Structural vibration control using nonlinear damping amplifier friction vibration absorbers

doi:10.1007/s10483-025-3248-7

Abstract

Abstract:

This paper introduces damping amplifier friction vibration absorbers (DAFVAs), compound damping amplifier friction vibration absorbers (CDAFVAs), nested damping amplifier friction vibration absorbers (NDAFVAs), and levered damping amplifier friction vibration absorbers (LDAFVAs) for controlling the structural vibrations and addressing the limitations of conventional tuned mass dampers (TMDs) and friction-tuned mass dampers (FTMDs). The closed-form analytical solution for the optimized design parameters is obtained using the $H 2$ and $H ∞$ optimization approaches. The efficiency of the recently established closed-form equations for the optimal design parameters is confirmed by the analytical examination. The closed form formulas for the dynamic responses of the main structure and the vibration absorbers are derived using the transfer matrix formulations. The foundation is provided by the harmonic and random-white noise excitations. Moreover, the effectiveness of the innovative dampers has been validated through numerical analysis. The optimal DAFVAs, CDAFVAs, NDAFVAs, and LDAFVAs exhibit at least 30% lower vibration reduction capacity compared with the optimal TMD. To demonstrate the effectiveness of the damping amplification mechanism, the novel absorbers are compared with a conventional FTMD. The results show that the optimized novel absorbers achieve at least 91% greater vibration reduction than the FTMD. These results show how the suggested designs might strengthen the structure's resilience to dynamic loads.

Key words: damping amplifier friction vibration absorber (DAFVA), compound damping amplifier friction vibration absorber (CDAFVA), nested damping amplifier friction vibration absorber (NDAFVA), levered damping amplifier friction vibration absorber (LDAFVA), $H 2$ and $H ∞$ optimization approaches

2010 MSC Number:

O322

S. CHOWDHURY, S. ADHIKARI. Structural vibration control using nonlinear damping amplifier friction vibration absorbers. Applied Mathematics and Mechanics (English Edition), 2025, 46(5): 965-988.

TrendMD

Figures/Tables 18

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 1

The structural system parameter for the SDOF system"

Primary structure	Governing system parameter	Value $ξ s$
SDOF	Damping ratio	0.01

Table 1

Table 2

The novel and conventional TMD's H2 optimized design parameters"

System	Reference	$H 2$ optimization
System	Reference	$κ b$	$ξ b$
DAFVA	Present	0.940 401	0.077 313 2
CDAFVA	Present	0.940 401	0.073 566 0
NDAFVA	Present	0.940 401	0.077 313 2
LDAFVA	Present	0.940 401	0.109 806 0
Conventional TMD1	Refs. [25] and [26]	$1 1 + μ ˜ d$	$μ ˜ d 2$
Conventional TMD2	Refs. [25] and [27]	$1 1 + μ ˜ d 2 + μ ˜ d 2$	$μ ˜ d (4 + 3 μ ˜ d) 8 (1 + μ ˜ d) (2 + μ ˜ d)$
Conventional TMD1: damper mass ratio $(μ ˜ d) = 0.05$ ; conventional TMD2: damper mass ratio $(μ ˜ d) = 0.05$ ; DAFVAs: damper mass ratio $(μ d) = 0.05$ , $ϕ = 40 o$ ; CDAFVAs: $μ d = 0.05$ , $ϕ = 40 o$ , $θ = 64 o$ ; NDAFVAs: $μ d = 0.05$ , $ϕ 1 = 40 o$ , $ϕ 2 = 45 o$ , $ϕ 3 = 45 o$ ; LDAFVAs: $μ d = 0.05$ , $b 1 / a 1 = 1$ , $b 2 / a 2 = 1$

Table 2

Fig. 9

Table 3

The values of each H∞ optimized design parameter for conventional and novel vibration absorbers"

System	Reference	$H ∞$ optimization
System	Reference	$κ b$	$ξ b$
DAFVA	Present	0.940 401	0.095 286 4
CDAFVA	Present	0.940 401	0.090 668 1
NDAFVA	Present	0.940 401	0.095 286 4
LDAFVA	Present	0.940 401	0.135 333 0
Conventional TMD1	Refs. [28] and [29]	$1 1 + μ ˜ d$	$3 μ ˜ d 8 (1 + μ ˜ d)$
Conventional TMD2	Ref. [30]	$1 1 + μ ˜ d$	$μ ˜ d 2 (1 + μ ˜ d)$
Conventional TMD1: damper mass ratio $(μ ˜ d) = 0.05$ ; conventional TMD2: damper mass ratio $(μ ˜ d) = 0.05$ ; DAFVAs: damper mass ratio $(μ d) = 0.05$ , $ϕ = 40 o$ ; CDAFVAs: $μ d = 0.05$ , $ϕ = 40 o$ , $θ = 64 o$ ; NDAFVAs: $μ d = 0.05$ , $ϕ 1 = 40 o$ , $ϕ 2 = 45 o$ , $ϕ 3 = 45 o$ ; LDAFVAs: $μ d = 0.05$ , $b 1 / a 1 = 1$ , $b 2 / a 2 = 1$

Table 3

Fig. 10

Fig. 11

Table 4

The optimal design parameters of FTMD"

System	Reference	Optimal parameter
System	Reference	$κ b$	$ξ b$
FTMD	Ref. [24]	1	0.029 1

Table 4

Fig. 12

Fig. 13

Fig. 14

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