Active traveling wave vibration control of elastic supported conical shells with smart micro fiber composites based on the differential quadrature method

doi:10.1007/s10483-025-3216-7

Abstract

Abstract:

This paper investigates the active traveling wave vibration control of an elastic supported rotating porous aluminium conical shell (CS) under impact loading. Piezoelectric smart materials in the form of micro fiber composites (MFCs) are used as actuators and sensors. To this end, a metal pore truncated CS with MFCs attached to its surface is considered. Adding artificial virtual springs at two edges of the truncated CS achieves various elastic supported boundaries by changing the spring stiffness. Based on the first-order shear deformation theory (FSDT), minimum energy principle, and artificial virtual spring technology, the theoretical formulations considering the electromechanical coupling are derived. The comparison of the natural frequency of the present results with the natural frequencies reported in previous literature evaluates the accuracy of the present approach. To study the vibration control, the integral quadrature method in conjunction with the differential quadrature approximation in the length direction is used to discretize the partial differential dynamical system to form a set of ordinary differential equations. With the aid of the velocity negative feedback method, both the time history and the input control voltage on the actuator are demonstrated to present the effects of velocity feedback gain, pore distribution type, semi-vertex angle, impact loading, and rotational angular velocity on the traveling wave vibration control.

Key words: rotating conical shell (CS), porous metal material, active vibration control, elastic support, differential quadrature method

2010 MSC Number:

TB123

Yuxin HAO, Lei SUN, Wei ZHANG, Han LI. Active traveling wave vibration control of elastic supported conical shells with smart micro fiber composites based on the differential quadrature method. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 305-322.

TrendMD

Figures/Tables 11

Fig. 1

Fig. 2

Table 1

Frequency parameters of CSs with CC, CF, and CS boundaries"

$n$	CC			CF			CS
$n$	Present	Ref. [41]	Error/%	Present	Ref. [41]	Error/%	Present	Ref. [41]	Error/%
0	1.002 5	1.003 0	0.05	0.831 0	0.831 2	0.02	0.831 0	0.831 2	0.02
1	0.964 6	0.965 1	0.05	0.676 7	0.676 8	0.01	0.676 7	0.676 8	0.01
2	0.875 3	0.875 9	0.07	0.483 0	0.483 1	0.02	0.483 0	0.483 1	0.02
3	0.776 3	0.777 0	0.09	0.355 1	0.355 3	0.07	0.355 1	0.355 3	0.07
4	0.691 3	0.692 6	0.18	0.274 8	0.275 1	0.12	0.274 8	0.275 1	0.12
5	0.627 9	0.629 2	0.20	0.228 5	0.229 0	0.24	0.228 5	0.229 0	0.24
6	0.586 9	0.588 5	0.27	0.210 8	0.211 5	0.32	0.210 8	0.211 5	0.32
7	0.567 6	0.569 6	0.36	0.218 7	0.219 5	0.38	0.218 7	0.219 5	0.38
8	0.568 7	0.571 2	0.44	0.247 0	0.248 0	0.42	0.247 0	0.248 0	0.42
9	0.588 9	0.591 9	0.51	0.290 2	0.291 4	0.40	0.290 2	0.291 4	0.40

Table 1

Table 2

Comparison of natural frequencies of CC rotational cylindrical shell"

$Ω ∗$	$n$	$ω b ∗$			$ω f ∗$
$Ω ∗$	$n$	Ref. [42]	Present	Error/%	Ref. [42]	Present	Error/%
0.005 0	2	0.062 15	0.062 16	0.010	0.054 60	0.054 16	0.81
	3	0.116 53	0.116 52	0.001	0.110 58	0.110 20	0.34
	4	0.214 87	0.214 86	0.001	0.210 18	0.208 73	0.69
	5	0.343 81	0.343 85	0.010	0.339 97	0.336 22	1.11

Table 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

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