Email this article Unsteady bending function for an unlimited anisotropic plate
- Authors: Serdiuk A.O.1, Serdiuk D.O.1, Fedotenkov G.V.1,2
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Affiliations:
- Moscow Aviation Institute (National Research University)
- Lomonosov Moscow State University, Institute of Mechanics,
- Issue: Vol 25, No 1 (2021)
- Pages: 111-126
- Section: Mechanics of Solids
- URL: https://journals.rcsi.science/1991-8615/article/view/60109
- DOI: https://doi.org/10.14498/vsgtu1793
- ID: 60109
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Abstract
This work is devoted to the study of non-stationary vibrations of a thin anisotropic unbounded Kirchhoff plate under the influence of random non-stationary loads.
The approach to the solution is based on the principle of superposition and the method of influence functions (the so-called Green functions), the essence of which is to link the desired solution to the load using an integral operator of the type of convolution over spatial variables and over time. The convolution core is the Green function for the anisotropic plate, which represents normal displacements in response to the impact of a single concentrated load in coordinates and time, mathematically described by the Dirac delta functions. Direct and inverse integral transformations of Laplace and Fourier are used to construct the Green function. The inverse integral Laplace transform is found analytically. The inverse two-dimensional integral Fourier transform is found numerically by integrating rapidly oscillating functions. The obtained fundamental solution allowed us to present the desired non-stationary deflection in the form of a triple convolution in spatial coordinates and time of the Green function with the non-stationary load function. The rectangle method is used to calculate the convolution integral and construct the desired solution.
The found deflection function makes it possible to study the space-time propagation of non-stationary waves in an unbounded Kirchhoff plate for various versions of the symmetry of the elastic medium: anisotropic, orthotropic, transversally isotropic, and isotropic. Examples of calculations are presented.
About the authors
Alexander O. Serdiuk
Moscow Aviation Institute (National Research University)
Email: serduksaha@yandex.ru
ORCID iD: 0000-0002-2109-7900
http://www.mathnet.ru/person158166
Postgraduate Student; Dep. of Materials Resistance, Dynamics and Machine Strength
4, Volokolamskoe Shosse, Moscow, 125993, Russian FederationDmitry O. Serdiuk
Moscow Aviation Institute (National Research University)
Author for correspondence.
Email: d.serduk55@gmail.com
ORCID iD: 0000-0003-0082-1856
SPIN-code: 4515-5386
Scopus Author ID: 57217994555
ResearcherId: AAB-7446-2022
http://www.mathnet.ru/person128979
PhD, Cand. Techn. Sci.; Associate Professor; Dep. of Materials Resistance, Dynamics and Machine Strength
4, Volokolamskoe Shosse, Moscow, 125993, Russian FederationGrigory V. Fedotenkov
Moscow Aviation Institute (National Research University);Lomonosov Moscow State University, Institute of Mechanics,
Email: greghome@mail.ru
ORCID iD: 0000-0002-9556-7442
SPIN-code: 5224-5838
Scopus Author ID: 15062584600
ResearcherId: AAC-2769-2021
http://www.mathnet.ru/person100015
PhD, Cand. Phys. & Math. Sci.; Associate Professor; Dep. of Materials Resistance, Dynamics and Machine Strength1; Senior Researcher; Lab. of Dynamic Tests2
4, Volokolamskoe Shosse, Moscow, 125993, Russian Federation; 1, Michurinsky prospekt, Moscow, 119192, Russian FederationReferences
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