On the shear coefficient in Timoshenko's beam theory

Some existing formulations for the shear coefficient in Timoshenko's beam theory are discussed, especially through evaluation of the accuracy to which natural frequencies of simply supported, prismatic, thin walled beams can be obtained. The main conclusion drawn is that if a consistent expression for the shear coefficient, such as those given by Cowper [1] or Stephen [2], is used in Timoshenko's beam theory, then very high accuracies can be expected for the natural frequencies, even for wavelengths of the same magnitude as the transverse dimension of the beam. It is noted that no reduction of the moment of inertia due to shear lag effects should be made as these effects are included in the consistent formulas for the shear coefficient. Finally, some apparently paradoxical results indicating that a reduction in shear stiffness occurs in rare cases if more material is added to a section are discussed and explained as resulting from the use of integrated rather than pointwise deflection measures in the derivation of consistent shear coefficient expressions. The results are discussed in the light of the importance of the shear stiffness of the hull girder in ship hull vibration analysis.     

Dynamical and spatial aspects of sandpile cellular automata

The Bak, Tang, and Wiesenfeld cellular automaton is simulated in 1, 2, 3, 4, and 5 dimensions. We define a (new) set of scaling exponents by introducing the concept of conditional expectation values. Scaling relations are derived and checked numerically and the critical dimension is discussed. We address the problem of the mass dimension of the avalanches and find that the avalanches are noncompact for dimensions larger than 2. The scaling of the power spectrum derives from the assumption that the instantaneous dissipation rate of the individual avalanches obeys a simple scaling relation. Primarily, the results of our work show that the flow of sand down the slope does not have a 1/f power spectrum in any dimension, although the model does show clear critical behavior with scaling exponents depending on the dimension. The power spectrum behaves as 1/f ² in all the dimensions considered.     

Spectra of regular quantum graphs

We consider a class of simple quasi-one-dimensional classically nonintegrable systems that capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is sufficiently simple to allow a detailed investigation of both classical and quantum regimes. Despite their classical chaoticity, these systems exhibit a “nonintegrable analogue” of the Einstein-Brillouin-Keller quantization formula that provides their spectra explicitly, state by state, by means of convergent periodic orbit expansions.     

A Remark on Lp-Boundedness of Wave Operators¶for Two Dimensional Schrödinger Operators

Let H=−Δ+V be a two dimensional Schr?dinger operator with a real potential V(x) satisfying the decay condition , δ > 6. Let H ₀=−Δ. We show that the wave operators are bounded in L ^p (R ²) under the condition that H has no zero resonances or bound states. In this paper the condition , imposed in a previous paper (K. Yajima, Commun. Math. Phys. 208, 125–152 (1999)), is removed. Received: 13 September 2001 / Accepted: 15 October 2001     

MCSCF/MCLR Studies of potential energy surfaces,spectra, and properties of the X1A1 and a3B2 states of ozone

Potential energy surfaces, properties, and spectra of singlet (X¹A₁) and triplet (a³B₂) ozone are investigated by means of MCSCF /MCLR analytical response theory calculations. MCSCF analytical gradients and Hessians are used to locate equilibrium and transition-state structures and to obtain associated vibrational and rotational constants, infrared intensities, and dipole moments. By means of MC linear response functions, electronic excitation energies, and oscillator strengths, static and dynamic polarizabilities as well as dispersion (C₆) coefficients are obtained. Good agreement is achieved, in some cases within experimental error margins, for properties where experimental data are known. A very low IR intensity for triplet ozone is predicted.     

A storage allocation scheme for ALGOL 60

A storage allocation scheme for a machine with a 2048-instruction core store and a magnetic drum is described. The use of the drum for storing program blocks and/or data must be directed by the programmer through auxiliary information in the ALGOL program. The administrative routines controlling the storage at run time are described in full. A detailed example is given.     

Spindle-inhibiting effects of organotin compounds. II. Induction of chromosomal supercontraction by di- and tri-alkyl and -aryl compounds

Spindle-inhibiting effects of chemical compounds may be studied indirectly by quantitation of chromosomal contraction. The effects of the trimethyltin (TMT), dimethyltin (DMT), tributyltin (TBT), dibutyltin (DBT), triphenyltin (TPhT) and diphenyltin (DPht) moieties as the chloride on chromosomal contraction was studied by measurement of the average length of chromosome No. 1 from asynchronous cultures of human peripheral lymphocytes. TMT, TBT, TPhT and DPhT appear to be very strong inducers of chromosomal supercontraction, indicating that these compounds conceivably are spindle inhibitors, whilst DMT and DBT seem to be ineffective. The different effects of aryl versus alkyl and trivalent versus divalent organic substituents of tin on chromosome length may relate to different modes of action.