Dynamic finite element analysis of axially vibrating nonlocal rods

S. Adhikari, T. Murmu, M.A. McCarthy

Research output: Contribution to journalArticle

Abstract

Free and forced axial vibrations of damped non local rods are investigated. Two types of non local damping models, namely, strain-rate-dependent viscous damping and velocity-dependent viscous damping, are considered. A frequency-dependent dynamic finite element method is developed to obtain the forced vibration response. Frequency-adaptive complex-valued shape functions are proposed to obtain the dynamic stiffness matrix in closed form. The stiffness and mass matrices of the non local rod are also obtained using the conventional finite element method. Results from the dynamic finite element method and conventional finite element method are compared. Using an asymptotic analysis it is shown that, unlike its local counterpart, a non local rod has a maximum cut-off frequency. A closed-form exact expression for this maximum frequency as a function of the non local parameter has been obtained for undamped and damped systems. The frequency response function obtained using the proposed dynamic finite element method shows extremely high modal density near the maximum frequency. This leads to clustering of resonance peaks which is not easily obtainable using classical finite element analysis.
Original languageEnglish
Pages (from-to)42-50
Number of pages9
JournalFinite Elements in Analysis and Design
Volume63
DOIs
Publication statusPublished - 1 Jan 2013
Externally publishedYes

Keywords

  • Axial vibration
  • Nonlocal mechanics
  • Dynamic stiffness
  • Asymptotic analysis
  • Frequency response

Cite this

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title = "Dynamic finite element analysis of axially vibrating nonlocal rods",
abstract = "Free and forced axial vibrations of damped non local rods are investigated. Two types of non local damping models, namely, strain-rate-dependent viscous damping and velocity-dependent viscous damping, are considered. A frequency-dependent dynamic finite element method is developed to obtain the forced vibration response. Frequency-adaptive complex-valued shape functions are proposed to obtain the dynamic stiffness matrix in closed form. The stiffness and mass matrices of the non local rod are also obtained using the conventional finite element method. Results from the dynamic finite element method and conventional finite element method are compared. Using an asymptotic analysis it is shown that, unlike its local counterpart, a non local rod has a maximum cut-off frequency. A closed-form exact expression for this maximum frequency as a function of the non local parameter has been obtained for undamped and damped systems. The frequency response function obtained using the proposed dynamic finite element method shows extremely high modal density near the maximum frequency. This leads to clustering of resonance peaks which is not easily obtainable using classical finite element analysis.",
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Dynamic finite element analysis of axially vibrating nonlocal rods. / Adhikari, S.; Murmu, T.; McCarthy, M.A.

In: Finite Elements in Analysis and Design, Vol. 63, 01.01.2013, p. 42-50.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Dynamic finite element analysis of axially vibrating nonlocal rods

AU - Adhikari, S.

AU - Murmu, T.

AU - McCarthy, M.A.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Free and forced axial vibrations of damped non local rods are investigated. Two types of non local damping models, namely, strain-rate-dependent viscous damping and velocity-dependent viscous damping, are considered. A frequency-dependent dynamic finite element method is developed to obtain the forced vibration response. Frequency-adaptive complex-valued shape functions are proposed to obtain the dynamic stiffness matrix in closed form. The stiffness and mass matrices of the non local rod are also obtained using the conventional finite element method. Results from the dynamic finite element method and conventional finite element method are compared. Using an asymptotic analysis it is shown that, unlike its local counterpart, a non local rod has a maximum cut-off frequency. A closed-form exact expression for this maximum frequency as a function of the non local parameter has been obtained for undamped and damped systems. The frequency response function obtained using the proposed dynamic finite element method shows extremely high modal density near the maximum frequency. This leads to clustering of resonance peaks which is not easily obtainable using classical finite element analysis.

AB - Free and forced axial vibrations of damped non local rods are investigated. Two types of non local damping models, namely, strain-rate-dependent viscous damping and velocity-dependent viscous damping, are considered. A frequency-dependent dynamic finite element method is developed to obtain the forced vibration response. Frequency-adaptive complex-valued shape functions are proposed to obtain the dynamic stiffness matrix in closed form. The stiffness and mass matrices of the non local rod are also obtained using the conventional finite element method. Results from the dynamic finite element method and conventional finite element method are compared. Using an asymptotic analysis it is shown that, unlike its local counterpart, a non local rod has a maximum cut-off frequency. A closed-form exact expression for this maximum frequency as a function of the non local parameter has been obtained for undamped and damped systems. The frequency response function obtained using the proposed dynamic finite element method shows extremely high modal density near the maximum frequency. This leads to clustering of resonance peaks which is not easily obtainable using classical finite element analysis.

KW - Axial vibration

KW - Nonlocal mechanics

KW - Dynamic stiffness

KW - Asymptotic analysis

KW - Frequency response

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DO - 10.1016/j.finel.2012.08.001

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SP - 42

EP - 50

JO - Finite Elements in Analysis and Design

JF - Finite Elements in Analysis and Design

SN - 0168-874X

ER -