Planar dynamics of a uniform beam with rigid bodies affixed to the ends

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided

Transverse vibration and buckling of a cantilevered beam with tip body under constant axial base acceleration

The planar transverse bending behavior of a uniform cantilevered beam with rigid tip body subject to constant axial base acceleration was analyzed. The beam is inextensible and capable of small elastic transverse bending deformations only. Two classes of tip bodies are recognized: (1) mass centers located along the beam tip tangent line; and (2) mass centers with arbitrary offset towards the beam attachment point. The steady state response is studied for the beam end condition cases: free, tip mass, tip body with restricted mass center offset, and tip body with arbitrary mass center offset. The first three cases constitute classical Euler buckling problems, and the characteristic equation for the critical loads/accelerations are determined. For the last case a unique steady state solution exists. The free vibration response is examined for the two classes of tip body. The characteristic equation, eigenfunctions and their orthogonality properties are obtained for the case of restricted mass center offset. The vibration problem is nonhomogeneous for the case of arbitrary mass center offset. The exact solution is obtained as a sum of the steady state solution and a superposition of simple harmonic motions

Supersymmetric Fluid Dynamics

Recently Navier-Stokes (NS) equations have been derived from the duality between the black branes and a conformal fluid on the boundary of AdS_5. Nevertheless, the full correspondence has to be established between solutions of supergravity in AdS_5 and supersymmetric field theories on the boundary. That prompts the construction of NS equations for a supersymmetric fluid. In the framework of rigid susy, there are several possibilities and we propose one candidate. We deduce the equations of motion in two ways: both from the divergenless condition on the energy-momentum tensor and by a suitable parametrization of the auxiliary fields. We give the complete component expansion and a very preliminary analysis of the physics of this supersymmetric fluid.Comment: 24 pages, Latex2

A Computer Algorithm For Engineering Off-Shell Multiplets With Four Supercharges On The World Sheet

We present an adinkra-based computer algorithm implemented in a Mathematica code and use it in a limited demonstration of how to engineer off-shell, arbitrary N-extended world-sheet supermultiplets. Using one of the outputs from this algorithm, we present evidence for the unexpected discovery of a previously unknown 8 - 8 representation of N = 2 world sheet supersymmetry. As well, we uncover a menagerie of (p, q) = (3, 1) world sheet supermultiplets.Comment: 52 pages, 64 figures, LaTeX twice, added note in proof, addition of comments about gauge invariance for 4D vector & tensor supermultiplet

Non-Abelian Tensors with Consistent Interactions

We present a systematic method for constructing consistent interactions for a tensor field of an arbitrary rank in the adjoint representation of an arbitrary gauge group in any space-time dimensions. This method is inspired by the dimensional reduction of Scherk-Schwarz, modifying field strengths with certain Chern-Simons forms, together with modified tensorial gauge transformations. In order to define a consistent field strength of a r-rank tensor B_{\mu_1...\mu_r}^I in the adjoint representation, we need the multiplet (B_{\mu_1...\mu_r}^I, B_{\mu_1...\mu_{r-1}}^{I J}, ..., B_\mu^{I_1...I_r}, B^{I_1... I_{r+1}}). The usual problem of consistency of the tensor field equations is circumvented in this formulation.Comment: 15 pages, no figure

On Supermultiplet Twisting and Spin-Statistics

Twisting of off-shell supermultiplets in models with 1+1-dimensional spacetime has been discovered in 1984, and was shown to be a generic feature of off-shell representations in worldline supersymmetry two decades later. It is shown herein that in all supersymmetric models with spacetime of four or more dimensions, this off-shell supermultiplet twisting, if non-trivial, necessarily maps regular (non-ghost) supermultiplets to ghost supermultiplets. This feature is shown to be ubiquitous in all fully off-shell supersymmetric models with (BV/BRST-treated) constraints.Comment: Extended version, including a new section on manifestly off-shell and supersymmetric BRST treatment of gauge symmetry; added reference

The Real Anatomy of Complex Linear Superfields

Recent work on classicication of off-shell representations of N-extended worldline supersymmetry without central charges has uncovered an unexpectedly vast number--trillions of even just (chromo)topology types--of so called adinkraic supermultiplets. Herein, we show by explicit analysis that a long-known but rarely used representation, the complex linear supermultiplet, is not adinkraic, cannot be decomposed locally, but may be reduced by means of a Wess-Zumino type gauge. This then indicates that the already unexpectedly vast number of adinkraic off-shell supersymmetry representations is but the proverbial tip of the iceberg.Comment: 21 pages, 4 figure

Non-Minimal String Corrections And Supergravity

We reconsider the well-known issue of string corrections to Supergravity theory. Our treatment is carried out to second order in the string slope parameter. We establish a procedure for solving the Bianchi identities in the non minimal case, and we solve a long standing problem in the perturbative expansion of D=10, N=1 string corrected Supergravity, obtaining the H sector tensors, torsions and curvatures.Comment: 19 pages, PACS number: 04.65.+