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Stiff Stiffness

Stiffness Stiffness is a spring-like property that describes the level of resisting force that results when a body undergoes a change in length. Units of stiffness are often given as pounds per inch (Ibf/in). Machine-trains have more than one stiffness property that must be considered in vibration analysis shaft stiffness, vertical stiffness, and horizontal stiffness. [Pg.677]

This problem is identical to that of calculating the configurational entropy for the case of perfectly stiff (stiff but not straight) chains and has been given previously 4-6), A little algebra shows that the logc(p) varies as... [Pg.34]

One problem that is encountered in solving the equations that describe real chemical oscillators is stiffness. Stiffness is a property of differential equations whose solutions contain two or more very different time scales. [Pg.146]

Yellows at high temp May smoke Hazy, translucent Absorbs moisture Yellows at high temp Splitty at low temps FR grades stiff Stiff at mod temps... [Pg.8482]

Contrast in stiffness (stiff, dense material over plastic material)... [Pg.324]

Contact stiffness — stiffness between debris and structure,... [Pg.269]

Figure 24. Predictions of PRISM theory with the PYclosure for the low wave vector common block collective structure factor for the athermal copolymer models listed in Table II. Note that the common block structure factor intensifies monotonicaily as the overall copolymer stiffness stiffness increases due to increasing B-block aspect ratio. Figure 24. Predictions of PRISM theory with the PYclosure for the low wave vector common block collective structure factor for the athermal copolymer models listed in Table II. Note that the common block structure factor intensifies monotonicaily as the overall copolymer stiffness stiffness increases due to increasing B-block aspect ratio.
Figure 30. Diagonal values (flexible-flexible and stiff-stiff) of the effective composition s as a function of reduced inverse temperature for various choices of the correiation radius R and / = ( for model C. The size of the flexible block is R f = 6.4 Figure 30. Diagonal values (flexible-flexible and stiff-stiff) of the effective composition s as a function of reduced inverse temperature for various choices of the correiation radius R and / = ( for model C. The size of the flexible block is R f = 6.4<f, the overall diblock size is R = 10.2d, the microdomain length scale is D = 32.8d.
Zinc oxide increases tack and cohesive strength in these polymers (and also plays an important chemical role in the vulcanization of butyl). Aluminum hydrate, lithopone, whiting, and the coarser carbon blacks such as thermal blacks also increase tack with moderate increase in cohesivity. Clays, hydrated silicas, calcium silicates, silico-aluminates, and the fine furnace and thermal blacks increase cohesive strength and stiffness. Stiffness can also be increased by use of very fine silica pigment and magnesium oxide or carbonate. [Pg.189]

The cantilever has to be reasonably stiff, or it would not penetrate the sample, and if it was too stiff, it would always penetrate. The cantilever and the sample are mechanically in series, and the best sensitivity is when the two are of similar stiffness. Stiff samples require stiff cantilevers. [Pg.104]

Solver Explicit/ implicit Single step/ multi-step Non- stiff/stiff Accuracy Method... [Pg.115]

The magnitudes of and increase with increasing chain stiffness stiffness is enhanced by the presence of chain double bonds and side groups that are either bulky or polar. [Pg.625]

Secondly, the stiffness of traditional viscoelastic damping polymers is much lower than the host composite structure. Carbon nanotube films on the other hand offer multifunctionality in terms of enhanced sfiength, stiffness, and fracture toughness, in addition to damping augmentation. The specific stiffness (stiffness/density ratio) of the nanotube-epoxy film developed is about three orders of magnitude greater than the Dyad-606 polymer film [94,95]. [Pg.205]

This type of coil was prepared from copper cladded printed circuit board material by applying photolithographic techniques. The p.c. board material is available with difierent copper thicknesses and with either a stiff or a flexible carrier. The flexible material offers the opportunity to adapt the planar coil to a curved three dimensional test object. In our turbine blade application this is a major advantage. The thickness of the copper layer was chosen to be 17 pm The period of the coil was 100 pm The coils were patterned by wet etching, A major advantage of this approach is the parallel processing with narrow tolerances, resulting in many identical Eddy current probes. An example of such a probe is shown in fig. 10. [Pg.303]

