This work presents the application of generalized finite continuous Ridgelet transform (GFCRT). The solution of Kirchhoff plates with rectangular and simply supported obeying Dirichlet boundary conditions is demonstrated using GFCRT. The inversion formula when applied to the stated problem represents an algebraic solution. In the concluding section, the obtained numerical results are discussed with uniformly distributed patch load, general distributed load and point load.

finite continuous Ridgelet transform, integral transform, testing function space, inversion theorem, operational calculus, uniqueness, heat equation.

Received: July 9, 2022; Revised: November 12, 2022; Accepted: January 9, 2023; Published: April 15, 2023

How to cite this article: Nitu Gupta and V. R. Lakshmi Gorty, Analysis of generalized finite continuous Ridgelet transforms with simply supported rectangular Kirchhoff plates, Advances in Differential Equations and Control Processes 30(2) (2023), 117-134. http://dx.doi.org/10.17654/0974324323008

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] A. H. Zemanian, Generalized Integral Transformations, Interscience Publishers, 1968.
[2] E. J. Candés, Harmonic analysis of neural networks, Applied and Computational Harmonic Analysis 6 (1999), 197-218.
[3] N. Gupta and V. R. Lakshmi Gorty, Finite continuous ridgelet transforms with applications to telegraph and heat conduction, Advances in Dynamical Systems and Applications (ADSA) 15 (2020), 83-100.
[4] R. Roopkumar, Extended ridgelet transform on distributions and Boehmians, Asian-European Journal of Mathematics 4 (2011), 507-521.
[5] R. S. Pathak and J. N. Pandey, Eigenfunction expansion of generalized functions, Nagoya Mathematical Journal 72 (1978), 1-25.
[6] S. Kostadinova, S. Pilipovi, K. Saneva and J. Vindas, The Ridgelet transform of distributions, Integral Transforms and Special Functions 25 (2014), 344-358.
[7] S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, New York, McGraw-Hill, 2 (1959), pp. 240-246.
[8] J. N. Reddy, ed., Theory and Analysis of Elastic Plates and Shells, CRC Press, 1999.
[9] B. O. Mama, C. U. Nwoji, C. C. Ike and H. N. Onah, Analysis of simply supported rectangular Kirchhoff plates by the finite Fourier sine transform method, International Journal of Advanced Engineering Research and Science 4 (2017), 285-291.
[10] N. Gupta and V. R. Lakshmi Gorty, Vibration of a rectangular plate using finite continuous Radon transform, Materials Today: Proceedings, Elsevier, 46 (2021), 7049-8894.
[11] V. R. Lakshmi Gorty and N. Gupta, Bending of fully clamped orthotropic rectangular thin plates using finite continuous ridgelet transform materials today: Proceedings, Elsevier, 47 (2021), 4199-4205.
[12] M. Ramazanov, M. Jenaliyev and N. Gulmanov, Solution of the boundary value problem of heat conduction in a cone, Opuscula Mathematica 42 (2022), 75-91.
[13] N. Gupta and V. R. Lakshmi Gorty, Generalized Finite Continuous Ridgelet Transform, In: S. Singh, M. A. Sarigöl and A. Munjal, eds., Algebra, Analysis and Associated Topics, Springer Nature, (2022), 227-237.