Rocking response of rectangular rigid blocks under random noise base excitations

The response of a rigid rectangular block resting on a rigid foundation and acted upon simultaneously by a horizontal and a vertical random white-noise excitation is considered. In the equation of motion, the energy dissipation is modeled through a viscous damping term. Under the assumption that the body does not topple, the steady-state joint probability density function of the rotation and the rotational velocity is obtained using the Fokker-Planck equation approach. Closed form solution is obtained for a specific combination of system parameters. A more general but approximate solution to the joint probability density function based on the method of equivalent non-linearization is also presented. Further, the problem of overturning of the block is approached in the framework of the diffusion methods for first passage failure studies. The overturning of the block is deemed incipient when the response trajectories in the phase plane cross the separatrix of the conservative unforced system. Expressions for the moments of first passage time are obtained via a series solution to the governing generalized Pontriagin-Vitt equations. Numerical results illustra- tive of the theoretical solutions are presented and their validity is examined through limited amount of digital simulations.

The scratch hardness and friction of a soft rigid-plastic solid

The paper describes an experimental and analytical study of the normal and scratch hardnesses of a model soft rigid-plastic solid. The material known as ‘Plasticine’, a mixture of dry particles and a mineral oil, has been deformed with a range of rigid conical indentors with included angles of between 30° and 170°. The sliding velocity dependence of the computed scratch hardness and friction has been examined in the velocity range 0.19 mm/s to 7.3 m/s. Data are also described for the time dependence of the normal hardness and also the estimated rate dependence of the intrinsic flow stress. The latter values were estimated from data obtained during the upsetting of right cylinders. Three major conclusions are drawn from these data and the associated analysis. (1) A first-order account of the scratching force may be provided by adopting a model which sums the computed plastic deformation and interfacial sliding contributions to the total sliding work. This is tantamount to the adoption of the two-term non-interacting model of friction. (2) For this system during sliding, at high sliding velocities at least, the interface shear stress which defines the boundary condition is not directly related to the bulk shear stress. The interface rheological characteristics indicate an appreciable dependence on the imposed strain or strain rate. In particular, the relative contributions of the slip and stick boundary conditions appear to be a function of the imposed sliding velocity. (3) The computed normal and scratch hardness values are not simply interrelated primarily because of the evolving boundary conditions which appear to exist in the scratching experiments.

Interaction analysis of strip footing resting on a non-homogeneous elastic medium

In this paper, a plane stress solution for the interaction analysis of strip footing resting on (i) a non-homogeneous elastic half-plane and (ii) a non-homogeneous elastic layer resting on a rigid stratum has been presented. The analysis has been done using a combined analytical and FEM method in which the discretization of the half-plane is not required and thereby minimizes the computational efforts considerably. The contact pressure distribution and the settlement profile for the selected cases of varying modulus half-plane, which has more relevance to foundation engineering, have been given. Experimental verification through a photoelastic method of stress analysis has been carried out for the case of footing on Gibson elastic half-plane, and the contact pressure distribution thus obtained has been compared with the theoretical results. Copyright (C) 1996 Elsevier Science Ltd

The chemistry of a non-natural product: Troger's base

Troger's base was the first amine to be resolved where the chirality was solely due to very high inversion barrier around nitrogen atom(s). Though the molecule was known over a century, work done during the past one decade has shown that Troger's base and its analogues could be used as chiral solvating agents, DNA-binding ligands and for the construction of biomimetic molecular receptors and clathrate hosts, Asymmetric synthesis of Troger's base analogues has also been achieved recently, Because of the rigid, 'V'-shaped chiral nature of this molecule, there is a growing interest for use of this unit in the design of potential host systems, This review article focuses on the chemistry of Troger's base along with the possible future utilities.

Stability of non-parabolic flow in a flexible tube

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such 'non-parabolic' flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

NON-GLYCINE RESIDUES IN THE DISALLOWED REGIONS OF THE RAMACHANDRAN MAP AND THEIR NEIGHBORHOOD PREFERENCES

The allowed and the ``disallowed'' regions in the celebrated Ramachandran map (phi-psi] map) was elegantly deduced by Ramachandran, Ramakrishnan and Sasisekharan even before the protein crystal structures became available. This powerful map was derived based on rigid geometry of the peptide group and later several investigations on protein crystal structures reported the occurrence of a small fraction of the phi-psi] torsion angles in the disallowed region. The question is what factors make these residues adopt disallowed conformations? Is it driven by the necessity to maintain the overall topology or is it associated with function or is it just that the disallowed conformations are extreme limits of the allowed conformations? Today, with the availability of a large number of high resolution crystal structures, we have revisited this problem. Apart from validating some of the earlier findings such as residue propensities, preferred location in the secondary structure, we have explored their spatial neighborhood preferences using the protein structure network PSN] approach developed in our lab. Finally, the structural and functional implications of the disallowed conformations are examined.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

