Determination of the complex shear modulus of structural adhesives using a doubly clamped sandwich beam

A method is described for calculating the complex shear modulus of structural adhesives from dynamic test data on a doubly clamped sandwich beam in which the adhesive is contained as a thin layer. The accuracy of the technique is validated by finite-element analysis. Values of modulus obtained using the doubly clamped beam technique are found to be in excellent agreement with values obtained from dynamic tests on bulk specimens of an epoxy adhesive.     

Recoil in macromolecular solutions according to rigid dumbbell kinetic theory

A macromolecular solution is represented by the simple model of rigid dumbbells suspended in a Newtonian fluid with Brownian motion included. Hydrodynamic interaction is not taken into account. It is found that for this model there will be recoil after the cessation of steady shearing flow. The ultimate shear recovery S _∞ is developed as a power series in κ^?, the shear rate prior to the cessation of the steady shear flow: $$S_\infty = (\theta _0 /2\eta _0 ) \kappa ^\user1{ - } + O(\kappa ^\user1{ - } )^3$$ where η₀ and θ₀ values of the viscosity and primary normal stress functions respectively at zero-shear rate. The coefficient of the term in (κ^?)³ is calculated. In addition, the behavior of the normal stresses during the recoil process is found; during recoil τ₂₂?τ₃₃ has the opposite sign from τ₁₁?τ₂₂.     

Reverse shear on inclined planes at the tip of a sharp crack

Plane strain plastic yielding at a crack tip has been represented by edge dislocations with Burgers vectors parallel to symmetrical planes inclined at 70° and 45° to the plane of the crack. The plastic displacement and the stresses near the crack tip were calculated by a numerical method and the effect of a reduction in applied stress was determined. Removal of the whole or a part of the initial load produces reverse shear in regions of the slip band nearest the crack tip. The amount of reverse shear depends only on the reduction in the load and not on its initial value. The reverse shear is associated with the presence of negative dislocations and the stresses near the crack tip may become compressive even though the applied (remote) stress is still tensile. The degree and extent of compression depends on the reduction in applied stress and on its original value. It is argued that the residual compressive stresses produced under fluctuating loads may produce crack closure and crack arrest. The effect of residual plasticity in a slip band left behind a growing crack has been estimated. It is shown that after an overload the excess residual plasticity opposing crack opening rises to a maximum value when the crack tip has advanced some distance from the point where the overload was applied.     

A strain-energy criterion for recognition of identified modes of continuous structural models

In structural modal analysis and modal testing, an important but difficult task is to match the identified natural frequencies and the corresponding modal deflections. This process is called the modal recognition in this paper. There were some treatments towards this problem for the lumped parameter structural models. For the distributed parameter models, however, little research has been reported on the modal recognition problem. In this paper, a strain-energy criterion for modal recognition has been developed. As an example, a distributed parameter model for a two-beam structural system has been formulated, which is expected to simulate the dynamics of a two-arm manipulating system fixed on a shuttle. Transfer matrix method has been used to set up the dynamic equation of the system. The natural frequencies are obtained from the solution of the characteristics equation. Consequently, the mode shape functions are found out analytically.

Strain energy can be viewed as a measure of the structural deformation. When performing modal analysis, we always assume that the structural system is vibrating at a particular natural frequency. The strain energy is, therefore, stored in the deflection caused by such a harmonic motion. The vibration at a particular natural frequency will not produce any strain energy in the other modal components. On the other hand, if a particular mode shape is contributed mostly by the deformation of a specific component of the global structural system, then the great percentage of the total strain energy will be stored in the deformation of that component. Based upon the calculation of the strain energy in the structural components we can find out which component is deformed most and in what motion it is deformed, thereby, the mode shape can be detected. The computer simulation demonstrated that the strain energy indicated an essentially perfect recognition of the identified natural frequencies with the corresponding mode shapes. The creation of the strain-energy criterion consummates the procedure of the distributed parameter modeling, modal identification and parameter estimation.     

The effect of a transverse shear acting on the edge of a circular cutout in a simply supported circular cylindrical shell

Summary First, the solution to the problem of a simply supported circular cylindrical shell (without a cutout) subjected to a circumferential segmental line load at the middle of the shell is derived. Next, the negatives of the stress resultants and stress couples at a given radius ₀, obtained from this solution, are combined with a transverse shear force to form the edge conditions for a circular cylindrical shell containing a circular cutout with radius ₀. The desired solution is finally obtained by superposing the above two solutions. The convergence of the series, obtained in the first part, is improved for the complete region near and on the segmental line load. Numerical results are presented.

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Übersicht Es wird zunächst die Lösung für die Spannungsverteilung in einer einfach gelagerten kreiszylindrischen Schale ohne Ausschnitt angegeben. Die Schale wird durch eine Linienlast längs eines Umfangs in der Mitte der Schale belastet. Die hierfür erhaltenen Kräfte und Momente für einen gegebenen Radius ₀ werden dann mit einer Quer-Schubkraft kombiniert, um die Randbedingungen für eine kreiszylindrische Schale mit rundem Ausschnitt vom Radius ₀ zu erhalten. Die gewünschte Lösung wird schließlich durch Überlagerung der beiden Teillösungen erhalten. Die Konvergenz der dabei auftretenden Reihenentwicklungen wird für den Bereich der Belastungslinie verbessert. Numerische Ergebnisse werden angegeben.

