Application of Maclaurin Series in Structural Analysis

In the simple theory of flexure of beams, the slope, bending moment, shearing force, load and other quantities are functions of a derivative of y with respect to x. It is shown that the elastic curve of a transversely loaded beam can be represented by the Maclaurin series. Substitution of the values of the derivatives gives a direct solution of beam problems. In this paper the method is applied to derive the Theorem or three moments and slope deflection equations. The method is extended to the solution of a rigid portal frame. Finally the method is applied to deduce results on which the moment distribution method of analyzing rigid frames is based.

Instabilities induced by variation of Brunt-Vaisala frequency in compressible stratified shear flows

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible fluid in the presence of a lower rigid boundary are studied. A jump in the Brunt-Vaisala frequency at a level different from the shear zone is introduced and the variation of the Brunt-Vaisala frequency with respect to the vertical coordinate in the middle layer of the three-layered model is considered. An analytic solution in each of the layers is obtained, and the dispersion relation is solved numerically for parameters relevant to the model. The effect of shear in the lowermost layer of the three-layered model for a Boussinesq fluid is discussed. The results are compared with the earlier studies of Lindzen and Rosenthal, and Sachdev and Satya Narayanan. In the present model, new unstable modes with larger growth rates are obtained and the most unstable gravity wave modes are found to agree closely with the observed ones at various heights. Physics of Fluids is copyrighted by The American Institute of Physics.

Bed Shear from Velocity Profiles: A New Approach

A new binary law of velocity distribution has been developed to describe the velocity profile for the entire flow region. The law is a combination of logarithmic law, valid in the wall (inner) region, and parabolic law, valid in the core (outer) region of the flow. The validity of the law has been established based on earlier data on flat plates, rough and smooth pipes and experimental data obtained from rigid-walled open channels with plane sand beds. A procedure of estimating bed shear stress from the proposed law of velocity distribution using the measured velocity profile has been evolved. Bed shear estimates made according to this procedure are in agreement with the values obtained from uniform flow analysis in the case of open channel flow over a sediment bed. The proposed method of estimating the bed shear stress from the observed velocity profiles is found to be particularly useful in cases where it is difficult to determine precisely the true bed level, such as in the case of flow over sediment beds.

Effect of density discontinuity on Alfvén internal gravity waves

The stability characteristics of Alfvén Internal gravity waves for an inviscid, nondissipative, Boussinesq fluid undergoing shear in the presence of a density discontinuity with and without a rigid boundary is studied.

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem o limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (xi(gamma)) is determined. On account of interference, the magnitude of xi(gamma) is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.

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.

Flow over a cylinder with a hinged-splitter plate

Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a hinged-splitter plate in the wake of a circular cylinder. The splitter plate can rotate about the hinge at the base of the cylinder due to the unsteady fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted as in the rigid splitter plate case. In our study, we investigate this problem in the limit where the stiffness and internal damping associated with the hinge are negligible, and the mass ratio of the splitter plate is small. The experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re, Re>4000. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force, and has been observed previously for transversely oscillating cylinders with no restorin force. In the present case, the saturation tip amplitude level can be tip to 0.45D, where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter ratio (L/D) is crucial in determining the character and magnitude of the oscillations. For small splitter plate length (L/D <= 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45D nearly independent of L/D. The nondiinensional oscillation frequencies (fD/U) on the other hand are found to continuously vary with L/D from fD/U approximate to 0.2 at L/D = 1 to fD/U approximate to 0.1 at L/D = 3. As the splitter plate length is further increased beyond L/D >= 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L/D >= 5.0. In the present case of the hinged-splitter plate, the sudden transition seen as the splitter plate length (L/D) is increased from 3 to 4 may be attributed to the fact that the wake vortices are no longer able to synchronize with the plate motions for larger splitter plate lengths. Hence, as observed in other vortex-induced vibration problems, the oscillations becomeaperiodic and the amplitude reduces dramatically.

Finite element analysis of moving contact in mechanically fastened joints

The Finite Element Method (FEM) has made a number of otherwise intractable problems solvable. An important aspect for achieving an economical and accurate solution through FEM is matching the formulation and the computational organisation to the problem. This was realised forcefully in the present case of the solution of a class of moving contact boundary value problems of fastener joints. This paper deals with the problem of changing contact at the pin-hole interface of a fastener joint. Due to moving contact, the stresses and displacements are nonlinear with load. This would, in general, need an interactive-incremental approach for solution. However, by posing the problem in an inverse way, a solution is sought for obtaining loads to suit given contact configuration. Numerical results are given for typical isotropic and composite plates with rigid pins. Two cases of loading are considered: (i) load applied only at the edges of the plate and (ii) load applied at the pin and reacted at a part of the edge of the plate. Load-contact relationships, compliance and stress-patterns are investigated. This paper clearly demonstrates the simplification achieved by a suitable formulation of the problem. The results are of significance to the design and analysis of fastener joints.