Direct measurements of growing amorphous order and non-monotonic dynamic correlations in a colloidal glass-former

The transformation of flowing liquids into rigid glasses is thought to involve increasingly cooperative relaxation dynamics as the temperature approaches that of the glass transition. However, the precise nature of this motion is unclear, and a complete understanding of vitrification thus remains elusive. Of the numerous theoretical perspectives(1-4) devised to explain the process, random first-order theory (RFOT; refs 2,5) is a well-developed thermodynamic approach, which predicts a change in the shape of relaxing regions as the temperature is lowered. However, the existence of an underlying `ideal' glass transition predicted by RFOT remains debatable, largely because the key microscopic predictions concerning the growth of amorphous order and the nature of dynamic correlations lack experimental verification. Here, using holographic optical tweezers, we freeze a wall of particles in a two-dimensional colloidal glass-forming liquid and provide direct evidence for growing amorphous order in the form of a static point-to-set length. We uncover the non-monotonic dependence of dynamic correlations on area fraction and show that this non-monotonicity follows directly from the change in morphology and internal structure of cooperatively rearranging regions(6,7). Our findings support RFOT and thereby constitute a crucial step in distinguishing between competing theories of glass formation.

Multiobjective Optimization of Piezoelectric Bimorph Actuator with Rigid Extension

Production of high tip deflection in a piezoelectric bimorph laminar actuator by applying high voltage is limited by many physical constraints. Therefore, piezoelectric bimorph actuator with a rigid extension of non-piezoelectric material at its tip is used to increase the tip deflection of such an actuator. Research on this type of piezoelectric bending actuator is either limited to first order constitutive relations, which do not include non-linear behavior of piezoelectric element at high electric field, or limited to curve fitting techniques. Therefore, this paper considers high electric field, and analytically models tapered piezoelectric bimorph actuator with a rigid extension of non-piezoelectric material at its tip. The stiffness, capacitance, effective tip deflection, block force, output strain energy, output energy density, input electrical energy and energy efficiency of the actuator are calculated analytically. The paper also discusses the multi-objective optimization of this type of actuator subjected to the mechanical and electrical constraints.

Non-Slipping Jkr Model For Transversely Isotropic Materials

A generalized plane strain JKR model is established for non-slipping adhesive contact between an elastic transversely isotropic cylinder and a dissimilar elastic transversely isotropic half plane, in which a pulling force acts on the cylinder with the pulling direction at an angle inclined to the contact interface. Full-coupled solutions are obtained through the Griffith energy balance between elastic and surface energies. The analysis shows that, for a special case, i.e., the direction of pulling normal to the contact interface, the full-coupled solution can be approximated by a non-oscillatory one, in which the critical pull-off force, pull-off contact half-width and adhesion strength can be expressed explicitly. For the other cases, i.e., the direction of pulling inclined to the contact interface, tangential tractions have significant effects on the pull-off process, it should be described by an exact full-coupled solution. The elastic anisotropy leads to an orientation-dependent pull-off force and adhesion strength. This study could not only supply an exact solution to the generalized JKR model of transversely isotropic materials, but also suggest a reversible adhesion sensor designed by transversely isotropic materials, such as PZT or fiber-reinforced materials with parallel fibers. (c) 2007 Elsevier Ltd. All rights reserved.

Bio-inspired mechanics of reversible adhesion: Orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials

Geckos and many insects have evolved elastically anisotropic adhesive tissues with hierarchical structures that allow these animals not only to adhere robustly to rough surfaces but also to detach easily upon movement. In order to improve Our understanding of the role of elastic anisotropy in reversible adhesion, here we extend the classical JKR model of adhesive contact mechanics to anisotropic materials. In particular, we consider the plane strain problem of a rigid cylinder in non-slipping adhesive contact with a transversely isotropic elastic half space with the axis of symmetry oriented at an angle inclined to the surface. The cylinder is then subjected to an arbitrarily oriented pulling force. The critical force and contact width at pull-off are calculated as a function of the pulling angle. The analysis shows that elastic anisotropy leads to an orientation-dependent adhesion strength which can vary strongly with the direction of pulling. This study may suggest possible mechanisms by which reversible adhesion devices can be designed for engineering applications. (C) 2006 Elsevier Ltd. All rights reserved.

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Eliminating False Matches for the Projective Registration of Free-Form Surfaces with Small Translational Motions

Liu, Yonghuai. Eliminating False Matches for the Projective Registration of Free-Form Surfaces with Small Translational Motions. IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics, vol. 35, no. 3, pp. 607-624, 2005.