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temperature, and load ratio on the endurance of heat-resistant steels IKh2M and KhI8N9," Probl. Prochn., No. 4, 35-40 (1980). 3. V. S. Ivanova and A. A. Shanyavskii, Quantitative Fractography. Fatigue Fracture [in Russian], Metallurgiya, Chelyabinsk (1988). 4. A. A. Kaminskii and G. V. Galatenko, "Study of the growth of fatigue cracks in strainhardening materials," Prikl. Mekh., 20, No. 4, 54-60 (1984). 5. B. I. Koval'chuk, A. A. Lebedev, and S. E. Umanskii, Mechanics of Inelastic Deformation of Structural Materials and Elements [in Russian], Naukova Dumka, Kiev (1987). 6. M. Ya. Leonov, "Elements of a theory of brittle fracture," Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 85-92 (1961). 7. S. B. Nizhnik, "Stress-strain curves of stable and metastable two-phase steel in relation to its structure and the volume contents of the phases," Probl. Prochn., No. 3, 57-61 (Z980). 8. V. N. Bastun, S. B. Nizhnik, V. P. Ostrovskaya, and T. Ya. Mel'nikova, "Effect of structure on the fracture toughness of austenitic steel under cyclic loading," Fiz.-Khim. Mekh. Mater., No. 2, 53-57 (1989). 9. A. A. Ostsemin, S. A. Deniskin, and L. L. Sitnikov, "Determination of the stress intensity factor by the methods of photoelastic modeling," Probl. Prochn., No. i, 33-37 (1990). 10. V. V. Panasyuk, Limit Equilibrium of Brittle Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1968). ii. V. Z. Parton and E. M. Morozov, Mechanics of Elastoplastic Fracture [in Russian], Nauka, Moscow (1985). 12. PD 50.345-82. Procedural Directive. Calculation and Testing of Strength in MachineBuilding. Methods of Mechanical Testing for Metals. Determination of Fracture Toughness (Crack Resistance) Characteristics under Static Loading. Izd-vo Standartov, Moscow (1982). 13. S. B. Nizhnik, B. I. Koval'chuk, E. S. Istomina, and E. A. Dmitrieva, "Structure and mechanical properties of austenitic steel in low-temperature deformation with linear and plane stress states," Probl. Prochn., No. 3, 81-86 (1978).

Developpement d'une methode spectrale pour resoudre le probleme de thermoviscoplasticite couple dans le cas d'une charge cyclique au-dela du point de plasticite macroscopique. Utilisation du modele de viscoplasticite de Bodner-Partom

The study of vibrations and vibrational heating of solids with amplitude-dependent characteristics is important for designing vibration-damping systems containing elements made of high-filler-content polymers [6, 12], metalwaveguides in ultrasonic welding units [i], etc. The most recent results obtained in this broad area at the juncture of physics and mechanics were generalized in the monographs [7-9]. The main tasks to be performed in the problem in question are: selection of governing equations, suitable formulation of the coupled thermoviscoelastic problem, development of methods of its numerical realization, and study of the therm0mechanical behavior of bodies. The present study is devoted to the first and part of the second questions, i.e., to analysis of different approaches to the construction of approximate governing equations of nonlinear viscoelastic bodies subjected to small periodic, deformations. i. Construction of the Governing Equations. Wewill study the structure of the governing equations of stable, nonlinear viscoelastic media, These equations describe the polyharmonic reaction to the stresses

The abundant use of poled p iezoe lec t r ic ce ramic ma te r i a l s in e lec t romechanica l energy t r ansduce r s has s t imulated the investigation of the i r p roper t i e s at var ious e lec t r ica l , mechanical , and the rmal activation levels [1, 2, 5, 7-10]. The influence of a stat ic compress ive s t r e s s applied to inc rease the strength of the active e lements on the d ie lec t r ic p rope r t i e s of the l a t t e r is impor tant in application to pulsed wideband radiators . It has been found [7-10] that under a constant static load the complex permi t t iv i ty ~ = e' --i6" of ce r ta in c e r a m i c s re laxes considerably. As in the mechanics of he red i t a ry media, re laxat ion is a manifestat ion of the dependence of the p roper t i e s of the ma te r i a l on the loading h i s to ry and is impor tant both in the physical aspect and f rom the point of view of improving methods for the engineering analysis of p iezoelec t r ic elements.

i. I. Ya. Amiro, V. A. Zarutskii, and P. S. Polyakov, Ribbed Cylindrical Shells [in Russian], Naukova Dumka, Kiev (1973). 2. I. Ya. Amiro and V. A. Zarutskii, "Investigation of ribbed shells in the stability region," Prikl. Mekh., 19, No. ii, 3-20 (1983). 3. Yu. A. Sannikov, "Investigation of stability of reinforced conical shells," Prikl. Mekh., 17, No. 12, 70-75 (1981). 4o A.S. Pal'chevskii and Yu. A. Sannikov, "Experimental investigation of stability of ribbed conical shells," Prikl. Mekh., 18, No. 8, 85-89 (1982).