Hamilton’s principle as inequality for inelastic bodies

Yang, Qiang; Lv, Qifeng; Liu, Yaoru

doi:10.1007/s00161-017-0557-y

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…Then, applying Hamilton's principle in variational form for inelastic materials (Kim et al, 2013;Yang et al, 2017), the equation of motion can be derived as…”

Section: Equation Of Motionmentioning

confidence: 99%

“…The property related to density is defined asin which ρA is the mass per unit length of the microbeam. Then, applying Hamilton’s principle in variational form for inelastic materials (Kim et al, 2013; Yang et al, 2017), the equation of motion can be derived asboundary conditions are expressed as w(0)=w(L)=(∂w/∂x)(0)=(∂w/∂x)(L)=0.…”

Section: Governing Equationsmentioning

confidence: 99%

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Nonlinear free vibration and damping analysis of a microbeam with pseudoelastic shape memory alloy layer based on the modified couple stress theory

Ashrafi

Ghaffari

Elahinia

et al. 2020

Journal of Vibration and Control

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The aim of this investigation is to evaluate the size effects on the nonlinear free vibration of the sandwich composite microbeam with an extensible shape memory alloy layer in the midplane. A one-dimensional constitutive model is considered to simulate the pseudoelastic behavior of the shape memory alloy layer. The governing equation of motion is derived using the Euler–Bernoulli beam theory together with the modified couple stress theory through the Hamilton’s principle. Midplane stretching and phase transformation of the shape memory alloy which are sources of nonlinearity were considered, and a numerical solution method is presented. A damped response of the sandwich composite microbeam is observed because of the hysteresis behavior of the extensible shape memory alloy layer in the midplane. Results are appraised by comparing with the available literature. The influence of material length scale, temperature, and initial velocity on the loss factor and other pivotal vibrational behavior is evaluated. Results show that increasing the material length scale to thickness ratio has a decreasing effect on damping capacity.

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“…Then, applying Hamilton's principle in variational form for inelastic materials (Kim et al, 2013;Yang et al, 2017), the equation of motion can be derived as…”

Section: Equation Of Motionmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

Nonlinear free vibration and damping analysis of a microbeam with pseudoelastic shape memory alloy layer based on the modified couple stress theory

Ashrafi

Ghaffari

Elahinia

et al. 2020

Journal of Vibration and Control

View full text Add to dashboard Cite

show abstract

“…The property related to density is described asin which ρA is the mass per unit length of the beam. Then, applying Hamilton’s principle in variational form for inelastic materials (Kim et al, 2013; Yang et al, 2017), the equation of motion can be derived…”

Section: Formulation Of Problemmentioning

confidence: 99%

A perturbation analysis in nonlinear free vibration of a microbeam reinforced by shape memory alloy layer based on the modified couple stress theory

Ghaffari

Mohammadi

2020

Journal of Vibration and Control

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Numerous applications have been found in various microelectromechanical systems for shape memory alloys. This study analyzes the nonlinear free vibrations of a sandwiched microbeam, consisting of a shape memory alloy core and two elastic layers on either side. The behavior of the shape memory layer is modeled with the one-dimensional Brinson model. The equation of motion is derived from Hamilton’s principle and the modified couple stress theory for the Euler–Bernoulli beam and then truncated into a reduced-order model through Galerkin’s technique. An approximate analytical solution is obtained using the Lindstedt–Poincare method for different temperatures. The effects of temperature, material length scale parameter, aspect ratio, and maximum vibration amplitude on nonlinear normalized frequency have been investigated. The results have been compared with those of some previous studies and can provide a better understanding of the design of sandwiched microbeams, which have a shape memory alloy layer.

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An analytical study of the plasticity of sandwich honeycomb panels subjected to low-velocity impact

Sun

Wowk

Mechefske

et al. 2019

Composites Part B: Engineering

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Hamilton’s principle as inequality for inelastic bodies

Cited by 5 publications

References 19 publications

Nonlinear free vibration and damping analysis of a microbeam with pseudoelastic shape memory alloy layer based on the modified couple stress theory

Nonlinear free vibration and damping analysis of a microbeam with pseudoelastic shape memory alloy layer based on the modified couple stress theory

A perturbation analysis in nonlinear free vibration of a microbeam reinforced by shape memory alloy layer based on the modified couple stress theory

An analytical study of the plasticity of sandwich honeycomb panels subjected to low-velocity impact

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