Vibration and response behaviors of composite sandwich cylindrical shells with a carbon nanotube-reinforced damping gel honeycomb core

doi:10.1007/s10483-025-3304-7

Abstract

Abstract:

This study provides a thorough investigation into the vibration behavior and impulse response characteristics of composite honeycomb cylindrical shells filled with damping gel (DG-FHCSs). To address the limitations of existing methods, a dynamic model is developed for both free and forced vibration scenarios. These models incorporate the virtual spring technology to accurately simulate a wide range of boundary conditions. Using the first-order shear deformation theory in conjunction with the Jacobi orthogonal polynomials, an energy expression is formulated, and the natural frequencies and mode shapes are determined via the Ritz method. Based on the Newmark- $β$ method, the pulse response amplitudes and attenuation characteristics under various transient excitation loads are analyzed and evaluated. The accuracy of the theoretical model and the vibration suppression capability of the damping gel are experimentally validated. Furthermore, the effects of key structural parameters on the natural frequency and vibration response are systematically examined.

Key words: dynamic model, honeycomb sandwich shell, damping gel, anti-vibration, transient response

2010 MSC Number:

O326

Peiyao XU, Zhuo XU, Shang GENG, Hui LI, Yan ZHOU, Haijun WANG, Jian XIONG, Zeng LIN, Jun LI. Vibration and response behaviors of composite sandwich cylindrical shells with a carbon nanotube-reinforced damping gel honeycomb core. Applied Mathematics and Mechanics (English Edition), 2025, 46(10): 1867-1882.

TrendMD

Figures/Tables 8

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Table 1

Geometrical and material characteristics of the FHCS and DG-FHCS"

Type	Parameter
Outside and inside skins	$E 1 f1,f2 = 258$ GPa, $E 2 f1,f2 = 35$ GPa, $G 12 f1,f2 = 3$ GPa, $G 12 f1,f2 = G 13 f1,f2 = 2$ GPa, $ν 12 f1,f2 = ν 21 f1,f2 = 0.3,$ $ρ f1,f2 = 1 500$ kg/m³, $h f1,f2 = 1$ mm, $κ k = [0 ∘ / 90 ∘ / 0 ∘]$
Honeycomb core	$E h = 80$ GPa, $ρ h = 1 750$ kg/m³, $G h = 32$ GPa, $h o = 0.008$ m, $θ h = 60 ∘,$ $a = 1 × 10 − 3$ m, $b = 1 × 10 − 2$ m
Damping gel Overall structure	$E o = G o = 4.217 × 10 − 4$ GPa, $ρ o = 930$ kg/m³ $L = 0.15$ m, $R = 0.04$ m

Table 1

Table 2

Table 3

Comparison of the test and computational peak-to-peak amplitude without damping gel filled"

Type	Rectangular	Triangular	Half-sine	Exponential
Experimental amplitude/m	$4.7 × 10 − 5$	$14.2 × 10 − 6$	$23.0 × 10 − 6$	$4.6 × 10 − 6$
Theoretical amplitude/m	$5.0 × 10 − 5$	$15.1 × 10 − 6$	$24.5 × 10 − 6$	$4.9 × 10 − 6$
Error/%	6.4	6.3	6.5	6.5

Table 3

Table 4

Comparison of the test and computational peak-to-peak amplitude with damping gel filled"

Type	Rectangular	Triangular	Half-sine	Exponential
Experimental amplitude/m	$3.1 × 10 − 5$	$12.4 × 10 − 6$	$20.3 × 10 − 6$	$3.3 × 10 − 6$
Theoretical amplitude/m	$3.3 × 10 − 5$	$13.2 × 10 − 6$	$21.6 × 10 − 6$	$3.5 × 10 − 6$
Error/%	6.4	6.5	6.4	6.1

Table 4

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Mode	FHCS		Error/%	DG-FHCS		Error/%
Mode	Experimental frequency/Hz	Theoretical frequency/Hz	Error/%	Experimental frequency/Hz	Theoretical frequency/Hz	Error/%
1st	1 010.0	1 034.8	2.5	989.5	1 014.2	2.5
2nd	1 157.5	1 207.4	4.3	1 134.0	1 183.9	4.4
3rd	1 802.0	1 881.6	4.9	1 765.5	1 855.5	5.1