Spline-Method for Numerical Calculation of Natural-Vibration Frequency of Beam with Variable Cross-Section

Zhernakov, V. S.; Pavlov, V. P.; Kudoyarova, V. M.

doi:10.1016/j.proeng.2017.10.542

Cited by 7 publications

(2 citation statements)

References 7 publications

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“…Taking into account (34) the equation 33is reduced to the form 6, we obtain a system of equations for the structure similar to (14) where: Then the desired values of support pliability are found by formulas (18) - (27).…”

Section: Extension Of the Methods For A Rod With A Variable Cross mentioning

confidence: 99%

Pliability Identification of Elastic Support for Elastic Cantilevered Rod Based on Eigenfrequencies of its Oscillations

Zhernakov¹,

Pavlov²,

Kudoyarova³

et al. 2019

Proceedings of the 21st International Workshop on Computer Science and Information Technologies (CSIT 2019)

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Currently, modern turbomachines, for example, aircraft gas turbine engines are equipped with highly intelligent automated monitoring and control systems, including a large number of sensors that control various parameters of the product being operated. In particular, there are sensors that monitor the oscillation frequencies of the most critical structural elements. This paper estimates the ability to determine the support stiffness of a cantilever rod under the two first eigenfrequencies of its oscillations. A similar problem arises in the non-destructive testing of the axial compressor blade root of a gas turbine engine when a certain decision of its further operation possibility or changing its operation mode is can be made on the basis of the blade oscillation eigenfrequencies spectrum. As a result of the implementation of the paper proposed method it was obtained that the identification error does not go beyond 28%, which is quite acceptable for assessing the technical condition of the support in the engine corresponding to the range of existing engines.

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Section: Extension Of the Methods For A Rod With A Variable Cross mentioning

confidence: 99%

Pliability Identification of Elastic Support for Elastic Cantilevered Rod Based on Eigenfrequencies of its Oscillations

Zhernakov¹,

Pavlov²,

Kudoyarova³

et al. 2019

Proceedings of the 21st International Workshop on Computer Science and Information Technologies (CSIT 2019)

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“…Arndt et al [61] presented an adaptive generalized FEM to determine the natural frequencies of nonuniform Euler-Bernoulli beams. The spline-method of degree 5 defect 1 is proposed by Zhernakov et al [62] to determine the natural frequencies of beam with variable cross section. Wang [63] studied the vibration of a cantilever beam with constant thickness and linearly tapered sides by means of a novel accurate, efficient initial value numerical method.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Axially Functionally Graded Beam

Cao¹,

Wang²,

Hu³

et al. 2020

Mechanics of Functionally Graded Materials and Structures

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Axially functionally graded (AFG) beam is a special kind of nonhomogeneous functionally gradient material structure, whose material properties vary continuously along the axial direction of the beam by a given distribution form. There are several numerical methods that have been used to analyze the vibration characteristics of AFG beams, but it is difficult to obtain precise solutions for AFG beams because of the variable coefficients of the governing equation. In this topic, the free vibration of AFG beam using analytical method based on the perturbation theory and Meijer G-Function are studied, respectively. First, a detailed review of the existing literatures is summarized. Then, based on the governing equation of the AFG Euler-Bernoulli beam, the detailed analytic equations are derived on basis of the perturbation theory and Meijer G-function, where the nature frequencies are demonstrated. Subsequently, the numerical results are calculated and compared, meanwhile, the analytical results are also confirmed by finite element method and the published references. The results show that the proposed two analytical methods are simple and efficient and can be used to conveniently analyze free vibration of AFG beam.

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Opportunities for Using Spline Method to Calculate Orthotropic Plate Under Bending Conditions

Zhernakov

Pavlov

Kudoyarova

2019

Lecture Notes in Mechanical Engineering

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Spline-Method for Numerical Calculation of Natural-Vibration Frequency of Beam with Variable Cross-Section

Cited by 7 publications

References 7 publications

Pliability Identification of Elastic Support for Elastic Cantilevered Rod Based on Eigenfrequencies of its Oscillations

Pliability Identification of Elastic Support for Elastic Cantilevered Rod Based on Eigenfrequencies of its Oscillations

Free Vibration of Axially Functionally Graded Beam

Opportunities for Using Spline Method to Calculate Orthotropic Plate Under Bending Conditions

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