Analysis of Dynamic Behavior of Beams with Variable Cross-section
- Authors: Saurin V.V.1
-
Affiliations:
- Ishlinsky Institute for Problems in Mechanics
- Issue: Vol 40, No 3 (2019)
- Pages: 364-374
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204186
- DOI: https://doi.org/10.1134/S1995080219030168
- ID: 204186
Cite item
Abstract
A formulation of a boundary value problem to find natural frequencies of an inhomogeneous beam in the framework of the Euler–Bernoulli hypotheses are represented. Questions related to various classical variational formulations for a spectral problem arising in the beam theory are discussed. Particularities of the application of the Hamiltonian principles to boundary-value problems are considered. The method of integro-differential relations, which is an alternative to the classical variational approaches is discussed. Various bilateral energy quality estimates for approximate solutions that follow from the method of integro-differential relations are proposed. In the final part of the paper advantages of the variational technique in problems of free vibrations of inhomogeneous beams are discussed based on a numerical example.
About the authors
V. V. Saurin
Ishlinsky Institute for Problems in Mechanics
Author for correspondence.
Email: saurin@ipmnet.ru
Russian Federation, pr. Vernadskogo 101, korp. 1, Moscow, 119526