Vibrations of a Beam in Variable Contact With a Flat Surface

We study small vibrations of cantilever beams contacting a rigid surface. We study two cases: the first is a beam that sags onto the ground due to gravity, and the second is a beam that sticks to the ground through reversible adhesion. In both cases, the noncontacting length varies dynamically. We first obtain the governing equations and boundary conditions, including a transversality condition involving an end moment, using Hamilton's principle. Rescaling the variable length to a constant value, we obtain partial differential equations with time varying coefficients, which, upon linearization, give the natural frequencies of vibration. The natural frequencies for the first case (gravity without adhesion) match that of a clamped-clamped beam of the same nominal length; frequencies for the second case, however, show no such match. We develop simple, if atypical, single degree of freedom approximations for the first modes of these two systems, which provide insights into the role of the static deflection profile, as well as the end moment condition, in determining the first natural frequencies of these systems. Finally, we consider small transverse sinusoidal forcing of the first case and find that the governing equation contains both parametric and external forcing terms. For forcing at resonance, w find that either the internal or the external forcing may dominate.

Penetration Rate Effect on Miniature Cone Tip Resistance for Different Cohesionless Materials

Cone penetrometer tests were carried out in a 140 mm diameter triaxial chamber by using a miniature cone of diameter 19.5 mm. The rate of cone penetration was varied from 0.01 mm/s to 0.1 mm/s. Tests were performed in (i) clean sand, (ii) silty sand, and (iii) sand added with fly ash. Two different effective vertical pressures (sigma(nu)), 100 kPa and 300 kPa, were employed. It was noted that for clean and silty sand, the effect of penetration rate on the ultimate tip resistance (q(cu)) of the cone was found to remain only marginal. On the other hand, for sand added with 30% fly ash, the variation in q(cu) values with penetration rate was found to become quite significant. The effect of penetratio rate on q(cu) in all the cases was found to increase with a decrease in the rate of cone penetration. It was noted that with an increase in sigma(nu), the effect of penetration rate on q(cu) was found to become smaller. The effect of the cone penetration rate on q(cu) generally reduces with an increase in the relative density of the material.

Size optimization of a cantilever beam under deformation-dependent loads with application to wheat stalks

In this paper, we consider the optimization of the cross-section profile of a cantilever beam under deformation-dependent loads. Such loads are encountered in plants and trees, cereal crop plants such as wheat and corn in particular. The wind loads acting on the grain-bearing spike of a wheat stalk vary with the orientation of the spike as the stalk bends; this bending and the ensuing change in orientation depend on the deformation of the plant under the same load.The uprooting of the wheat stalks under wind loads is an unresolved problem in genetically modified dwarf wheat stalks. Although it was thought that the dwarf varieties would acquire increased resistance to uprooting, it was found that the dwarf wheat plants selectively decreased the Young's modulus in order to be compliant. The motivation of this study is to investigate why wheat plants prefer compliant stems. We analyze this by seeking an optimal shape of the wheat plant's stem, which is modeled as a cantilever beam, by taking the large deflection of the stem into account with the help of co-rotational finite element beam modeling. The criteria considered here include minimum moment at the fixed ground support, adequate stiffness and strength, and the volume of material. The result reported here is an example of flexibility, rather than stiffness, leading to increased strength.

A laminated anisotropic curved beam and shell stiffening finite element

The details of development of the stiffness matrix of a laminated anisotropic curved beam finite element are reported. It is a 16 dof element which makes use of 1-D first order Hermite interpolation polynomials for expressing it's assumed displacement state. The performance of the element is evaluated considering various examples for which analytical or other solutions are available.

Design of laterally loaded piles in clays based on cone penetration test data: a reliability-based approach

The behaviour of laterally loaded piles is considerably influenced by the uncertainties in soil properties. Hence probabilistic models for assessment of allowable lateral load are necessary. Cone penetration test (CPT) data are often used to determine soil strength parameters, whereby the allowable lateral load of the pile is computed. In the present study, the maximum lateral displacement and moment of the pile are obtained based on the coefficient of subgrade reaction approach, considering the nonlinear soil behaviour in undrained clay. The coefficient of subgrade reaction is related to the undrained shear strength of soil, which can be obtained from CPT data. The soil medium is modelled as a one-dimensional random field along the depth, and it is described by the standard deviation and scale of fluctuation of the undrained shear strength of soil. Inherent soil variability, measurement uncertainty and transformation uncertainty are taken into consideration. The statistics of maximum lateral deflection and moment are obtained using the first-order, second-moment technique. Hasofer-Lind reliability indices for component and system failure criteria, based on the allowable lateral displacement and moment capacity of the pile section, are evaluated. The geotechnical database from the Konaseema site in India is used as a case example. It is shown that the reliability-based design approach for pile foundations, considering the spatial variability of soil, permits a rational choice of allowable lateral loads.

