Physics of basic motions in asymmetric continuum

We consider the advantages of a formalism based on concept of the asymmetric continuum and we present some equivalence theorems relating it to the asymmetric elasticity and to micropolar and micromorphic theories as founded by Nowacki, Cosserats and Eringen. We consider the basic processes in an asymmetric continuum which could be reduced to the point basic motions/deformations. The co-action of spin and shear motions is assumed to play the main role in fracturing process, while the constitutive relation between the antisymmetric stresses and rotations replaces the friction constitutive law.     

Fluid theory with asymmetric molecular stresses: Difference between vorticity and spin equations

We present a new development in fluid theory, incorporating into it the velocity and spin fields; special attention is given to the structure of transport.The theory includes asymmetric molecular stresses and independent rotation velocity, i.e., spin. Our approach is based on our former studies on the asymmetric continuum theory with the balance and constitutive laws for displacement velocity and independent rotation motion, and points out the role of a related characteristic length unit. It is assumed that the vorticity caused by velocities can induce a spin transport counterpart. Thus, under certain conditions, an additional transport term due to rotational velocity fields may be incorporated to the velocity transport, which may lead to the vortex fields included directly into the theory.     

Symmetropy of earthquake patterns: asymmetry and rotation in a disordered seismic source

We demonstrate that the idea of symmetropy can be used for quantification of earthquake patterns. The symmetropy can be considered as a measure of asymmetry. A pattern is richer in asymmetry when the symmetropy is smaller. The specific results of its applications are obtained as follows. In a discrete model of a seismic source with self-organized criticality, the spatial patterns of earthquakes during critical states and sub-critical states are distinguished by the behaviour of the symmetropy: sub-critical patterns show that the symmetropy is approximately a constant but this has various values during critical states. The critical patterns show asymmetric property without any asymmetric force from the outside and without asymmetric intracellular rule. We show that the emergence of asymmetric patterns is a generic feature of dynamic ruptures in our model. Such a generic asymmetry results from the model which is an inherently discrete system consisting of finite-sized cells. These cells may represent geometrical disordered fault zones. We further discuss rotational motions that generate seismic rotational waves. In micromorphic continuum theory, such rotations are attributed to dynamic ruptures in disordered systems. We note that the concept of disorder in this theory is expressed by a set of finite-sized microstructures and is consistent with the concept of disorder modelled in the present study. Thus, we suggest that the spatially asymmetric patterns of earthquakes might be related to the rotational motions, because both come from dynamic ruptures in a discrete fault zone without a well-defined continuum limit.     

Introduction to asymmetric continuum: dislocations in solids and extreme phenomena in fluids

We present a new approach to the continuum theories: for solids, our version includes the asymmetric stresses, symmetric strains and antisymmetric rotations, while for fluids we take the similar assumptions but related to the respective time rates of these fields. We consider the constitutive relations and the balance laws: those related to the antisymmetric stresses are equivalent and substitute the required relations for the angular moment; a similar approach with rates of these fields is applied for fluids. The stress-dislocation relations are derived and the role of rotation motions in the fracture processes in solids is studied. A new theory of the extreme motion phenomena in fluids is developed.     

Rotation and strain seismology

Asymmetric continuum theory points to the equal roles of the rotation motions and those related directly to shear or confining strains. The strain motions could be quite independent or mutually related with the eventual phase shifts, while the displacements have only a mathematical sense; a real displacement may appear along the fracture slip only. Formally, any deformation could be presented as related to the displacements; however, its origin in a fracture source should be considered either as belonging to an individual process or to complex correlated events; in these cases, the confining, shear and rotation strains can be related mathematically to the different displacement fields. Some of these related deformations could be emitted from a source with a phase shift, while the observed displacements (deduced from records) result as a sum of these independent displacements. An important influence on a source process and on the premonitory micro-events has the material defects, their distribution, and mobility. The defect arrays lead to a concentration of stresses and their local reorganization. Thus, in this paper, we consider the induced stresses and strains related to defect content and to its modification and redistribution. Moreover, an important role in understanding the complex correlated events in a source plays the release?Crebound mechanism. The release?Crebound mechanism in an earthquake source processes leads to a possible direct or phase-shifted correlations between the emitted motions; in this aspect, a propagation of the coupled strain and rotation waves is discussed. In particular, we consider the point fracture events as related either to a confining load or/and to the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves. In some important seismic regions, we have the recording system which permits to record the strains and rotations. However, we should point that the wordwide seismological network is not adequate to record the complex strain deformations released in the fracture processes and remains quite insufficient to understand the global stress changes and related strain waves of a very low period. Consideration on a recording mechanism of the long displacement waves indicates the insufficiencies of the present global recording system and points that recording of the global strain and rotation waves is an important and urgent task.     

