Rotary diffeomorphisms on Euclidean spaces

Translated from Matematicheskie Zametki, Vol. 47, No. 3, pp. 52–57, March, 1990.     

Infinitesimal Rotary Deformations of Surfaces and Their Application to the Theory of Elastic Shells

We present a variational generalization of the problem of infinitesimal geodesic deformations of surfaces in the Euclidean space E ³. By virtue of rotary deformation, the image of every geodesic curve is an isoperimetric extremal of rotation (in the principal approximation). The results are associated in detail with rotary-conformal deformations. The application of these results to the mechanics of elastic shells is given.     

Radiation of acoustic pulses from a multimodal cylindrical transducer in an elastic baffle

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine. Translated from Prikladnaya Mekhanika, Vol. 30, No. 6, pp. 33–41, June, 1994.     

On the conformal, concircular, and spin mappings of gravitational fields

A mapping ρ: of two Riemannian or pseudo-Riemannian spaces is called aspin mapping if for each geodesic curve γ in M_n its image ρ^oγ is a spin-curve in the space . In gravitational fields spin-curves describe the trajectories of uniformly accelerated particles of constant mass with simultaneous self-rotation. We prove: 1) a conformal mapping is a spin mapping only when it is concircular; 2) every conformal mapping of Einstein space is a spin mapping. The latter makes it possible to give a local representation of the metrics of all gravitational fields that admit spin mappings. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 44–47. Original article submitted March 17, 1993.     

Operation of a system of two parallel multimodal cylindrical piezoelectric transducers with transient electrical excitation

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 3, pp. 66–75, March, 1995.     

Nonsteady-state problem of the emission of acoustic waves by a cylindrical piezoelectric transducer near a planar boundary

We study processes developing when a cylindrical piezoceramic shell with split electrodes located near a planar boundary is excited by nonsteady-state electrical signals. We solve the problem using the Laplace integral transform with respect to time. The boundary conditions are satisfied in the space of the originals. Under these conditions, the unknowns are found from a system of Volterra integral equations. We present the calculation results and their analysis. Translated from Prikladnaya Mekhanika, Vol. 33. No. 12, pp. 60–67, December, 1997.