Abstract
The paper considers the relationship between the dynamic and static parameters of circular isotropic plates under various boundary conditions. The studies of the plates were carried out under static and dynamic loading, taking into account the variability of the thickness. The authors established the relationship between the maximum deflection and the natural frequencies of the transverse vibrations of the plates, and assessed the matching of the coefficient K obtained by numerical studies with its analytical one. The curves for the frequencies of free vibrations and deflections under the static load and the change in the coefficient K depending on the thickness of the plate and boundary conditions were plotted. Studies showed that the coefficient K complies within 5% of the dependence of Professor V.I. Korobko only when the ratio of the thickness in the center to the thickness on the support t2/t1 = 60/50 < 1.2 for both support schemes. This is due to the fact that formula (16) was derived for isotropic plates with constant thickness and the distribution of mass evenly over the entire area of the plate leads to a significant error already at the stage of a small difference between the thicknesses at the support and in the center. With a thickness ratio t2/t1 = 100/50 = 2, the difference between the K coefficient and the analytical one is about 16%.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Rzhanitsyn, Calculation of composite plates with absolutely tight cross couplings. Researches on the theory of constructions, issue XXII (Stroyizdat, Moscow, 1976)
Rzhanitsyn, Composite rods and plates (Stroyizdat, Moscow, 1986)
Kalmanok, Structural mechanics of plates (Mashstroyizdat, Moscow, 1950)
N. Shaposhnikov, Calculation of plates on a bend according to the finite-element method (Works of MITE, 1968)
Korobko V (1989) Journal construction and architecture 11:32–36
Korobko A, Chernyaev, Shlyakhov S (2016) Building and reconstruction 4, 19-29
Korobko A, Chernyaev, Shlyakhov S (2017) Building and reconstruction 1, 39-49
Korobko, Savin S (201) Building and reconstruction 5, 29–34
Korobko, Savin S (2013) Building and reconstruction 5, 13–18
Korobko V, Savin SY, Filatova SA (2016) Determination of stiffness and fundamental frequency of oscillations of fixed circuit plates, Izv Vyss Uchebnykh Zaved Seriya Teknol Tekst Promyshlennosti 3, 290–295
Korobko VI et al (2015) Determination of maximum deflection at cross bending parallelogram plates using conformal radius ratio interpolation technique. J Serbian Soc Comput Mech 9(1):36–45
Korobko VI et al (2016) Solving the transverse bending problem of thin elastic orthotropic plates with form factor interpolation method. J Serbian Soc Comput Mech 10(2):9–17
Hsueh H, Luttrell CR, Becher PF (2006) Modelling of bonded multilayered disks subjected to biaxial flexure tests, Int J Solids Struct 43, 20, 6014–6025 https://doi.org/10.1016/j.ijsolstr.2005.07.020
Wu K-C, Hsiao P-S (2015) An exact solution for an anisotropic plate with an elliptic hole under arbitrary remote uniform moments. Compos B Eng 75:281–287. https://doi.org/10.1016/j.compositesb.2015.02.003
Gohari S et al (2021) A new analytical solution for elastic flexure of thick multi-layered composite hybrid plates resting on Winkler elastic foundation in air and water. Ocean Eng 235:109372. https://doi.org/10.1016/j.oceaneng.2021.109372
Bharati RB, Mahato PK, Filippi M, Carrera E (2021) Flutter analysis of rotary laminated composite structures using higher-order kinematics. Composites Part C: Open Access 4:100100. https://doi.org/10.1016/j.jcomc.2020.100100
Perel VY, Palazotto AN (2003) Dynamic geometrically nonlinear analysis of transversely compressible sandwich plates, Int J Non-Linear Mech 38, 3, 337–356 https://doi.org/10.1016/S0020-7462(01)00065-8
Rao BN, Pillai SRR (1992) Large-amplitude free vibrations of laminated anisotropic thin plates based on harmonic balance method, J Sound Vib 154, 1, 173–177 https://doi.org/10.1016/0022-460X(92)90411-P
Wang Z, Yu Xing (2021) An extended separation-of-variable method for free vibrations of orthotropic rectangular thin plate assemblies. Thin-Walled Structures 169, 108491 https://doi.org/10.1016/j.tws.2021.108491
Semenov, Gabitov F (2015) The SCAD project computer system in educational process (ASV publishing house, Moscow)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Turkov, A., Marfin, K., Finadeeva, E., Poleshko, S. (2024). Deflections and Free Vibrations of Circular Isotropic Plates of Thickness Varying in Accordance with a Parabola. In: Vatin, N., Pakhomova, E.G., Kukaras, D. (eds) Modern Problems in Construction. MPC 2022. Lecture Notes in Civil Engineering, vol 372. Springer, Cham. https://doi.org/10.1007/978-3-031-36723-6_22
Download citation
DOI: https://doi.org/10.1007/978-3-031-36723-6_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-36722-9
Online ISBN: 978-3-031-36723-6
eBook Packages: EngineeringEngineering (R0)