An experimental investigation of wave propagation in a rubber string impacted by a projectile2

Transverse perpendicular impact on long rubber strings of 0.140 and 0.277 in. dia was studied using a special apparatus consisting of a system of oscilloscopes, stroboscopes, camera and air pressure gun. The rubbers used in tests came from two manufacturers and were classified as pure gum rubbers. Three different initial stretches λ₀ were chosen for each string, and the impact velocities ranged from 1000 to 3000 in. sec. Maximum stretch, kink angles and impact velocities were measured and the following relations recorded : nominal stress vs stretch, kink angle vs impact velocity, maximum stretch λ_max vs impact velocity and the difference λ_max ? λ₀ vs non-dimensional impact velocity. Some of the results are compared with the theoretical data for the Mooney-Rivlin and the Isihara-Hashitsume-Tatibana-Zahorski materials, and others with the results of theoretical equations upon inserting experimental data.     

Nonlinear vibrations of an elastic disk rotating in a viscous fluid

Summary The von Kármán equations are extended to the dynamic case and to manifest the effects of the viscosity of fluid in which the motion takes place. The hydrodynamic aspect of the problem is analyzed and the flow pattern based on the von Kármán solution derived. The system of two nonlinear coupled differential equations is solved for weakened boundary conditions using the Galerkin procedure. A numerical example given for the mode of two nodal diameters and no nodal circles shows that: (a) the period of linear vibrations, T, is markedly increased by the presence of the viscous fluid; (b) the ratio T ^*/T(T ^* = period of nonlinear vibrations) decreases with an increasing amplitude, increases with an increasing speed of rotation, and increases with conversion to vacuum.

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Nichtlineare Schwingungen einer in einer viskosen Flüssigkeit rotierenden, elastischen Scheibe

Übersicht Die von Kármánschen Gleichungen werden auf den dynamischen Fall erweitert, und der Einfluß der Viskosität der Flüssigkeit, in der die Scheibe rotiert, wird in die Untersuchung einbezogen. Dabei werden sowohl der hydrodynamische als auch der elastodynamische Aspekt des Problems behandelt. Das System von zwei nichtlinearen, gekoppelten Differentialgleichungen wird mit Hilfe des Verfahrens von Galerkin für abgeschwächte Randbedingungen gelöst.Ein numerisches Beispiel für zwei Knotendurchmesser und keine Knotenkreise zeigt: a) die Schwingungsdauer T der linearen Schwingungen wird durch die viskose Flüssigkeit beträchtlich erhöht; b) das Verhältnis T ^*/T (T ^* = Periode der nichtlinearen Schwingungen) nimmt mit wachsender Amplitude ab, wächst mit steigender Drehzahl und wächst beim Übergang zu Vakuum.

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This work was partially supported by the University of Delaware     

Sequence, structure, and function of peptide self-assembled monolayers

Cysteine is commonly used to attach peptides onto gold surfaces. Here we show that the inclusion of an additional linker with a length of four residues (-PPPPC) and a rigid, hydrophobic nature is a better choice for forming peptide self-assembled monolayers (SAMs) with a well-ordered structure and high surface density. We compared the structure and function of the nonfouling peptide EKEKEKE-PPPPC-Am with EKEKEKE-C-Am. Circular dichroism, attenuated total internal reflection Fourier transform IR spectroscopy, and molecular dynamics results showed that EKEKEKE-PPPPC-Am forms a secondary structure while EKEKEKE-C-Am has a random structure. Surface plasmon resonance sensor results showed that protein adsorption on EKEKEKE-PPPPC-Am/gold is very low with small variation while protein adsorption on EKEKEKE-C-Am/gold is high with large variation. X-ray photoelectron spectroscopy results showed that both peptides have strong gold-thiol binding with the gold surface, indicating that their difference in protein adsorption is due to their assembled structures. Further experimental and simulation studies were performed to show that -PPPPC is a better linker than -PC, -PPC, and -PPPC. Finally, we extended EKEKEKE-PPPPC-Am with the cell-binding sequence RGD and demonstrated control over specific versus nonspecific cell adhesion without using poly(ethylene glycol). Adding a functional peptide to the nonfouling EK sequence avoids complex chemistries that are used for its connection to synthetic materials.     