Drag reduction by a forward facing aerospike for a large angle blunt cone in high enthalpy flows

Drag reduction studies are conducted using a flat disc tipped aerospike for a 120-degree apex angle blunt cone model in high enthalpy flows. Accelerometer based force balance is used for the drag force measurement in the newly established free piston driven shock tunnel, HST3. Drag reduction upto about 58 percent has been achieved for Mach 8 flow of 5 MJ/kg specific enthalpy at zero degree angle of attack.

Drag reduction by counterflow supersonic jet for a blunt cone in high enthalpy flows

Counterflow supersonic jet is used as a drag reduction device during the experiments in free piston driven shock tunnel, HST3. Accelerometer based force balance is employed to measure the drag force experienced by the 60-degree apex angle blunt cone model without and with the supersonic jet opposing the hypersonic flow. It is observed that the drag force decreases with increase in injection pressure ratio until the critical injection pressure is reached. Maximum reduction in drag force of 44 percent is recorded at the critical injection pressure ratio 22.36. Further increase in injection pressure ratio has reduced the percentage drag reduction. Change in nature of the flowfield around the model has also been observed across the critical injection pressure ratio.

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

Orbit perturbation theory of beam-plasma instability

The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.

Radio frequency emission in electron beam-plasma and beam-beam interaction

A linear excitation of electromagnetic modes at frequencies (n + ı89 in a plasma through which two electron beams are contra-streaming along the magnetic field is investigated. This may be a source of the observed {cote emissions at auroral latitudes.

Anomalous plasma heating by an intense laser beam

Heating of laser produced plasmas by an instability is investigated. For intense laser beams anomalous absorption is found. A comparison is made with the experiment.

Use of transverse beam polarization to probe anomalous V V H interactions at a Linear Collider

We investigate use of transverse beam polarization in probing anomalous coupling of a Higgs boson to a pair of vector bosons, at the International Linear Collider (ILC). We consider the most general form of V V H (V = W/Z) vertex consistent with Lorentz invariance and investigate its effects on the process e(+)e(-) -> f (f) over barH, f being a light fermion. Constructing observables with definite C P and naive time reversal ((T) over tilde) transformation properties, we find that transverse beam polarization helps us to improve on the sensitivity of one part of the anomalous Z Z H Coupling that is odd under C P. Even more importantly it provides the possibility of discriminating from each other, two terms in the general Z Z H vertex, both of which are even under C P and (T) over bar. Use of transversebeam polarization when combined with information from unpolarized and linearly polarized beams therefore, allows one to have completely independent probes of all the different parts of a general ZZH vertex.

The hydrogen bond: a molecular beam microwave spectroscopist's view with a universal appeal

In this manuscript, we propose a criterion for a weakly bound complex formed in a supersonic beam to be characterized as a `hydrogen bonded complex'. For a `hydrogen bonded complex', the zero point energy along any large amplitude vibrational coordinate that destroys the orientational preference for the hydrogen bond should be significantly below the barrier along that coordinate so that there is at least one bound level. These are vibrational modes that do not lead to the breakdown of the complex as a whole. If the zero point level is higher than the barrier, the `hydrogen bond' would not be able to stabilize the orientation which favors it and it is no longer sensible to characterize a complex as hydrogen bonded. Four complexes, Ar-2-H2O, Ar-2-H2S, C2H4-H2O and C2H4-H2S, were chosen for investigations. Zero point energies and barriers for large amplitude motions were calculated at a reasonable level of calculation, MP2(full)/aug-cc-pVTZ, for all these complexes. Atoms in molecules (AIM) theoretical analyses of these complexes were carried out as well. All these complexes would be considered hydrogen bonded according to the AIM theoretical criteria suggested by Koch and Popelier for C-H center dot center dot center dot O hydrogen bonds (U. Koch and P. L. A. Popelier, J. Phys. Chem., 1995, 99, 9747), which has been widely and, at times, incorrectly used for all types of contacts involving H. It is shown that, according to the criterion proposed here, the Ar-2-H2O/H2S complexes are not hydrogen bonded even at zero kelvin and C2H4-H2O/H2S complexes are. This analysis can naturally be extended to all temperatures. It can explain the recent experimental observations on crystal structures of H2S at various conditions and the crossed beam scattering studies on rare gases with H2O and H2S.