Generalized stiffness and effective mass coefficients for power-law Euler–Bernoulli beams

Piotr Sebastian Skrzypacz; Daulet Nurakhmetov; Dongming Wei

doi:10.1007/s10409-019-00912-8

Generalized stiffness and effective mass coefficients for power-law Euler–Bernoulli beams

Piotr Sebastian Skrzypacz, Daulet Nurakhmetov, Dongming Wei

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon’s power-law materials. We provide the generalized stiffness and effective mass coefficients for the power-law Euler–Bernoulli beams under standard geometric and load conditions. In particular, our mass-spring lumped parameter models reduce to the classical models when Hollomon’s law reduces to Hooke’s law. Since there are no known solutions to the dynamic power-law beam equations, solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.

Original language	English
Journal	Acta Mechanica Sinica/Lixue Xuebao
Volume	36
Issue number	1
DOIs	https://doi.org/10.1007/s10409-019-00912-8
Publication status	Published - Feb 1 2020

Keywords

Effective mass coefficient
Generalized stiffness coefficient
Lumped parameter modelsPower-law Euler–Bernoulli beams
Power-law Euler–Bernoulli beams

ASJC Scopus subject areas

Applied Mathematics
Materials Science (miscellaneous)
Mechanical Engineering

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title = "Generalized stiffness and effective mass coefficients for power-law Euler–Bernoulli beams",

abstract = "We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon{\textquoteright}s power-law materials. We provide the generalized stiffness and effective mass coefficients for the power-law Euler–Bernoulli beams under standard geometric and load conditions. In particular, our mass-spring lumped parameter models reduce to the classical models when Hollomon{\textquoteright}s law reduces to Hooke{\textquoteright}s law. Since there are no known solutions to the dynamic power-law beam equations, solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.",

keywords = "Effective mass coefficient, Generalized stiffness coefficient, Lumped parameter modelsPower-law Euler–Bernoulli beams, Power-law Euler–Bernoulli beams",

author = "Skrzypacz, {Piotr Sebastian} and Daulet Nurakhmetov and Dongming Wei",

note = "The derived mass lumped model parameters are functions of the power-law index. In the case of the linear materials, they coincide with the well-known coefficients from the literature.",

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T1 - Generalized stiffness and effective mass coefficients for power-law Euler–Bernoulli beams

AU - Skrzypacz, Piotr Sebastian

AU - Nurakhmetov, Daulet

AU - Wei, Dongming

N1 - The derived mass lumped model parameters are functions of the power-law index. In the case of the linear materials, they coincide with the well-known coefficients from the literature.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon’s power-law materials. We provide the generalized stiffness and effective mass coefficients for the power-law Euler–Bernoulli beams under standard geometric and load conditions. In particular, our mass-spring lumped parameter models reduce to the classical models when Hollomon’s law reduces to Hooke’s law. Since there are no known solutions to the dynamic power-law beam equations, solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.

AB - We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon’s power-law materials. We provide the generalized stiffness and effective mass coefficients for the power-law Euler–Bernoulli beams under standard geometric and load conditions. In particular, our mass-spring lumped parameter models reduce to the classical models when Hollomon’s law reduces to Hooke’s law. Since there are no known solutions to the dynamic power-law beam equations, solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.

KW - Effective mass coefficient

KW - Generalized stiffness coefficient

KW - Lumped parameter modelsPower-law Euler–Bernoulli beams

KW - Power-law Euler–Bernoulli beams

U2 - 10.1007/s10409-019-00912-8

DO - 10.1007/s10409-019-00912-8

M3 - Article

VL - 36

JO - Acta Mechanica Sinica/Lixue Xuebao

JF - Acta Mechanica Sinica/Lixue Xuebao

SN - 0567-7718

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