A major advance in force measurement was the development by Tabor, Win-terton and Israelachvili of a surface force apparatus (SFA) involving crossed cylinders coated with molecularly smooth cleaved mica sheets [11, 28]. A current version of an apparatus is shown in Fig. VI-4 from Ref. 29. The separation between surfaces is measured interferometrically to a precision of 0.1 nm the surfaces are driven together with piezoelectric transducers. The combination of a stiff double-cantilever spring with one of a number of measuring leaf springs provides force resolution down to 10 dyn (10 N). Since its development, several groups have used the SFA to measure the retarded and unretarded dispersion forces, electrostatic repulsions in a variety of electrolytes, structural and solvation forces (see below), and numerous studies of polymeric and biological systems. [Pg.236]

Modification of an AFM to operate in a dynamic mode aids the study of soft biological materials [58]. Here a stiff cantilever is oscillated near its resonant frequency with an amplitude of about 0.5 nm forces are detected as a shift to a new frequency... [Pg.297]

The index J can label quantum states of the same or different chemical species. Equation (A3.13.20) corresponds to a generally stiff initial value problem [42, 43]. In matrix notation one may write ... [Pg.1050]

When the lever is intended for use with the tip separated from the surface, the lever stiffness is usually greater... [Pg.1693]

Pulsed-force mode AFM (PFM-AFM) is a method introduced for fast mapping of local stiffness and adliesion with lower required data storage than recording force-distance curves at each point on the x-y plane [115]. A sinusoidal or triangular modulation is applied between the tip and sample (either via lever or sample piezo) at a lower frequency than that of either the piezo or cantilever resonance frequency. Tip and sample then come... [Pg.1700]

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. [Pg.2366]

Salto N, Takahashi K and Yunoli Y 1967 The statistical mechanical theory of stiff chains J Phys. See. Japan 22 219... [Pg.2384]

It is not possible to apply (C2.1.1) down to the level of monomers and replace by the degree of polymerization N and f by the sum of the squares of the bond lengths in the monomer because the chemical constitution imposes some stiffness to the chain on the length scale of a few monomer units. This effect is accounted for by introducing the characteristic ratio defined as C- — The characteristic ratio can be detennined... [Pg.2517]

Ceramic fonning typically involves using pressure to compact and mould particles to the desired size and shape. Ceramics can be fonned from slurries, pastes, plastic bodies (i.e. such as a stiff mud), and from wet and dry powders. [Pg.2766]

In this section we describe the behavior of a ligand subjected to three types of external forces a constant force, forces exerted by a moving stiff harmonic spring, and forces exerted by a soft harmonic spring. We then present a method of reconstruction of the potential of mean force from SMD force measurements employing a stiff spring (Izrailev et al., 1997 Balsera ct al., 1997). [Pg.55]

Stiff Spring For a stiff spring, satisfying K (fiUjdx, under the overdamped condition assumed in (3) the average force measured by the spring can be expressed as... [Pg.57]

The rupture force measured in AFM experiments is given, therefore, by the average slope of the energy profile minus a correction related to the effects of thermal fluctuations. Equation (11) demonstrates that the rupture force measured in AFM experiments grows linearly with the activation energy of the system (Chilcotti et ah, 1995). A comparison of (10) and (11) shows that the unbinding induced by stiff springs in SMD simulations, and that induced by AFM differ drastically, and that the forces measured by both techniques cannot be readily related. [Pg.58]

M. E. Tuckerman and B. J. Berne. Molecular dynamics in systems with multiple time scales Systems with stiff and soft degrees of freedom and with short and long range forces. J. Comp. Chem., 95 8362-8364, 1992. [Pg.258]

E. Hairer and G. Wanner. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, volume 14 of Springer Series in Computational Mathematics. Springer-Verlag, New York, New York, second edition, 1996. [Pg.259]

