Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 534.121.1
FUNDAMENTAL FREQUENCY DETERMINATION FOR SANDWICH PLATE SIMPLY SUPPORTED IN FOUR CORNERS
P. O. Deev*, A. V. Lopatin
Siberian State Aerospace University named after academician M. F. Reshetnev 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660014, Russian Federation Е-mail: prokhor777@gmail.com
Sandwich plates with free edges are widely used in modern aerospace constructions making power base of non-hermetical spaceship bodies. Fundamental frequency of sandwich plate is very useful for weight efficiency assessment of construction that is significant in engineering calculations. The article deals with the problem of fundamental frequency calculation for rectangular sandwich plate with free edges and all corners simply-supported. The plate has symmetrical sandwich package structure consisting of two identical face-sheets and orthotropic core. In this formulation the problem has no analytical solution yet. This is due to the necessity of exact satisfaction of static boundary conditions on free edges of the plate; which is very hard to do. In the article the authors provide an analytical solution of the problem, where the sandwich plate model is based on Reissner-type layered composites theory. Variational equation of plate free vibrations derived from Hamilton principle. Solution procedure uses generalized Galerkin method to solve the variational equation. This method allows applying approximating functions that do not necessarily exactly satisfy static boundary conditions on free edges of the plate, as these conditions are satisfied integrally along each edge. In this paper trigonometric functions are applied as approximating functions. For the case of plate with four corners simply-supported, trigonometric functions give good accuracy in approximation of plate deflection and rotation along the corresponding coordinate axis. The result of generalized Galerkin method implementation is a system of homogeneous linear algebraic equations and then, an analytical formula for fundamental frequency derives from the condition for the nontrivial solution existence of the system. Fundamental frequencies are calculated using this analytical formula for several variants of plates with different combinations of plate dimensions. Verification by fundamental frequency calculations for the same plates in finite-element package shows very good correlation with obtained analytical formula results. Thereby, resulting analytical formula for fundamental frequency could be successfully used in engineering and design calculations with minimal computational cost and enough accuracy.
sandwich plate, fundamental frequency, generalized Galerkin method.
References
  1. Kogan E. A., Yurchenko A. A. [Non-linear vibration of sandwich plates clamped along the contour]. Problemy mashinostroeniya i nadezhnosti mashin, 2010, no. 5, p. 25–34 (In Russ.).
  2. Frostig Y., Schwarts-Givli H., Rabinovitch O. Free Vibrations of Delaminated Unidirectional Sandwich Panels with a Transversely Flexible Core – A Modified Galerkin Approach. J. of Sound and Vibration, 2007, vol. 301, no. 2, p. 253–277.
  3. Paimushin V. N., Polyakova T. V. [Exact solutions of flexural buckling and free vibration problems for rectangular orthotropic plate with free edges]. Uchenye zapiski Kazanskogo universiteta. Seriya: Fiziko-matematicheskie nauki, 2010, vol. 152, no 1, p. 181–198 (In Russ.).
  4. Rao M. K. et al. Natural Vibrations of Laminated and Sandwich Plates. J. of Engineering Mech., 2004, vol. 130, no. 11, p. 1268–1278.
  5. Liu J. et al. A Semi-Analytical Method for Bending, Buckling, and Free Vibration Analyses. Int. J. of Struct. Stability and Dynamics, 2010, vol. 10, no. 1, p. 127–151.
  6. Lee C. R., Kam T. Y., Sun S. J., Free-Vibration Analysis and Material Constants Identification of Laminated Composite Sandwich Plates. J. of Engineering Mech., 2007, vol. 133, no. 8, p. 12–23.
  7. Leonenko D. V. [Vibration of circular sandwich plates, connected with elastic base, under sinusoidal loads]. Problemy mashinostroeniya i avtomatizatsii, 2009, no. 3, p. 89–93 (In Russ.).
  8. Sekine H., Shirahata H., Matsuda M. Vibration Analysis of Composite Sandwich Plates and Layup Optimization. Sandwich Structures: Advancing with Sandwich Structures and Materials. 2005, vol. 7, p. 557–566.
  9. Brischetto S., Carrera E., Demasi L. Free vibration of sandwich plates and shells by using Zig-Zag function. Shock and Vibration, 2009, vol. 16, p. 495–503.
  10. Lok T. S., Cheng Q. H. Free Vibration of Clamped Orthotropic Sandwich Panel. J. of Sound and Vibration, 2000, vol. 229, no. 2, p. 311–327.
  11. Frostig Y., Shwartz-Givli H., Rabinovich O. Free Vibration of Delaminated Unidirectional Sandwich Panels with a Transversely Flexible Core and General Boundary Conditions – A High-Order Approach. J. of Sandwich Struct. and Materials, 2008, vol. 10, p. 99–131.
  12. Lopatin A. V., Deev P. O. [Fundamental frequency determination for rectangular sandwich plate with free edge]. Vestnik SibGAU. 2010, no. 2(36), p. 53–61 (In Russ.).
  13. Vasiliev V. V. Mechanics of composite structures. Taylor & Francis, 1993.
  14. Lopatin A. V., Deev P. O. [Fundamental frequency determination for rectangular sandwich plate with two free edges]. Vestnik SibGAU. 2011, no. 1(34), p. 46–50 (In Russ.).
  15. Deev P. O. [Fundamental frequency determination for rectangular sandwich plate clamped in the central point]. Vestnik SibGAU. 2011, no. 4(33), p. 54–62 (In Russ.).

Deev Prokhor Olegovich – postgraduate student, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: prokhor777@gmail.com

Lopatin Aleksander Vitalyevich – Dr. Sc., professor, head of Computer modeling department, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: lopatin@krasmail.ru