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Investigation on vibration mitigation methodology with synergistic friction and electromagnetic damping energy dissipation

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Abstract

Friction dampers are widely used in vibration control of mechanical and civil architectures as a highly robust contact-based energy dissipation strategy. The energy dissipation principle of electromagnetic dampers is to convert the mechanical energy of vibration into electrical energy through a mechanical–magnetic–electric coupling mechanism and dissipate it through an external load circuit or store it in a battery or capacitor. It should be noted that the frictional energy dissipation is displacement dependent, while the electromagnetic energy dissipation is velocity dependent; hence, a synergistic energy dissipation with a combination of frictional and electromagnetic elements can be implemented to obtain satisfactory vibration suppression. This work presents a bi-stable energy scavenging inspired dynamic vibration absorber (DVA) consisting of negative stiffness spring components, electromagnetic conversion elements and friction pairs. The multiple periodic inter-well motion and chaotic motion are understood to illuminate the efficient energy shunt contributed by the bi-stable mechanism. The effects of mass ratio, potential barrier height and friction force on the energy scavenging and vibration suppression performance of this proposed prototype are parametrically analyzed. Numerical simulations have found that the bi-stable DVA with small mass ratio has a significant attenuation effect on the vibration energy of the host structure excited by harmonic excitation or transient shocks. The results indicate that an increase in the barrier height of the bi-stable oscillator leads to an increase in the optimal mass ratio required to achieve optimal energy dissipation efficiency. The small mass ratio bi-stable damper can achieve the best vibration suppression performance by actively regulating the friction force according to the change of ambient vibration. In addition, it is evident that the presence of critical friction minimizes the vibration displacement and energy of the host structure. However, when the friction force exceeds the critical threshold, the dynamic response of the host structure is amplified and the vibration energy increases, which is not conducive to vibration control. Therefore, implementing an appropriate friction force can improve the devastating dynamic response of the structure and facilitate the conversion of vibration energy into available energy.

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Data availability

Data in this work will be made available on reasonable request from the corresponding author.

Abbreviations

m 1 :

Mass of the host structure, kg

m 2 :

Mass of the bi-stable DVA, kg

b 1 :

Linear viscous damping of the host structure, N s/m

b 2 :

Linear viscous damping in the coupling, N s/m

k 1 :

Linear stiffness of the host structure, N/m

k 3 :

Linear stiffness term of the bi-stable DVA, N/m

k 4 :

Cubic stiffness term of the bi-stable DVA, N/m3

k f :

The grounded stiffness of the bi-stable DVA, N/m

b f :

The grounded friction damping of the bi-stable DVA, N s/m

R c :

Coil resistance, Ω

R L :

Load resistance, Ω

k e :

Transduction factor, T m

b e :

Electromechanical damping coefficient, N s/m

μ :

Mass ratio, 1

λ :

Dimensionless linear viscous damping term of the host structure, 1

ζ :

Dimensionless linear viscous damping term in the coupling, 1

β :

Dimensionless electromechanical damping coefficient term, 1

ξ :

Dimensionless negative linear stiffness of the bi-stable DVA, 1

ξ f :

Dimensionless grounded stiffness of the bi-stable DVA, 1

f v :

The nominal friction force, N

f c :

The Coulomb friction force, N

f s :

The maximum static friction force, N

v s :

The Stribeck speed, m/s

f ext :

The sum of all the external forces except friction, N

F n :

The normal force of contact interface, N

χ :

The empirical constant, 1

η :

The lubricant viscosity, Pa s

h :

The film thickness, m

p :

The film pressure, Pa

τ :

The dimensionless time, 1

α :

Dimensionless distance between adjacent potential wells, 1

P :

The harvested power, W

γ :

Dimensionless force coefficient term, 1

y 1 :

Displacement of the primary system, m

y 2 :

Displacement of the bi-stable DVA mass, m

F :

Amplitude of harmonic force, N

ω :

Circular frequency of harmonic force, rad/s

ω n :

Natural frequency of the primary system, rad/s

Ω:

The frequency ratio, 1

A :

Displacement of the primary system, m

E k :

Remaining kinetic energy of the host structure, J

Y r :

Amplitude of the host structure, m

V 0 :

Initial velocity of an impulse, m/s

\(\eta_{{\text{h}}}\) :

Efficiency of energy harvesting, %

\(\eta_{{\text{k}}}\) :

Remaining kinetic energy ratio of the primary system, %

E h :

The total harvested energy, J

DVA:

Dynamic vibration absorber

NES:

Nonlinear energy sink

BMPA:

Bi-stable magneto-pieozelastic absorber

VAEH:

Vibration absorber and energy harvester

SPL:

Dound pressure level

SAFD:

Semi-active friction damper

LCFD:

Leverage-type controllable friction damper

EHL:

Elastohydrodynamic lubrication

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Funding

The work is supported by National Natural Science Foundation of China (52305103), Changsha Natural Science Foundation Project (kq2208025), Distinguished Young Scholars Fund of National Natural Science Foundation of China (52025082) and Key Support Project of National Natural Science Foundation of China - "Ye Qisun" Science Foundation (U2141242).

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Authors and Affiliations

  1. Key Laboratory for Bridge and Wind Engineering of Hunan Province, College of Civil Engineering, Hunan University, Changsha, 410082, Hunan, China

    Xingbao Huang, Zhiwen Huang, Xugang Hua & Zhengqing Chen

  2. Vibration and Shock Technology Research Center, Hunan University, Changsha, 410082, Hunan, China

    Xingbao Huang, Zhiwen Huang, Xugang Hua & Zhengqing Chen

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  1. Xingbao Huang
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Correspondence to Zhiwen Huang.

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Huang, X., Huang, Z., Hua, X. et al. Investigation on vibration mitigation methodology with synergistic friction and electromagnetic damping energy dissipation. Nonlinear Dyn 111, 18885–18910 (2023). https://doi.org/10.1007/s11071-023-08832-w

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