As our first model problem, we take the motion of a diatomic molecule under an external force field. For simplicity, it is assumed that (i) the motion is pla nar, (ii) the two atoms have equal mass m = 1, and (iii) the chemical bond is modeled by a stiff harmonic spring with equilibrium length ro = 1. Denoting the positions of the two atoms hy e 71, i = 1,2, the corresponding Hamiltonian function is of type... [Pg.286]

The standard discretization for the equations (9) in molecular dynamics is the (explicit) Verlet method. Stability considerations imply that the Verlet method must be applied with a step-size restriction k < e = j2jK,. Various methods have been suggested to avoid this step-size barrier. The most popular is to replace the stiff spring by a holonomic constraint, as in (4). For our first model problem, this leads to the equations d... [Pg.288]

We apply the semi-implicit algorithm to handle the weak potentials Vi, and the energy conserving method (16) for the stiff forces. The maximal error in the total energy, i.e. [Pg.292]

Next, we replace the stiff spring potential a(r — 1) /2 by the Morse potential... [Pg.293]


See other pages where Stiff Stiffness is mentioned: [Pg.209]    [Pg.360]    [Pg.531]    [Pg.69]    [Pg.237]    [Pg.213]    [Pg.92]    [Pg.341]    [Pg.1728]    [Pg.49]    [Pg.49]    [Pg.135]    [Pg.236]    [Pg.399]    [Pg.855]    [Pg.878]    [Pg.901]    [Pg.1696]    [Pg.1696]    [Pg.1701]    [Pg.1701]    [Pg.1701]    [Pg.1709]    [Pg.2250]    [Pg.2253]    [Pg.2353]    [Pg.2367]    [Pg.2367]    [Pg.2524]    [Pg.2760]    [Pg.3008]    [Pg.41]    [Pg.42]    [Pg.43]    [Pg.50]    [Pg.57]    [Pg.57]    [Pg.58]    [Pg.143]   
See also in sourсe #XX -- [ Pg.31 , Pg.58 , Pg.111 , Pg.115 , Pg.128 , Pg.255 ]




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Acoustics to Select for Stiffness

Adherends stiffness

Adhesive stiff

Adhesive stiffness

Algorithms for stiff problems

Angle-ply laminate stiffnesses

Atomic stiffness

Axial stiffness

Beams stiffness factor

Bending and Fiber Stiffness

Bending beam rheometer test for flexural creep stiffness

Bending stiffness and

Bending stiffness factor

Bending stiffness matrix

Block copolymer strength/stiffness

Bond Stiffness versus Modulus

Bond stiffness

Breeding for Increased Stiffness

Calculated surface stiffness and tip penetration

Calculated surface stiffness and tip penetration depths

Cantilever stiffness

Capsule stiffness

Cellulose Chain stiffness

Cellulose stiffness

Chain flexibility stiffness

Chain segment stiffness

Chain stiffening/stiffness

Chain stiffness

Chain stiffness factor

Chain stiffness parameter

Chain stiffness physical properties

Chain stiffness, measure

Chain stiffness, polymer glass formation

Chemical potential stiffness

Coating stiffness

Coefficient of stiffness

Combined Stiffness and Impact Properties

Composites stiffness

Composites strength and stiffness

Conformation conformational stiffness

Conservation equations stiffness

Contact stiffness

Contact stiffness mechanical properties

Contact stiffness, response amplitude

Continuous stiffness measurement

Continuous stiffness module

Control valves stiffness

Cooling stiffness

Copolymers stiffness

Cortical bone stiffness

Coupling stiffness matrix

Coupling stiffnesses

Crack stiffness

Craze stiffness

Cross-coupling stiffness

Cross-ply laminate stiffnesses

Cylinder stiffness

Debye stiffness

Deformation of Networks with Stiff Aromatic Segments and Relatively Flexible Aliphatic Junctions Created from Reactive End-Caps

