Nonlinear dynamics and vibration reduction of a dry friction oscillator with SMA restraints

Fu, Shihui; Lu, Qishao

doi:10.1007/s11071-012-0353-y

Cited by 11 publications

(7 citation statements)

References 29 publications

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“…Odeny D. et al [8] studied the nonlinearity of the aeroelastic behavior of reinforced SMA hybrid composite (SMAHC) cylindrical plate on a microscopic mechanics model of carbon fiber-SMAHC laminated plate using a layered Rayleigh-Ritz procedure. Akhavan-Rad B. et al [9] applied the high-order sandwich panel theory to the vibration of SMA wire-embedded laminated plate Materials 2021, 14, 4022 2 of 13 and provided an analytical solution to the nonlinear control equation for simply-supported sandwich panels under uniform and sinusoidal loading. Reza Razavilar et al [10] developed a semi-analytical method to examine the free and forced vibration of SMA beams, modeled the control dynamic equation for SMA beams coupled with deformation strain, and analyzed the dynamic characteristics of these beams using phase trajectory.…”

Section: Introductionmentioning

confidence: 99%

“…Brinson’s constitutive model is widely used because of its simplicity and effectiveness. Fu [ 13 ] addressed the free vibration of SMA fiber-embedded composite laminated beams using Brinson’s polynomial constitutive model to consider their stress–strain relation. Asadi [ 14 , 15 ] built a control equation for laminated beams with SMA fibers that considered the effects of thermal and aerodynamic loads using Brinson’s polynomial constitutive model; they investigated the thermodynamic behavior of SMA laminated beams.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Dynamic Analysis of Axially Moving Laminated Shape Memory Alloy Beam with 1:3 Internal Resonance

Hao

Gao

et al. 2021

Materials

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The remarkable properties of shape memory alloys (SMA) are attracting significant technological interest in many fields of science and engineering. In this paper, a nonlinear dynamic analytical model is developed for a laminated beam with a shape memory alloy layer. The model is derived based on Falk’s polynomial model for SMAs combined with Timoshenko beam theory. In addition, axial velocity, axial pressure, temperature, and complex boundary conditions are also parameters that have been taken into account in the creation of the SMA dynamical equation. The nonlinear vibration characteristics of SMA laminated beams under 1:3 internal resonance are studied. The multi-scale method is used to solve the discretized modal equation system, the characteristic equation of vibration modes coupled to each other in the case of internal resonance, as well as the time-history and phase diagrams of the common resonance amplitude in the system are obtained. The effects of axial velocity and initial conditions on the nonlinear internal resonance characteristics of the system were also studied.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Analysis of Axially Moving Laminated Shape Memory Alloy Beam with 1:3 Internal Resonance

Hao

Gao

et al. 2021

Materials

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“…Since the start of constitutive modeling of SMA in the 1980s, a large number of constitutive models, including piecewise-linear model, Brinson's polynomial constitutive model and Falk's model, have been developed to describe the shape memory and pseudoelasticity of SMA. Fu and Lu (2012) focused on the dynamic response of SMA laminated beams under a piecewise linear resilience model and examined how external excitation amplitude and temperature affected the system response behavior. Lu et al (2009) proposed a relatively common constitutive SMA fiber constitutive relation and built a bending theory model of SMA fiber-reinforced composite laminated beams without considering the stress relation between the SMA layer and the matrix layer.…”

Section: Introductionmentioning

confidence: 99%

The 1/3rd subharmonic and 3rd superharmonic resonance of a shape memory alloy (SMA) laminated beam

Zhang¹,

Gao²,

Hao³

2020

Journal of Theoretical and Applied Mechanics

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This paper examines the 1/3rd subharmonic resonance and the 3rd superharmonic resonance of simply-supported shape memory alloy (SMA) laminated beams. First, the dynamic equation for SMA laminated beams under transverse load is established using physical equations, force equilibrium conditions, the compatibility equation of deformation, and a constitutive model of SMA polynomial functions. Then, a differential equation for transverse vibration of the SMA laminated beams is derived by the Galerkin process assuming the boundary conditions for simply-supported beams. Next, the amplitude-frequency response equations for the 1/3rd subharmonic resonance and the 3rd superharmonic resonance of these beams are derived by an averaging method before their respective transition sets are calculated, and their amplitude-frequency response diagrams were plotted using singularity theory. The results show two different types of amplitude-frequency responses to nonlinear vibration under the 1/3rd subharmonic resonance and the 3rd superharmonic resonance: quasi-linear and hard characteristic. In the quasi-linear area, SMA thickness A does not make much difference to the response of the system, whereas in the hard-characteristics area, under the same excitation amplitude f , the resonance frequency increases with A. In the nonlinear area, SMA can obviously reduce vibration amplitude, but it is not obvious for the 1/3rd subharmonic resonance. The nonlinear solution of both the 1/3rd subharmonic resonance and 3rd superharmonic resonance are stable.

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“…Savi et al [16] studied the nonlinear dynamics of shape memory alloy systems and established the constitutive model of the SMA. Fu and Lu [17] investigated the nonlinear dynamics and vibration damping of dry friction oscillators with SMA restraints. Costa et al [18] applied the extended time-delayed feedback approach to investigate the chaos control of an SMA two-bar truss.…”

Section: Introductionmentioning

confidence: 99%

Bogdanov–Takens Bifurcation in a Shape Memory Alloy Oscillator with Delayed Feedback

Wang

2020

Complexity

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This work is focused on a shape memory alloy oscillator with delayed feedback. The main attention is to investigate the Bogdanov–Takens (B-T) bifurcation by choosing feedback parameters A 1,2 and time delay τ . The conditions for the occurrence of the B-T bifurcation are derived, and the versal unfolding of the norm forms near the B-T bifurcation point is obtained by using center manifold reduction and normal form. Moreover, it is demonstrated that the system also undergoes different codimension-1 bifurcations, such as saddle-node bifurcation, Hopf bifurcation, and saddle homoclinic bifurcation. Finally, some numerical simulations are given to verify the analytic results.

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Nonlinear dynamics and vibration reduction of a dry friction oscillator with SMA restraints

Cited by 11 publications

References 29 publications

Nonlinear Dynamic Analysis of Axially Moving Laminated Shape Memory Alloy Beam with 1:3 Internal Resonance

Nonlinear Dynamic Analysis of Axially Moving Laminated Shape Memory Alloy Beam with 1:3 Internal Resonance

The 1/3rd subharmonic and 3rd superharmonic resonance of a shape memory alloy (SMA) laminated beam

Bogdanov–Takens Bifurcation in a Shape Memory Alloy Oscillator with Delayed Feedback

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