Vibration Control of a Non-homogeneous Circular Thin Plate

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Vibration Control of a Non-homogeneous Circular Thin Plate. / Smirnov, Andrei L.; Vasiliev, Grigory P.

Advanced Structured Materials. Springer Nature, 2022. p. 267-276 (Advanced Structured Materials; Vol. 151).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Author

Smirnov, Andrei L. ; Vasiliev, Grigory P. / Vibration Control of a Non-homogeneous Circular Thin Plate. Advanced Structured Materials. Springer Nature, 2022. pp. 267-276 (Advanced Structured Materials).

BibTeX

@inbook{8cc43011461242cd93d48f4d03ed9aba,

title = "Vibration Control of a Non-homogeneous Circular Thin Plate",

abstract = "Abstract Transverse vibrations of an inhomogeneous circular thin plate are studied. The plates, which geometric and physical parameters slightly differ from constant and depend only on the radial coordinate, are analyzed. After separation of variables the obtained homogeneous ordinary differential equations together with homogeneous boundary conditions form a regularly perturbed boundary eigenvalue problem. For frequencies of free vibrations of a plate, which thickness and/or Young{\textquoteright}s modulus nonlinearly depend on the radial coordinate asymptotic formulas are obtained by means of the perturbation method. The effect of the small perturbation parameter on behavior of frequencies is analyzed under special conservation conditions: i) for a plate, the mass of which is fixed, if the thickness is variable, and ii) for a plate with the fixed average sti_ness, if Young{\textquoteright}s modulus is variable. Asymptotic results for the lower vibration frequencies well agree with the results of finite element analysis with COMSOL Multiphysics 5.4.",

keywords = "Free vibrations of plates, Inhomogeneous circular plate, Perturbation method",

author = "Smirnov, {Andrei L.} and Vasiliev, {Grigory P.}",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2022",

doi = "10.1007/978-3-030-87185-7_20",

language = "English",

series = "Advanced Structured Materials",

publisher = "Springer Nature",

pages = "267--276",

booktitle = "Advanced Structured Materials",

address = "Germany",

}

RIS

TY - CHAP

T1 - Vibration Control of a Non-homogeneous Circular Thin Plate

AU - Smirnov, Andrei L.

AU - Vasiliev, Grigory P.

PY - 2022

Y1 - 2022

N2 - Abstract Transverse vibrations of an inhomogeneous circular thin plate are studied. The plates, which geometric and physical parameters slightly differ from constant and depend only on the radial coordinate, are analyzed. After separation of variables the obtained homogeneous ordinary differential equations together with homogeneous boundary conditions form a regularly perturbed boundary eigenvalue problem. For frequencies of free vibrations of a plate, which thickness and/or Young’s modulus nonlinearly depend on the radial coordinate asymptotic formulas are obtained by means of the perturbation method. The effect of the small perturbation parameter on behavior of frequencies is analyzed under special conservation conditions: i) for a plate, the mass of which is fixed, if the thickness is variable, and ii) for a plate with the fixed average sti_ness, if Young’s modulus is variable. Asymptotic results for the lower vibration frequencies well agree with the results of finite element analysis with COMSOL Multiphysics 5.4.

AB - Abstract Transverse vibrations of an inhomogeneous circular thin plate are studied. The plates, which geometric and physical parameters slightly differ from constant and depend only on the radial coordinate, are analyzed. After separation of variables the obtained homogeneous ordinary differential equations together with homogeneous boundary conditions form a regularly perturbed boundary eigenvalue problem. For frequencies of free vibrations of a plate, which thickness and/or Young’s modulus nonlinearly depend on the radial coordinate asymptotic formulas are obtained by means of the perturbation method. The effect of the small perturbation parameter on behavior of frequencies is analyzed under special conservation conditions: i) for a plate, the mass of which is fixed, if the thickness is variable, and ii) for a plate with the fixed average sti_ness, if Young’s modulus is variable. Asymptotic results for the lower vibration frequencies well agree with the results of finite element analysis with COMSOL Multiphysics 5.4.

KW - Free vibrations of plates

KW - Inhomogeneous circular plate

KW - Perturbation method

UR - http://www.scopus.com/inward/record.url?scp=85122437033&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/51eabf90-0e6c-3274-8f1f-6191bd54f9ef/

U2 - 10.1007/978-3-030-87185-7_20

DO - 10.1007/978-3-030-87185-7_20

M3 - Chapter

AN - SCOPUS:85122437033

T3 - Advanced Structured Materials

SP - 267

EP - 276

BT - Advanced Structured Materials

PB - Springer Nature

ER -

ID: 91323002