Finite element analysis of moving contact in mechanically fastened joints

The Finite Element Method (FEM) has made a number of otherwise intractable problems solvable. An important aspect for achieving an economical and accurate solution through FEM is matching the formulation and the computational organisation to the problem. This was realised forcefully in the present case of the solution of a class of moving contact boundary value problems of fastener joints. This paper deals with the problem of changing contact at the pin-hole interface of a fastener joint. Due to moving contact, the stresses and displacements are nonlinear with load. This would, in general, need an interactive-incremental approach for solution. However, by posing the problem in an inverse way, a solution is sought for obtaining loads to suit given contact configuration. Numerical results are given for typical isotropic and composite plates with rigid pins. Two cases of loading are considered: (i) load applied only at the edges of the plate and (ii) load applied at the pin and reacted at a part of the edge of the plate. Load-contact relationships, compliance and stress-patterns are investigated. This paper clearly demonstrates the simplification achieved by a suitable formulation of the problem. The results are of significance to the design and analysis of fastener joints.

Conformational studies of phynyl and isoxazolyl penicillins

Conformational energy calculations have been carried out on a few representative b-lactamase resistant and susceptible, phenyl and isoxazolyl penicillins. These studies, in agreement with those of earlier workers, show that the 6b-side chains of resistants penicillins are highly rigid as compared to those of susceptible penicillins. The present studies also suggest that the degree of resistant to b-lactamases depends not only on the rigidity of the side chain but also on the nature and orientation of the substituent, beyond the amide carbonyl group in the side chain. The overall shapes of these penicillins correlate well with their antibacterial properties.

Response of Circular Footings to Vertical Vibrations

In this paper, analog solutions are presented for the response of a circular footing resting on an elastic half-space with uniform and parabolic contact pressure distributions and subjected to frequency dependent and frequency independent excitations. In addition, an analog solution to a rigid circular footing subjected to frequency dependent excitation is also presented. The results have been compared with the rigorous solution of Sung and the agreement is found to be good.

Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic Forces

A mechanics based linear analysis of the problem of dynamic instabilities in slender space launch vehicles is undertaken. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The effects of the coupling between the combustion process (mass variation, developed thrust etc.) and the variables involved in the flexible body dynamics (displacements and velocities) are clearly brought out. The model is one-dimensional, and it can be employed to idealised slender vehicles with complex shapes. Computer simulations are carried out using a standard eigenvalue problem within h-p finite element modelling framework. Stability regimes for a vehicle subjected to propulsive thrust are validated by comparing the results from published literature. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and propulsive thrust as the parameters. The phenomena of static instability (divergence) and dynamic instability (flutter) are observed. The results at low Mach number match closely with the results obtained from previous models published in the literature.

Crystal structure from packing studies: application to the triclinic structure of the cyclic hexapeptide cyclo-(gly-tyr-gly)2

The paper describes a novel method of finding the position and orientation of a relatively rigid molecule in the unit cell from criteria concerning allowed contact distances between atoms. On application to the crystal structure of a hexapeptide, C25H31N6O8.2H2O, it was possible to solve the structure from this starting point, by a series of SFLS refinements with an increasingly larger number of reflexions at successive stages. The packing analysis succeeded, even though the water molecules were not included to start with.

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.

Metal-insulator transition of naxwo3 studied by angle-resolved photoemission spectroscopy

The electronic structure of sodium tungsten bronzes NaxWO3 is investigated by high-resolution angle-resolved photoemission spectroscopy (ARPES). The ARPES spectra measured in both insulating and metallic phases of NaxWO3 reveals the origin of metal-insulator transition (MIT) in sodium tungsten bronze system. It is found that in insulating NaxWO3 the states near the Fermi level (E-F) are localized due to the strong disorder caused by the random distribution of Na+ ions in WO3 lattice. Due to the presence of disorder and long-range Coulomb interaction of conduction electrons, a soft Coulomb gap arises, where the density of states vanishes exactly at E-F. In the metallic regime the states near E-F are populated and the Fermi level shifts upward rigidly with increasing electron doping (x). Volume of electron-like Fermi surface (FS) at the Gamma(X) point of the Brillouin zone gradually increases with increasing Na concentration due to W 5d t(2g) band filling. A rigid shift of the Fermi energy is found to give a qualitatively good description of the Fermi surface evolution. As we move from bulk-sensitive to more surface sensitive photon energy, we found the emergence of Fermi surfaces at X(M) and M(R) point similar to the one at the Gamma(X) point in the metallic regime, suggesting that the reconstruction of surface was due to rotation/deformation of WO6 octahedra.