Forced Axisymmetric Vibrations of an Electrically Excited Hollow Sphere Made of a Continuously Inhomogeneous Piezoceramic Material*

International Applied Mechanics - The forced axisymmetric vibrations of a hollow sphere made of a functionally graded radially polarized piezocelectric material are studied using the spatial theory...     

Molecular Dynamics Study of the Complex Formation of TEM-Type β-Lactamases with Substrates and Inhibitors

The complex formation of TEM-1 β-lactamase and its three mutant forms TEM-32, TEM-37, and TEM-39 with substrates cephalothin and CENTA and serine beta-lactamase inhibitors sulbactam, tazobactam, and clavulanic acid is studied using the methods of molecular dynamics. It is found that the stability of the complexes is caused by the electrostatic attraction between the deprotonated carboxyl group of the β-lactam ring of the substrate (inhibitor) and the positively charged amino groups of the lysine 234 and 73 residues, located in the active site of the enzymes. The formation of a hydrogen bond between this substrate group or its carbonyl oxygen with the hydroxyl group of the catalytic serine 70 residue and also between the negatively charged substituent groups and the positive charge region formed by the arginine 244 guanidine group and the asparagine 276 amino group is observed for some complexes. The binding energy of CENTA with TEM-1 β-lactamase is below the analogous binding energy of cephalothin, which is confirmed by the values of the Michaelis constants, determined experimentally. It is also found that the inhibitors bind to the mutant forms of β-lactamases related to the inhibitor-resistant phenotype, with higher affinity than TEM-1 β-lactamase.     

Properties of composites based on epoxy-modified derivatives of 2-vinyloxyethoxymethyloxirane

In connection with some drawbacks inherent to the traditional procedure of synthesizing epoxy oligomers, an essentially different approach, i.e., the interaction between vinylox and a polyhydroxyl-containing compound, is proposed. About 100 grades of new epoxyoligomers are synthesized and properties of cured polymers are studied. It is concluded that vinylox-based epoxy oligomers are of undoubted interest for the development of freeze-resistant adhesives and sealants for radio and electrical engineering, as well as for electronics.     

Analysis of the stress-strain state of noncircular cylindrical shells subject to thickness viration and weight retention

The stress-strain state of noncircular shells has been analyzed based upon solution of boundary value static problems of variable shell thickness using the methods of spline-collocation and discrete orthogonization. Shell weight was preserved depending on the degree of change in the thickness and the value of the eccentricity. Three classes of problems were considered in which the thickness varied along the generatrix, the guide, and in two coordinate directions; data are presented about the deflection and tangential force in the cross section under different values of the parameters. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine, Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 39–47, June, 1999.     

Theory for the ultrafast dynamics of excited clusters: interplay between elementary excitations and atomic structure

We present a theoretical study of the short-time relaxation of clusters in response to ultrafast excitations using femtosecond laser pulses. We analyze the excitation of different types of clusters (Hg_n, Ag_n, Si_n, C₆₀ and Xe_n) and classify the relaxation dynamics in three different regimes, depending on the intensity of the exciting laser pulse. For low-intensity pulses (I<10¹² W/cm²) we determine the time-dependent structural changes of clusters upon ultrashort ionization and photodetachment. We also study the laser-induced non-equilibrium fragmentation and melting of Si_n and C₆₀ clusters, which occurs for moderate laser intensities, as a function of the pulse duration and energy. As an example for the case of high intensities (I>10¹⁵ W/cm²), the explosion of clusters under the action of very intense ultrashort laser fields is described. Received: 26 November 1999 / Published online: 2 August 2000     

Some approaches to studying deformation of flexible shells

Some approaches to solving nonlinear boundary-value problems of the theory of flexible shells described by ordinary and partial differential equations are presented. One-dimensional problems for a system of anisotropic shells of rotation in the subcritical and supercritical regions of deformation, as well as two-dimensional problems for shells of canonical and noncanonical forms, are considered. The solution of nonlinear problems is performed on the basis of numerical and numerical-analytic methods with the use of discrete orthogonalization and Fourier discrete series.     

Stress–strain state of nonthin orthotropic spherical shells of variable thickness

The stress–strain state of an orthotropic spherical shell with thickness varying in two coordinate directions is analyzed. Different boundary conditions are considered, and a refined problem statement is used. A numerical analytic method based on spline-approximation and discrete orthogonalization is developed. The stress–strain state of spherical orthotropic shells with variable thickness is studied     

Nonaxisymmetric electroelastic vibrations of a hollow sphere made of functionally gradient piezoelectric material

The nonaxisymmetric problem of natural vibrations of a hollow sphere made of functionally gradient piezoelectric material is solved based on 3D electroelasticity. The properties of the material change continuously along a radial coordinate according to an exponential law. The external surface of the sphere is free of tractions and either insulated or short-circuited by electrodes. After separation of variables and representation of the components of the displacements and of the stress tensor in terms of spherical functions, the initially three-dimensional problem is reduced to a boundary-value problem for the eigenvalues expressed by ordinary differential equations. This problem is solved by a stable discrete-orthogonalization technique in combination with a step-by-step search method with respect to the radial coordinate. Moreover, a numerical investigation is performed based on the algorithm used for solving the problem. In particular, we investigate the influence of the geometric and electric parameters on the frequency spectrum at the nonaxisymmetry of natural vibrations of an inhomogeneous piezoceramic thick-walled sphere.