Density stiffness

Design considerations stiffness aspects

Design for Stiffness

Design of stiffness rings

Design stiffness increase

Design stiffness-critical

Designing for stiffness

Determination of stiffness modulus and other moduli

Determining stiffness parameter values

Dielectric stiffness constant

Differential equations stiffness

Dynamic stiffness

Dynamic stiffness measurements

Dynamical systems stiffness

Effect of Stiffness

Effect of internal rotation and stiff chains

Effective contact stiffness

Elastic modulus from contact stiffness

Elastic properties stiffness

Elastic stiffness

Elastic stiffness coefficients

Elastic stiffness modulus, complex

Elastic stiffness tensor

Elastomers stiff fillers

Element stiffness matrix

Epoxy network chain stiffness

Epoxy stiffness

Equivalent stiffness tensor

Estimation of stiffness modulus

Exchange constant stiffness)

Exchange stiffness

Experimental Determination of Strength and Stiffness

Extensional stiffness matrix

Extrusion stiffness

Fabric bending stiffness

Fabric bending stiffness test

Fastener stiffness

Fiber chain stiffness

Fibers stiffness

Flexible-stiff

Flexible-stiff polymers

Flexible-stiff side group size

Flexural creep stiffness

Flexural stiffness

Flexural stiffness matrix

Force and interaction stiffness curves

Frame stiffness

Functional Integration Stiff Polymer Chains

Gehman Torsional Stiffness Tester

Geometric stiffness

Glass transition temperature contact stiffness

Glass-transition temperature chain stiffness

Global stiffness matrix

Global stiffness properties

Gough stiffness

Graphite stiffness

Homopolymer stiff

Hydrogen bonds bond stiffness

Impact modification Balancing stiffness with toughness

In-plane stiffness matrix

Increase in Stiffness during Cure Isothermal MDR

Increasing strength and stiffness

Independent stiffness constants

Indicative stiffness modulus results

Influence of substrate stiffness on surface stability

Initial value problems stiffness

Interfacial stiffness

Interphase stiffness

Invariant Laminate Stiffnesses

Invariant stiffness concepts

Inversion of Stiffness Equations

Joint stiffness

Lambs, stiffness

Lamina stiffness

Lamina stiffness plane

Lamina stiffness shear

Lamina stiffness unidirectional reinforcement

Laminate plate and shell stiffness classical lamination theory (CLT)

Laminate stiffness experimental mechanics

Laminate stiffnesses

Laminated plates stiffnesses

Lateral contact stiffness

Lateral stiffness

Linear stiffness matrix

Local stiffness approximation

Longitudinal stiffness

Macromolecules stiff

Magnetic stiffness

Mapping surface: stiffness imaging

Material properties stiffness

Materials science stiffness

Mathematically stiff equations

Matrix stiffness tensor

Measurement of stiffness

Mechanical properties stiffness

Mechanical responses bending stiffness

Mechanical stiffness

Modeling approaches stiffness

Modeling the stiffness and strength of aerospace structural elements

Modulus and stiffness

Morning stiffness

Multivalue Algorithms for Stiff Problems

Muscle/tendon stiffness

Nausea neck, stiff

Neck stiffness

Neck, stiff

Networks with Flexible Chains and Stiff Mesogenic Groups

Networks with Stiff Hydrocarbon Segments

Networks with Stiff Main-Chain Mesogens, Flexible spacers and Rigid Branchpoints

Networks with Stiff Pendant Mesogens Connected at Both Ends to Flexible Main Chains

