FORCED VIBRATION OF AN INITIALLY STRESSED THICK RECTANGULAR PLATE MADE OF AN ORTHOTROPIC MATERIAL WITH A CYLINDRICAL HOLE S. D. Akbarov, a,b, * N. Yahnioglu, c and U. Babuscu Yesil c Keywords: initial stretching force, forced vibration, cylindrical hole, orthotropic thick plate, fundamental fre- quency, finite-element method The forced vibration of an initially statically stressed rectangular plate made of an orthotropic material is studied. The plate is simply supported along all its edges and contains an internal across-the-width cylindrical hole of rectangular cross section with rounded corners. The initial stresses are created by uniformly distrib- uted normal forces applied to opposite end faces of the plate. Because of the hole, these stresses are not uni- form in the plate and significantly affect the stress field caused by additional time-harmonic dynamical forces acting on the upper face of the plate. Hence, for solving the boundary-value problem considered, the superpo- sition principle is unsuitable. Therefore, our investigations are carried out within the framework of the three-dimensional linearized theory of elastic waves in initially stressed bodies. The corresponding bound- ary-value problems on determining the initial and additional, dynamical stress states are solved by using the three-dimensional finite-element method. Numerical results on stress concentrations around the cylindrical hole and the fundamental frequencies, and on the influence of the initial stresses on the frequencies are pre- sented. Introduction In engineering applications, one of the fundamental problems of material mechanics is the determination of concentra- tion of stresses or strains near a hole or another kind of defects in structural elements, because these defects, regarded as stress or strain generators, reduce the strength of materials significantly. It is known that a wide range of such problems have been studied by many researchers, who have determined the effects of a hole on the concentration of stresses or strains [1-10] and on 287 0191-5665/10/4603-0287 © 2010 Springer Science+Business Media, Inc. a Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering, Yildiz Campus, 34349, Besiktas, Istanbul, Turkey. b Institute of Mathematics and Mechanics of National Academy of Science of Azerbaijan, 37041, Baku, Azerbaijan. c Yildiz Technical University, Faculty of Chemical and Metallurgical Engineering, De- partment of Mathematical Engineering, Davutpasa Campus, 34210, Esenler Istanbul, Turkey. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 46, No. 3, pp. 415-430, May-June, 2010. Original article submitted March 10, 2010. *Corresponding author; e-mail: akbarov@yildiz.edu.tr . Mechanics of Composite Materials, Vol. 46, No. 3, 2010