Asymmetric continuum and anisotropy

We present a relation between stress moments and antisymmetric part of stresses and the related constitutive law joining those stresses with the particle/point rotations. Correspondence of the asymmetric continuum theory to the micromorphic theory is considered. An extension of the asymmetric continuum theory for the case of 2D anisotropy for antisymmetric stresses leads us to the problems of friction anisotropy and fracture pattern.     

Spin and twist motions in the earthquake preparation processes: Analysis of records

Three seismic events in L’Aquila region and one in western Greece have been chosen for comparative analysis of two kinds of seismic motions, spin and twist. These torque components of the seismic field were detected in horizontal plane with the rotational seismometers. Homologous parts were sought in the signals of spin and twist components — curve of one component was compared to the other directly and after transformations: phase-shifting and sign reversal. To achieve better clarity, these operations were done on the data divided into several descendant signals with the use of band-pass filtration. Conformities of spin and twist, revealed in this way, are assumed to be results of distant processes in the source, where relations between rotational and shear motions include retardations.     

Seismic response of reduced micropolar elastic half-space

This paper explores reduced micropolar theory to simulate ground motion during an earthquake. In this theory, rotational motions are kinematically independent of translational motions. Analytical expressions for ground displacement and rotational motions due to a buried seismic source are presented in this paper. This theory requires two additional material constants which characterise the microstructure of the medium compared with linear elastic theory. Ground motions are simulated for an earthquake of magnitude (M _w) 5.0. The sensitivity of ground motion to these new material constants is reported. It is observed that rotations are sensitive to microstructure of the medium. A comparison with recorded rotations of the M _w 5.2 Izu peninsula, Japan event is also presented in this article.     

Perturbation theory in low rate seismology

Summary In the case of low frequency motions in an elastic continuum, first-order perturbation theory can be used to estimate the effect of real-world deviations from the ideal model. Although the effects are often small, some interesting results can be found fairly easily. In spite of the simplicity in the structure of the formalism, nontrivial applications lead to remarkably complicated results.     

偶应力理论框架下的弹性波数值模拟与分析

在经典地震学理论框架下,先人发展了数不胜数的地震技术,为社会发展做出了巨大贡献;可是,当前的技术仍有难以逾越的障碍,亟需破局.高铁地震学联合研究组,在河北定兴采集到大量数据;其中可见含有大量的旋转运动分量.由于基于经典连续介质力学推导弹性波动方程时,从理论出发点上就去除了旋转项,且在其理论框架内,介质被视为一个连续的质量体.而事实上,不论是人造还是天然的介质都存在着复杂的内部结构,广义连续介质力学更适合描述具有更加复杂内部结构的情况.于是,我们尝试启用广义连续介质力学理论,推导偶应力理论框架下的弹性波动方程;将其数学表达形式以及数值模拟结果与传统弹性波动方程进行对比.研究探索推导的具非对称性的波动方程所具有的理论意义和应用价值.     

Seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions

An approximation approach of seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions is proposed. The procedures of uncoupled modal response history analysis (UMRHA) are extended to two‐way asymmetric buildings simultaneously excited by two horizontal components of ground motion. Constructing the relationships of two‐way base shears versus two‐way roof translations and base torque versus roof rotation in ADRS format for a two‐way asymmetric building, each modal pushover curve bifurcates into three curves in an inelastic state. A three‐degree‐of‐freedom (3DOF) modal stick is developed to simulate the modal pushover curve with the stated bifurcating characteristic. It requires the calculation of the synthetic earthquake and angle β. It is confirmed that the 3DOF modal stick is consistent with single‐degree‐of‐freedom modal stick in an elastic state. A two‐way asymmetric three‐story building was analyzed by UMRHA procedure incorporating the proposed 3DOF modal sticks. The analytical results are compared with those obtained from nonlinear response history analysis. It is shown that the 3DOF modal sticks are more rational and effective in dealing with the assessment of two‐way asymmetric building systems under two‐directional seismic ground motions. Copyright © 2007 John Wiley & Sons, Ltd.     

