To the Solution of Three-Dimensional Problems of Oscillations in the Theory of Elasticity in Thick Plates of Variable Thickness

Show more

References

[1] Koreneva, E.B. (2009) Analytical Methods for Calculating the Plates of Variable Thickness and Their Practical Applications. Associations of Construction Universities, Moscow, 240 p.

[2] Morgachev, K.S. (2007) Dynamics of Plates (Tymoshenko’s Model) of Constant and Variable Thickness. Monograph, Samara State University of Architecture and Civil Engineering, Samara, 113 p.

[3] Gabbasov, R.F., Moussa, S. and Filatov, V.V. (2006) Oscillations of Plates of Variable Rigidity. Izvestiya of Universities. Construction, No. 5, 9-15.

[4] Budak, V.D., Grigorenko, A.Ya. and Puzyrev, S.V. (2007) Solution of the Problem of Free vibrations of Rectangular in Plane Flat Shells of Variable Thickness. Applied Mechanics, 43, 89-99.

[5] Ceribasi, S. and Altay, G. (2009) Free Vibration of Super Elliptical Plates with Constant and Variable Thickness by Ritz Method. Journal of Sound and Vibration, 319, 668-680.

[6] Wanyama, W. (2000) Analytical Investigation of the Acoustic Radiation from Linearly-Varying Thin Circular Plates. Ph.D. Thesis, Texas Tech University, Lubbock, Tx.

[7] Antonenko, E.V. and Khloptseva, N.S. (2006) Axisymmetric Form of Stability Loss of Thin-Walled Cylinders of Variable Thickness. Mathematics. Mechanics: Sat. sci. tr. The Sarat Publishing House, Saratov, 165-167.

[8] Abdukarimov, R.A. (2010) Numerical Study of Nonlinear Oscillation of a Viscoelastic Plate of Variable Rigidity. Problems of Architecture and Construction, No. 1, 37-42.

[9] Abdukarimov, R.A. (2010) Mathematical Model of Nonlinear Oscillation of a Viscoelastic Plate of Variable Rigidity under Different Boundary Conditions. Problems of Architecture and Construction, No. 1, 44-47.

[10] Karpov, V.V. (1999) Geometrically Nonlinear Problems for Plates and Shells and Methods for their Solution. Publishing House of the ACB, Moscow, 154 p.

[11] Ignatiev, O.V., Karpov, V.V. and Filatov, V.N. (2001) Variation-Parametric Method in the Nonlinear Theory of Shells of Step-Variable Thickness. VolGASA, Volgograd, 210 p.

[12] Abrosimov, A.A. and Filippov, V.N. (2007) Investigation of Stress-Strain State of Plates of Variable Thickness in a Geometrically Nonlinear Statement with Different Systems of Approximating Functions. Applied Mathematics and Mechanics: Sat. sci. tr. Ulyanov. State-techn. University Ulyanovsk, UlSTU, 3-8.

[13] Usarov, M.K. (2014) Bimoment Theory of Bending and Oscillations of Thick Orthotropic Plates. Bulletin of the NUUz, No. 2/1, 127-132.

[14] Usarov, M.K. (2015) Bending of Orthotropic Plates with Account of Bimoments. St. Petersburg Engineering and Construction Magazine, No. 1, 80-90.

[15] Usarov, М.K., Usarov, D.М. and Ayubov, G.T. (2016) Bending and Vibrations of a Thick Plate with Consideration of Bimoments. Journal of Applied Mathematics and Physics, 4, 1643-1651.

http://www.scirp.org/journal/jamp

https://doi.org/10.4236/jamp.2016.48174

[16] Usarov, М.K. (2016) Dynamic Design of Thick Orthotropic Cantilever Plates with Consideration of Bimoments. World Journal of Mechanics, 6, 341-356.