Nonlinear resonant response of imperfect extensible Timoshenko microbeams

Hamed Farokhi; Mergen H. Ghayesh

doi:10.1007/s10999-015-9316-z

Nonlinear resonant response of imperfect extensible Timoshenko microbeams

Hamed Farokhi, Mergen H. Ghayesh^*

^*Corresponding author for this work

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

73 Citations (Scopus)

Abstract

This paper investigates the nonlinear size-dependent dynamics of an imperfect Timoshenko microbeam, taking into account extensibility. Based on the modified couple stress theory, the nonlinear equations of motion for the longitudinal, transverse, and rotational motions are derived via Hamilton’s energy method. A high-dimensional finite degree-of-freedom system of ordinary differential equations is obtained by the application of the Galerkin scheme. This set of equations is solved through use of the pseudo-arclength continuation method. A stability analysis is conducted via use of the Floquet theory. The resonant motion characteristics of the microbeam are examined by plotting the frequency-response and force-response curves. The effect of system parameters on the resonant response of the system is highlighted.

Original language	English
Pages (from-to)	43-55
Number of pages	13
Journal	International Journal of Mechanics and Materials in Design
Volume	13
Issue number	1
Early online date	17 Jul 2015
DOIs	https://doi.org/10.1007/s10999-015-9316-z
Publication status	Published - 1 Mar 2017

Keywords

Modified couple stress theory
Nonlinear dynamics
Timoshenko beam theory
Timoshenko microbeam

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10.1007/s10999-015-9316-z

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title = "Nonlinear resonant response of imperfect extensible Timoshenko microbeams",

abstract = "This paper investigates the nonlinear size-dependent dynamics of an imperfect Timoshenko microbeam, taking into account extensibility. Based on the modified couple stress theory, the nonlinear equations of motion for the longitudinal, transverse, and rotational motions are derived via Hamilton{\textquoteright}s energy method. A high-dimensional finite degree-of-freedom system of ordinary differential equations is obtained by the application of the Galerkin scheme. This set of equations is solved through use of the pseudo-arclength continuation method. A stability analysis is conducted via use of the Floquet theory. The resonant motion characteristics of the microbeam are examined by plotting the frequency-response and force-response curves. The effect of system parameters on the resonant response of the system is highlighted.",

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AU - Farokhi, Hamed

AU - Ghayesh, Mergen H.

PY - 2017/3/1

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N2 - This paper investigates the nonlinear size-dependent dynamics of an imperfect Timoshenko microbeam, taking into account extensibility. Based on the modified couple stress theory, the nonlinear equations of motion for the longitudinal, transverse, and rotational motions are derived via Hamilton’s energy method. A high-dimensional finite degree-of-freedom system of ordinary differential equations is obtained by the application of the Galerkin scheme. This set of equations is solved through use of the pseudo-arclength continuation method. A stability analysis is conducted via use of the Floquet theory. The resonant motion characteristics of the microbeam are examined by plotting the frequency-response and force-response curves. The effect of system parameters on the resonant response of the system is highlighted.

AB - This paper investigates the nonlinear size-dependent dynamics of an imperfect Timoshenko microbeam, taking into account extensibility. Based on the modified couple stress theory, the nonlinear equations of motion for the longitudinal, transverse, and rotational motions are derived via Hamilton’s energy method. A high-dimensional finite degree-of-freedom system of ordinary differential equations is obtained by the application of the Galerkin scheme. This set of equations is solved through use of the pseudo-arclength continuation method. A stability analysis is conducted via use of the Floquet theory. The resonant motion characteristics of the microbeam are examined by plotting the frequency-response and force-response curves. The effect of system parameters on the resonant response of the system is highlighted.

KW - Modified couple stress theory

KW - Nonlinear dynamics

KW - Timoshenko beam theory

KW - Timoshenko microbeam

UR - https://www.scopus.com/pages/publications/84937141740

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DO - 10.1007/s10999-015-9316-z

M3 - Article

AN - SCOPUS:84937141740

SN - 1569-1713

VL - 13

SP - 43

EP - 55

JO - International Journal of Mechanics and Materials in Design

JF - International Journal of Mechanics and Materials in Design

IS - 1

ER -

Nonlinear resonant response of imperfect extensible Timoshenko microbeams

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