     

Multistep energy and electron transfer processes in novel rotaxane donor–acceptor hybrids generating microsecond-lived charge separated states

A new set of [Cu(phen)₂]⁺ based rotaxanes, featuring [60]-fullerene as an electron acceptor and a variety of electron donating moieties, namely zinc porphyrin (ZnP), zinc phthalocyanine (ZnPc) and ferrocene (Fc), has been synthesized and fully characterized with respect to electrochemical and photophysical properties. The assembly of the rotaxanes has been achieved using a slight variation of our previously reported synthetic strategy that combines the Cu(i)-catalyzed azide–alkyne cycloaddition reaction (the “click” or CuAAC reaction) with Sauvage''s metal-template protocol. To underline our results, complementary model rotaxanes and catenanes have been prepared using the same strategy and their electrochemistry and photo-induced processes have been investigated. Insights into excited state interactions have been afforded from steady state and time resolved emission spectroscopy as well as transient absorption spectroscopy. It has been found that photo-excitation of the present rotaxanes triggers a cascade of multi-step energy and electron transfer events that ultimately leads to remarkably long-lived charge separated states featuring one-electron reduced C₆₀ radical anion (C₆₀˙^–) and either one-electron oxidized porphyrin (ZnP˙⁺) or one-electron oxidized ferrocene (Fc˙⁺) with lifetimes up to 61 microseconds. In addition, shorter-lived charge separated states involving one-electron oxidized copper complexes ([Cu(phen)₂]²⁺ (τ < 100 ns)), one-electron oxidized zinc phthalocyanine (ZnPc˙⁺; τ = 380–560 ns), or ZnP˙⁺ (τ = 2.3–8.4 μs), and C₆₀˙^– have been identified as intermediates during the sequence. Detailed energy diagrams illustrate the sequence and rate constants of the photophysical events occurring with the mechanically-linked chromophores. This work pioneers the exploration of mechanically-linked systems as platforms to position three distinct chromophores, which are able to absorb light over a very wide range of the visible region, triggering a cascade of short-range energy and electron transfer processes to afford long-lived charge separated states.     

Direct Photoredox‐Catalyzed Reductive Difluoromethylation of Electron‐Deficient Alkenes

Photoredox‐catalyzed reductive difluoromethylation of electron‐deficient alkenes was achieved in one step under tin‐free, mild and neutral conditions. This protocol affords a facile method to introduce RCF₂ (R=H, Ph, Me, and CH₂N₃) groups at sites β to electron‐withdrawing groups. It was found that TTMS (tris(trimethylsilyl)silane) served nicely as both the H‐atom donor and the electron donor in the catalytic cycle. Experimental and DFT computational results provided evidence that RCF₂ (R=H, Ph, Me) radicals are nucleophilic in nature.     

Dynamic plastic response of foil gages

Little research has been devoted to the accuracy of the response of resistance strain gages to dynamic plastic strain because of the lack of an easy-to-use comparative strain-measuring technique. The dynamic interferometric strain gage provides a suitable standard of comparison. Foil-gage response is compared directly with interferometric strain-gage response in a longitudinal-impact experiment. The accuracy of the foil gage does not decrease with increasing maximum strain (up to 8 percent). The error in shape of the strain wave does not vary drastically with distance from the point of impact. In contrast to previous work, foil gages are found to be reasonably accurate strain transducers for dynamic plastic strain.     

Measurement of unsteady surface pressure on a slender wing undergoing a self-induced oscillation

Summary The methodology outlined here was shown to be an effective means by which detailed unsteady surface pressure measurements may be obtained on a wing undergoing a self-induced oscillation in a wind tunnel study. Previous methods have relied on forcing the wing through a sinusoidal motion at a fixed amplitude and frequency. The advantage of the technique outlined here is that pressure measurements are obtained for the exact motion time history, including all transient motions. In fact, almost any self-induced or forced motion may be implemented by the system. The method also has the advantage of a significant reduction in the cost of pressure transducers due to the repeatability of the unsteady flowfield.Funds for the support of this study have been allocated by the NASA-Ames Research Center, Moffett Field, California, under Interchange No. NCA2406, and the University of Notre Dame     

Design and stress evaluation of a nonsymmetric pressure vessel

Presently, the large variation in demand for electrical power at different periods of the day imposes new considerations in the evaluation of pressure components in large steam-generating equipment. In the past, pressure components such as valve bodies have been designed for static pressure conditions against bursting with sufficient stiffness to assure operation ability. In today's plant operation, the response of the valve body to thermal transients will have a major influence on the life of the valve. Since the valve body is a compact nonsymmetric body, the direct calculation of stresses is very complex. The evaluation of the behavior of nonsymmetric pressure components under the loads imposed by various operational modes requires information from both analytical and experimental methods of analysis. The contributions from modern computer-calculation programs and three-dimensional photoelasticity are discussed as applied to the evaluation of a valve body used in a large, supercritical steam generator. In the analysis, computer procedures are used to develop the preliminary geometry for pressure loading. Because of the close proximity of the nonsymmetrical openings, a three-dimensional photoelastic analysis is used to calibrate the computer model. Once a satisfactory computer model has been developed for pressure loading, it is used to calculate the thermal stresses. Since stresses have little meaning in themselves, a design basis is necessary to evaluate the significance of the calculated stresses. The design basis must consider the types of failures which are possible and is thus dependent on the temperature at which the valve must operate. A design basis is discussed for the evaluation of pressure components in a boiler system.