Peng ◽  
S. C. Power

The main purpose of the paper is an investigation of the stability of a certain class of Bravais lattices, namely, those with a rhombohedral cell of arbitrary angle. The potential energy is assumed to consist of two terms, each proportional to a reciprocal power of the distance. In the continuous series of lattices obtained by changing the rhombohedral angle, there are included the three cubic Bravais lattices, the simple (s), the face-centred (f) and the body-centred (b) lattices. It is shown that (f) and (b) correspond to a minimum of the potential energy, and (s) to a maximum. A method for calculating the potential energy for the intermediate rhombohedral lattices is developed, and, with the help of a certain characteristic function, it is shown by numerical calculation that the (f) lattice corresponds to the absolute minimum of potential energy, and that no extrema, other than (f), (s) and (b), exist. In the last section, the case of a compound (non-Bravais lattice) is considered, and it is shown that the equilibrium and stability conditions for the law of force assumed can be divided into one set for change of volume, and an independent set for change of shape.We take this opportunity of expressing our sincere thanks to Prof. Born for his interest in our work, and for much valuable advice.


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