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Group Approaches to the Vibration and Static Deformation Analysis for Bars and Disks

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Abstract

A complex of new methods for construction of analytical solutions to the problems of vibration or static deformation of elastic bodies (bars, disks, plates), which are modeled by differential second-order equations with variable coefficients, is described. The methods are based on group approaches, which make use of differential equation symmetries. Examples of analytical calculations of longitudinal vibrations of bars, torsional vibrations of disks, bending of round plates and axisymmetric tension of disks are given for the cases of variable characteristics where these calculations cannot be made by traditional analytical procedures.

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  1. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine

    A. G. Trapezon

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  1. A. G. Trapezon
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Trapezon, A.G. Group Approaches to the Vibration and Static Deformation Analysis for Bars and Disks. Strength of Materials 33, 380–391 (2001). https://doi.org/10.1023/A:1012416812818

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