New optical methods for measuring laminate stiffness

Notch stiffness

Numerical Method of Lines for Stiff Nonlinear PDEs

Numerical Solution of Stiff Equations

Numerical integration stiff problems

Octahedral shear stiffness

Operator Splitting and Stiffness

Optical tweezers stiffness

Ordinary differential equations stiffness conditions

Ordinary differential equations with stiffness

Ordinary differential equations, initial value stiffness

Other prediction models of asphalt stiffness

Overconsolidated stiff clays

Pad Hardness, Youngs Modulus, Stiffness, and Thickness Effects

Parameter Identification Step 2 Stiffness and Fine-Tuning

Passive stiffness

Persistence length and the stiff chain

Persistence length stiff chain polymers

Phonon Frequency and Segmental Stiffness

Poly stiffness

Polyelectrolyte chain stiffness

Polyethylene elastic stiffness constants

Polymer blends stiffness

Polymer chain structure stiffness

Polymer selection stiffness

Polymer stiffness

Polymer stiffness chain

Polymers stiff

Polymers with Stiff, Bulky Substituents

Polyolefin polymer stiffness

Polypropylene stiffness/toughness properties

Polypropylenes stiffness

Positioner/actuator stiffness

Post-Fire Stiffness

Prediction of asphalt stiffness

Quantitative measurements of contact stiffness

Quasi-stiffness

Really Stiff Structures Bars

Reduced bending stiffness

Reduced stiffnesses

Reduction and Degradation of Stiffness

Rigid Networks from Stiff End-Capped Segments

Robertson-StifF model

Robertson-Stiff rheology model

SFM-Based Stiffness Mapping in Force Modulation Microscopy (FMM) Mode

Sandwich structures continued stiffnesses

Scaffold stiffness

Scaling indices Stiff-Davis index

Secondary stiffness

Selectivity stiff differential equations

Shape selection to optimise stiffness

Shape stiffness-stress

Shear stiffness

Soft tissues stiffness

Solubilization stiff surfactant systems

Special Angle-Ply Laminate Stiffnesses

Special Cross-Ply Laminate Stiffnesses

Special Results for Invariant Laminate Stiffnesses

Specific stiffness

Spring stiffness

Step stiffness

Stick stiffness

Sticking Stiffness

Stiff

Stiff Equations and Implicit Methods

Stiff Model Problems

Stiff ODE Models

Stiff ODEs

Stiff Stiffening

Stiff Stiffer

Stiff Virus Particles Polymer

Stiff and Davis Saturation

Stiff chain macromolecules

Stiff chain polymer

Stiff chains

Stiff chains wormlike

Stiff clay or silt

Stiff differential equations

Stiff dynamical systems

Stiff dynamical systems numerical simulation

Stiff equation and

Stiff equation sets

Stiff equations Newton iteration

Stiff equations explicit methods

Stiff equations implicit methods

Stiff equations model problem

Stiff extrusion

Stiff fibres

Stiff foam

Stiff gels, ceramics

Stiff host lattice

Stiff integration

Stiff integration algorithm

Stiff integration package

Stiff integrator

Stiff lamb disease

Stiff limbs

Stiff macroscopic defect

Stiff mixes

Stiff molecule

Stiff nonlinear partial differential

Stiff nonlinear partial differential equations

Stiff ordinary differential equations

Stiff ordinary differential equations solver

Stiff phenomenon

Stiff polymer molecules

Stiff polymers bending energy

Stiff polymers stiffness expansion

Stiff problems

Stiff quantum systems

Stiff shaft design

Stiff stability of BDF methods

Stiff structure

Stiff substituents, polyesters

Stiff surfactant systems

Stiff system of differential equations

Stiff systems

Stiff tissue

Stiff vibration

Stiff-Davis Saturation

Stiff-Davis index

Stiff-Davis saturation index

Stiff-equations

Stiff-flexible polymers formation mechanisms

Stiff-flexible polymers side group size

Stiff-man syndrome

Stiff-oscillatory system

Stiff-person syndrome

Stiffness

Stiffness

Stiffness , lumber

Stiffness Analysis of Solid Polymeric Materials

Stiffness Dimensioning

Stiffness PVC

Stiffness Strain compatibility

Stiffness Wormlike, chain

Stiffness analysis of polymer composites filled with spherical particles

Stiffness and Buckling

Stiffness and Elasticity

Stiffness and Strength

