Nonlinear traveling wave vibration of rotating ferromagnetic functionally graded cylindrical shells under multi-physics fields

doi:10.1007/s10483-025-3302-9

Abstract

Abstract:

The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded (FG) cylindrical shells under multi-physics fields is investigated. Grounded in the Kirchhoff-Love thin shell theory, the geometric nonlinearity is incorporated into the model, and the constitutive equations are derived. The physical parameters of functionally graded materials (FGMs), which exhibit continuous variation across the thickness gradient, are of particular interest. The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton’s principle. The nonlinear partial differential equations are discretized with the Galerkin method, and the analytical expression of traveling wave frequencies is derived with an approximate method. The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions. Finally, the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies. The results show that the factors including the power-law index, temperature, magnetic field intensity, and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.

Key words: ferromagnetic functionally graded (FG) cylindrical shell, nonlinear traveling wave vibration, multi-physics field, approximate analytical method

2010 MSC Number:

O322

Feng LIAO, Yuda HU, Tao YANG, Xiaoman LIU. Nonlinear traveling wave vibration of rotating ferromagnetic functionally graded cylindrical shells under multi-physics fields. Applied Mathematics and Mechanics (English Edition), 2025, 46(10): 1921-1938.

TrendMD

Figures/Tables 13

Fig. 1

Fig. 2

Fig. 3

Table 1

Comparison of frequencies (rad/s) between the present solution and PSD (m=1, n=2, A=0.006 m, N=10, Ω=10 000 r/min, ΔT=300 K, and Hn=2 000 A/m)"

Method	S-S		C-F		S-C		C-C
Method	$ω f$	$ω b$	$ω f$	$ω b$	$ω f$	$ω b$	$ω f$	$ω b$
PSD	1 641	3 692	812	2 872	2 256	4 308	2 872	4 923
Present	1 592	3 690	785	2 868	2 239	4 276	2 875	4 856

Table 1

Table 2

Temperature-dependent coefficients of Ni and Si3N4[50]"

Material	Parameter	$P 0$	$P 1$	$P 2$	$P 3$
Ni	$E$ /Pa	$223.95 × 109$	$− 2.794 × 10 − 4$	$− 3.998 × 10 − 9$	0.0
Ni	$α$ /K^-1	$9.920 9 × 10 − 6$	$8.705 × 10 − 4$	0.0	0.0
Si₃N₄	$E$ /Pa	$348.43 × 109$	$− 3.070 × 10 − 4$	$2.16 × 10 − 7$	$− 8.946 × 10 − 11$
Si₃N₄	$α$ /K^-1	$5.872 3 × 10 − 6$	$9.095 × 10 − 4$	0.0	0.0

Table 2

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Table 3

Variations of ωb and ωf with Ω, ΔTc, and N"

Parameter	$Δ T c$ /K	$Ω = 5 000$ r/min		$Ω = 10 000$ r/min		$Ω = 15 000$ r/min
Parameter	$Δ T c$ /K	$N = 1$	$N = 10$	$N = 1$	$N = 10$	$N = 1$	$N = 10$
$ω b / (rad ⋅ s − 1)$	0	$A 1$ (4 806)	$A 2$ (3 498)	$A 3$ (5 663)	$A 4$ (4 361)	$A 5$ (6 795)	$A 6$ (5 567)
	300	$B 1$ (4 421)	$B 2$ (3 140)	$B 3$ (5 311)	$B 4$ (4 082)	$B 5$ (6 489)	$B 6$ (5 334)
	600	$C 1$ (3 994)	$C 2$ (2 752)	$C 3$ (4 929)	$C 4$ (3 790)	$C 5$ (6 164)	$C 6$ (5 097)
$ω f / (rad ⋅ s − 1)$	0	$D 1$ (3 747)	$D 2$ (2 446)	$D 3$ (3 549)	$D 4$ (2 272)	$D 5$ (3 633)	$D 6$ (2 437)
	300	$E 1$ (3 362)	$E 2$ (2 088)	$E 3$ (3 198)	$E 4$ (1 985)	$E 5$ (3 267)	$E 6$ (2 202)
	600	$F 1$ (2 935)	$F 2$ (1 700)	$F 3$ (2 817)	$F 4$ (1 692)	$F 5$ (3 002)	$F 6$ (1 965)

Table 3

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