Torsional balance of plan‐asymmetric structures with frictional dampers: experimental results

This investigation deals with the measured seismic response of a six‐storey asymmetric structural model with frictional dampers. Its main objective is to experimentally prove the concept of weak torsional balance for mass‐ and stiffness‐eccentric model configurations. The goal is to control the torsional response of these asymmetric structures and to achieve, if possible, a weak form of torsional balance by placing the so‐called empirical centre of balance (ECB) of the structure at equal distance from the edges of the building plan. The control of the dynamic response of asymmetric structures is investigated herein by using steel–teflon frictional dampers. As expected from theory, experimental results show that the mean‐square and peak displacement demand at the flexible and stiff edges of the plan may be similar in magnitude if the dampers are optimally placed. Frictional dampers have proven equally effective in controlling lateral‐torsional coupling of torsionally flexible as well as stiff structures. On the other hand, it is shown that impulsive ground motions require larger frictional capacities to achieve weak torsional balance. Copyright © 2006 John Wiley & Sons, Ltd.     

CRITICAL CROSS POWER SPECTRAL DENSITY FUNCTIONS AND THE HIGHEST RESPONSE OF MULTI-SUPPORTED STRUCTURES SUBJECTED TO MULTI-COMPONENT EARTHQUAKE EXCITATIONS

The highest response of multi-supported structures subjected to partially specified multi-component earthquake support motions is considered. The seismic inputs are modelled as incompletely specified vector Gaussian random processes with known autospectral density functions but unknown cross spectral densities and these unknown functions are determined such that the steady state response variance of a given linear system is maximized. The resulting cross power spectral density functions are shown to be dependent on the system properties, autospectra of excitation and the response variable chosen for maximization. It emerges that the highest system response is associated neither with fully correlated support motions, nor with independent motions, but, instead, specific forms of cross power spectral density functions are shown to exist which produce bounds on the response of a given structure. Application of the proposed results is demonstrated by examples on a ground based extended structure, namely, a 1578 m long, three span, suspension cable bridge and a secondary system, namely, an idealized piping structure of a nuclear power plant.     

A preliminary dynamic view of the circulation of Jupiter's atmosphere

Summary The problem of the gross nature of the Jovian atmospheric circulation is examined from the viewpoint of the following previous findings of the writer and others. 1) The equatorial acceleration cannot be accounted for by axisymmetric motions. 2) The departures from symmetry in a rotating system having an equatorial acceleration must impart angular momentum selectively to those particles moving toward the jet maximum and abstract it from those moving away. 3) These selective (pressure) torques and associated sorting processes arise spontaneously in the presence of a vertical convection mode involving motions not independent of longitude, if the cell sizes and other conditions are right.Since there is evidence that Jovian dark spots have statistical maxima of occurrence along the tropical shear lines flanking the equator, these are assumed to be vertical convective systems forming, in effect,convective vortex sheets which generate the high angular momentum of the equatorial zone. Various additional concepts are discussed, and many comparisons with conditions in the sun and in the earth's atmosphere are made.     

Bi‐directional coupled tuned mass dampers for the seismic response control of two‐way asymmetric‐plan buildings

This paper proposes bi‐directional coupled tuned mass dampers (BiCTMDs) for the seismic response control of two‐way asymmetric‐plan buildings subjected to bi‐directional ground motions. The proposed BiCTMD was developed from the three‐degree‐of‐freedom modal system, which represents the vibration mode of a two‐way asymmetric‐plan building. The performance of the proposed BiCTMD for the seismic response control of elastic two‐way asymmetric‐plan buildings was verified by investigating the reductions of the amplitudes of the associated frequency response functions. In addition, the investigation showed that the proposed BiCTMD is effective in reducing the seismic damage of inelastic asymmetric‐plan buildings. Therefore, the BiCTMD is an effective approach for the seismic response control of both elastic and inelastic two‐way asymmetric‐plan buildings. Copyright © 2010 John Wiley & Sons, Ltd.     