Stiffness and compliance transformations

Stiffness and deformation

Stiffness and toughness

Stiffness applications

Stiffness aramid/epoxy

Stiffness balance

Stiffness carbon/polyimide

Stiffness classical lamination theory

Stiffness coefficient matrix

Stiffness coefficients

Stiffness compliance transformations

Stiffness conformational

Stiffness constant

Stiffness critical products

Stiffness effective

Stiffness enhancement

Stiffness equation

Stiffness experimental data

Stiffness factor

Stiffness fibre

Stiffness flame retardants

Stiffness glass/epoxy composite

Stiffness high-density polyethylene

Stiffness in shear

Stiffness in torsion

Stiffness laminate properties

Stiffness linear elasticity

Stiffness mapping, scanning force

Stiffness matrix

Stiffness method

Stiffness mismatch

Stiffness modelling

Stiffness modelling analytical approaches

Stiffness modelling method of inclusions

Stiffness models

Stiffness modulus

Stiffness modulus of asphalts

Stiffness notched specimen

Stiffness of ODEs

Stiffness of Reaction Kinetic Models

Stiffness of bitumen

Stiffness of chain

Stiffness of fabrics

Stiffness of fill mass Settlements, horizontal deformations and tolerances

Stiffness of fill material

Stiffness of materials (with reference to GRP)

Stiffness of subsoil

Stiffness of the Covalent Bonds

Stiffness of the chain

Stiffness of the testing machine

Stiffness off-axis in-plane shear modulus for

Stiffness parameter

Stiffness polyimide

Stiffness properties

Stiffness ratio

Stiffness reduction effect

Stiffness response

Stiffness rubber

Stiffness system

Stiffness techniques

Stiffness temperature effects

Stiffness tensile

Stiffness tensor

Stiffness the model

Stiffness transverse shear modulus

Stiffness unidirectional composites

Stiffness values

Stiffness versus weight

Stiffness “persistence

Stiffness, defined

Stiffness, mathematical

Stiffness, numerical methods

Stiffness, of materials

Stiffness, of polymers

Stiffness, pad

Stiffness, significance

Stiffness-Impact Energy Relationship

Stiffness-Viscoelasticity

Stiffness-proportional method

Stiffness-sensitive structures

Stiffness-to-density ratios

Stiffness-to-weight ratio

Stiffness-toughness balance

Stiffness/steric interactions

Stiffnesses and Bucklings

Stiffnesses bending

Stiffnesses bending-extension

Stiffnesses compression

Stiffnesses definition

Stiffnesses elastic constants

Stiffnesses extensional

Stiffnesses index

Stiffnesses inversion

Stiffnesses materials

Stiffnesses measurement

Stiffnesses restrictions

Stiffnesses symmetry

Stiffnesses transformation

Stiffnesses transformed reduced

Strain-Induced Stiffness

Strength and Stiffness Advantages

Strength and Stiffness of Adhesives

Strength stiffness

Stress stiffness equation

Stress-strain relations stiffnesses

Stress-strain stiffness

Subgrade design CBR and surface stiffness modulus

Superstructure stiffness

Surface stiffness

Symmetric laminate stiffnesses

Tackling stiffness in process simulations by modifications to the model

Tackling stiffness in process simulations the properties of a stiff integration algorithm

Tests to characterise the stiffness and strength of pultruded GFRP joints

The problem of stiffness

The stiffness problem

Theoretical and Measured Cross-Ply Laminate Stiffnesses

Theoretical stiffness

Thermally Driven Density and Phonon-Stiffness Oscillation

Thin film coatings surface stiffness

Third-order stiffnesses

Three-dimensional reduced stiffness

Torsion stiffness

Torsional stiffness

Torsional stiffness tests

Transverse stiffness

Ultrasonic force microscopy stiffness

Understanding and predicting stiffness in advanced fibre-reinforced polymer (FRP) composites for structural applications

Understanding lamina stiffness

Use of Invariant Laminate Stiffnesses in Design

Variable stiffness laminates

Ventricular stiffness

Viscoelastic stiffness

Voigt elastic stiffnesses

Water structure, stiffness

Weak Stiffness

Woven composites stiffness modelling

Xanthan stiffness

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