Thermoelastic problem for shells of revolution exhibiting temperature dependent properties

Summary Analysis of the axially symmetric steady state thermoelastic problem for thin shells of revolution is given, assuming temperature dependent elastic and thermal properties of the material. Three governing equations are established involving components of the displacement along and normal to the meridian as well as the shearing force.A multi-parameter perturbation scheme is used with two perturbation parameters, one associated with the shear modulus and the other with Poisson's ratio.Illustrative examples are solved concerning cylindrical, conical and spherical shells as well as compound shells, such as spherico-conical, conicocylindrical and conico-conical.The results presented in this paper are taken from a thesis by the first author submitted in partial fulfilment of the requirements for the Ph. D. degree at the University of Delaware. The research was supported by a grant of the National Science Foundation.     

Novel nanomaterials based on electronic and mixed conductive glasses

Novel nanomaterials based on lithium–vanadate-phosphate (LVP) and lithium–iron-phosphate (LFP) glasses were prepared and their electrical properties were investigated by impedance spectroscopy. It was found out that the electronic conductivity of the original glasses of both systems can be considerably enhanced by appropriate annealing at temperatures close to beginning of crystallization temperatures determined by DSC/DTA methods. Increase in conductivity arises from the modification of the microstructure. It was shown by XRD and SEM studies that by appropriate heat-treatment glasses of both systems can be turned into nanomaterials consisting of crystallites smaller than 100 nm embedded in the glassy matrix. It was postulated that the major role in the conductivity enhancement of these nanomaterials is played by the developed interfacial regions between nanocrystalline and glassy phases, in which the concentration of V⁴⁺–V⁵⁺ or Fe²⁺–Fe³⁺, pairs responsible for electron hopping in those systems, is higher than inside the glassy matrix and the formed nanocrystallites.     

Cylindrically orthotropic circular plates with large deflections

Zusammenfassung Es werden die Verschiebungs- und Spannungszustände in einer Kreisplatte mit grossen Durchbiegungen und zylindrischer Orthotropie mit Hilfe zweier Methoden untersucht, nämlich der Methode des kleinen Parameters vonPoincaré und einer modifizierten Methode vonGalerkin.Ein numerisches Beispiel für gleichmässige Belastung der Platte, die Poissonsche Zahlv =1/4 und die Beziehungv :v _r =4 wird gegeben.

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This work has been sponsored by the United States Army under contract No. DA-11-002-ORD-2059     

A Betti-Rayleigh theorem for elastic bodies exhibiting temperature dependent properties

Summary The reciprocal theorem of Betti and Rayleigh is extended to thermoelastic problems concerning temperature dependent properties of the bodies. Illustrative examples are solved concerning extension and flexural rotation of a bar, change of volume of a body without and with a cavity, and the thermoelastic displacement. This work has been sponsored by the United States Army under contract No. DA-11-022-ORD-2059.     

On the impossibility of determination of stepwise binding constants for the 1 : 2 complex of (+)-camphor with alpha-cyclodextrin

Knowledge of stepwise binding constants for complexes with higher than 1:1 stoichiometry would allow one to study the cooperativity of their formation. However, a detailed analysis of partitioning of the overall binding constant beta 12 determined by NMR titrations for the 1:2 complex of (+)-camphor with alpha-cyclodextrin into the stepwise ones K1 and K2 carried out analogously to published procedures revealed that the partitioning cannot be carried out unequivocally for K1 < K2. The programs for partitioning cannot be used as a black box and a satisfactory reproduction of the experimental dependence of relative shifts as a function of relative CD concentration should not be the only criterion of the reliability of the stepwise binding constants obtained using such programs.     

Note on the applications of the Fréchet derivative

A brief review of the main concepts underlying the operation of differentiation of non-linear mappings is followed by examples of the application of the operation; two of the five examples given concern the theory of the non-linear viscoelaslicity and the theory of the non-linear non-local elasticity.