Non-linear vibrations of three-layer beams with viscoelastic cores,II: Experiment

Experimental results are presented for large amplitude, forced motion of damped, three-layer beams. The beams are constructed with a viscoelastic material constrained between stiff, elastic, outer layers. The sandwich beam is axially restrained; therefore large amplitude displacements cause non-linear response. When the beam is forced at one-half of the lateral vibration resonant frequency, superharmonic response occurs. The experiment is briefly described and frequency response characteristics, spatial shapes and a measure of superharmonic response are presented. The results are compared with predictions from a previously developed theory.     

Selective Homogeneous Palladium(0)-Catalyzed Hydrogenation of Alkynes to (Z)-Alkenes

Zero-valent palladium precatalysts containing rigid bidentate bis(arylimino)acenaphthene ligands (shown schematically) facilitate the highly stereoselective homogeneous catalytic hydrogenation of alkynes to (Z)-alkenes. Internal, terminal, aryl-substituted, and cyclic alkynes are suitable substrates, as are some enynes, which are chemoselectively hydrogenated to dienes. E=CO(2)Me; R(1), R(2)=4-OCH(3), 4-CH(3), 2,6-(CH(3))(2).     

Photoelastic determination of stresses in multiple-pin connectors

The design, fabrication, and testing of photoelastic models of double-lap, multiple-pin connectors are discussed. Interest is in the stresses in the inner laps. These stresses are determined by constructing models with photoelastic inner laps and transparent-acrylic outer laps. The connectors have two pins, in tandem, parallel to the load direction. A photoelastic-isotropic point is shown to permit the evaluation of load sharing between the two pins. A numerical scheme, utilizing the isochromatic- and isoclinic-photoelastic data and a finite-difference representation of the planestress equilibrium equations, is used to compute the stresses around the two pins. Representative stress distributions and stress-concentration factors are shown.     

Non-linear vibrations of three-layer beams with viscoelastic cores I. Theory

Approximate equations of motion are developed for large amplitude motions of three-layer axially restrained unsymmetrical beams with viscoelastic cores. The external force consists of a constant plus an oscillatory term. The combination of this form of forcing and the large amplitude motions cause the beam to respond at multiples of the forcing frequency. This can lead to difficulties in the complex modulus approach to viscoelasticity. These are overcome here through use of hereditary integrals and their relationships with complex moduli. Theoretical results on the frequency response of clamped, symmetrical beams are compared with earlier experimental work. On the whole, reasonable agreement is found.     

Stresses in a quasi-isotropic pin-loaded connector using photoelasticity

Birefringent glass-epoxy and a numerical stress-separation scheme are used to compute the stresses in the vicinity of a pin-loaded hole. The radial and circumferential stresses at the hole edge, and the net-section and shear-out stresses are computed. The numerical and experimental results of other investigators are compared with the computed stresses. The fixture used to load the connector is discussed and typical isochromatic- and isoclinic-fringe patterns are presented. The stress-separation scheme is briefly described.     

Natural vibration of unsymmetric cross-ply laminates

This study considers the linear vibration characteristics of square [0_n/90_n]_T laminates relative to their room-temperature static equilibrium configurations. A Rayleigh-Ritz approach combined with Hamilton's principle is used to provide approximate solutions to this vibration problem. The vibration mode shapes are assumed to have the same spatial dependence as used in past investigations to study the room-temperature configurations of these laminates, and are thus assumed to be perturbations on the static equilibrium configurations. Hamilton's principle then results in the so-called zero- and first-order equations. The zero-order equations lead to the classic static equilibrium results of past investigations, presented here in nondimensional form with analytical solutions at the bifurcation point. The first-order equations, combined with zero-order results, lead to the vibration characteristics for each zero-order static configuration. Interest centers on the lowest natural frequency and the associated mode shape for laminates clamped at their midpoints, with special attention as to how these vibration characteristics depend on the laminate side-length-to-thickness ratio. With an imaginary-valued frequency, the static saddle configuration for side-length-to-thickness ratios larger than the critical value is correctly assessed as unstable. A finite element model is also used to study the vibration characteristics and to compare with the findings for the developed analysis. The qualitative comparisons between the developed analysis and the finite element model are generally good, and the quantitative comparisons are also satisfactory.