Temperature and heat flux spectra in the turbulent buoyancy subrange

The physical nature of motions with scales intermediate between approximately isotropic turbulence and quasi-linear internal gravity waves is not understood at the present time. Such motions play an important role in the energetics of small scales processes, both in the ocean and in the atmosphere, and in vertical transport of heat and constituents. This scale range is currently interpreted either as a saturated gravity waves field or as a buoyancy range of turbulence.We first discuss some distinctive predictions of the classical (Lumley, Phillips) buoyancy range theory, recently improved (Weinstock, Dalaudier and Sidi) to describe potential energy associated with temperature fluctuations. This theory predicts the existence of a spectral gap in the temperature spectra and of an upward mass flux (downward buoyancy and heat fluxes), strongly increasing towards large scales. These predictions are contrasted with an alternate theory, assuming energetically insignificant buoyancy flux, proposed by Holloway.Then we present experimental evidences of such characteristic features obtained in the lower stratosphere with an instrumented balloon. Spectra of temperature, vertical velocity, and cospectra of both, obtained in homogeneous, weakly turbulent regions, are compared with theoretical predictions. These results are strongly consistent with the improved classical buoyancy range theory and support the existence of a significant downward heat flux in the buoyancy range.The theoretical implications of the understanding of this scale range are discussed. Many experimental evidences consistently show the need for an anisotropic theory of the buoyancy range of turbulence.     

Early‐stage aeolian protodunes: Bedform development and sand transport dynamics

Early‐stage aeolian bedforms, or protodunes, are elemental in the continuum of dune development and act as essential precursors to mature dunes. Despite this, we know very little about the processes and feedback mechanisms that shape these nascent bedforms. Whilst theory and conceptual models have offered some explanation for protodune existence and development, until now, we have lacked the technical capability to measure such small bedforms in aeolian settings. Here, we employ terrestrial laser scanning to measure morphological change at the high frequency and spatial resolution required to gain new insights into protodune behaviour. On a 0.06 m high protodune, we observe vertical growth of the crest by 0.005 m in two hours. Our direct measurements of sand transport on the protodune account for such growth, with a reduction in time‐averaged sediment flux of 18% observed over the crestal region. Detailed measurements of form also establish key points of morphological change on the protodune. The position on the stoss slope where erosion switches to deposition is found at a point 0.07 m upwind of the crest. This finding supports recent models that explain vertical dune growth through an upwind shift of this switching point. Observations also show characteristic changes in the asymmetric cross‐section of the protodune. Flow‐form feedbacks result in a steepening of the lee slope and a decline in lower stoss slope steepness (by 3°), constituting a reshaping of protodune form towards more mature dune morphology. The approaches and findings applied here, (a) demonstrate an ability to quantify processes at requisite spatial and temporal scales for monitoring early‐stage dune evolution, (b) highlight the crucial role of form‐flow feedbacks in enabling early‐stage bedform growth, alluding to a fluctuation in feedbacks that require better representation in dune models, and (c) provide a new stimulus for advancing understanding of aeolian bedforms. Copyright © 2017 John Wiley & Sons, Ltd.     

Molecular transport in fracture processes

The Asymmetric Continuum Theory based on deformation fields includes the strain rotation as an equally important deformation part as the shear and confining strains; all these fields can be related to their origin in the fracture processes by some displacement motions in a source. Some of these motions may belong to an individual process, some to complex correlated events; in this latter case the displacements related to these strains could be shifted in phase. Moreover, we may expect an appearance of some molecular transport motions; the molecular transport may be helpful for understanding an interaction of the molecular processes and related molecular momentum flux. These correlated events should be mutually related in a source by the release-rebound mechanism. In particular, we consider the point fracture events as associated with a confining load or/and with the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves. It is to be pointed out that such molecular motions are too small to be observed by the existing seismological networks.     

A generalized continuum method for dynamic analysis of asymmetric tall buildings

The paper presents a continuum method for dynamic analysis of asymmetric tall buildings with uniform cross-section in which the horizontal stiffness is provided by shear walls and columns of arbitrary shape and layout, coupled by horizontal beams. The equations of motions are formulated in variational terms, including axial strain energy. Numerical solutions, obtained by using finite time differences and infinite polynomials, are presented for the response of a twenty-storey building with six shear walls to an impact load and earthquake accelerations. It is shown that omission of the axial deformations results in a substantially distorted pattern of behaviour, some of its effects being:

• 1 Overestimation of the bending stiffness of the coupled shear walls, with corresponding changes in their stiffness ratios.
• 2 Underestimation of the periods of the principal modes, with a corresponding change in the dynamic response.
• 3 Distortion of the magnitude, form, time of onset and coupling of the maximum displacements.
• 4 Pronounced change in the shear force and moment diagrams for the shear walls, the beams and the building as a whole.