Analytical Calculation of Beam Supports Stiffness to Provide the First Eigenfrequency and Critical Load


Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций

Конференция: 8th International Conference on Industrial Engineering, ICIE 2022

Год издания: 2023

Идентификатор DOI: 10.1007/978-3-031-14125-6_44

Ключевые слова: analytical solution, axial force, buckling, elastic supports, euler-bernoulli beam, first eigenfrequency, free vibrations

Аннотация: This paper is concerned with the problem of ensuring both the first eigenfrequency of the a two-support beam and its first critical force by determining the required stiffness of supports. This is a quite complex mathematical problem and well-known scientific literature usually offers a solution only in graphic or tabular form. OneПоказать полностьюof the main problems is the highly nonlinear dependence of results on supports stiffness at free vibrations and stability loss. In the paper, these difficulties are overcome by approximation of nonlinear dependencies using the least-squares method and getting analytical quadratic approximating functions instead. As a result, we get a closed-form solution for the problem in the form of a fourth-degree resolving equation that has an analytical solution. This solution allows determining support stiffness which provides the first eigenfrequency of a two-support beam and its first critical force. Replacing the strongly nonlinear dependencies with simpler quadratic functions, however, adversely affected the calculation error which can reach 10%. To reduce this error, it is recommended that the stiffness of both supports be equal or of the same order. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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Журнал: Lecture Notes in Mechanical Engineering

Номера страниц: 441-450

ISSN журнала: 21954356

Издатель: Springer Science and Business Media Deutschland GmbH


  • Kudryavtsev I.V. (Siberian Federal University, 79, Svobodny pr., Krasnoyarsk, 660041, Russian Federation)
  • Brungardt M.V. (Siberian Federal University, 79, Svobodny pr., Krasnoyarsk, 660041, Russian Federation)
  • Khomutov M.P. (Kuban State Technological University, 2, Moskovskaya, Krasnodar, 350072, Russian Federation)
  • Rabetskaya O.I. (Reshetnev Siberian State University of Science and Technology, 31, Krasnoyarskij rabochij, Krasnoyarsk, 660037, Russian Federation)
  • Mityaev A.E. (Siberian Federal University, 79, Svobodny pr., Krasnoyarsk, 660041, Russian Federation)

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