EXTRACTION OF GLOBAL MODE FUNCTIONS AND CONSTRUCTION OF STATE SPACE MODEL FOR A COMPOSITE FLEXIBLE STRUCTURE

doi:10.6052/0459-1879-18-356

Abstract

Abstract:

With the scale enlarging and flexibility of the actual engineering structures utilized in aerospace and other fields, the issues on the study of nonlinear vibration and active vibration control of the structure become more and more important. The key process of dealing with the vibration and control for such a kind of structure is to establish the nonlinear dynamic model and formulate the state space model of the system. For composite flexible structures composed of flexible components, rigid bodies and flexible joints, because of the vibration coupling between each part of the structure, the modes of an individual flexible component with the cantilever, simply supported and free stationary boundary are different from the real mode of the structure. In this paper, an analytic extraction method of global modes of composite flexible structures is presented, and the nonlinear dynamic model and the state-space model of the system can be obtained by the global mode discretization. Adopting the Cartesian coordinates to describe the motion of the system, establishing the motion equations of the system, and combining with the partial differential equation of the flexible part, the ordinary differential motion equation of the rigid body, the matching condition of force, moment, slope of the deflection curve and displacement at the interface, and the boundary condition of the system, the frequency equation of uniform form is given by using the separating variable method. Consequently, the natural frequencies and the global mode representation of the analytic function of the system are obtained. The global mode extraction method presented here not only facilitates the parametric analysis of the natural frequencies and global modes of composite flexible structures, but also provides an effective way to establish the low dimensional nonlinear dynamic model and the state space model of the composite flexible structure, which is of great significance for the study of nonlinear dynamic responses and the design of active vibration control of this kind of structures.

Key words: flexible structures, global modes, analytic method, nonlinear dynamics, vibration control

CLC Number:

TB122

Jin Wei, Dengqing Cao, Tao Yu. EXTRACTION OF GLOBAL MODE FUNCTIONS AND CONSTRUCTION OF STATE SPACE MODEL FOR A COMPOSITE FLEXIBLE STRUCTURE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 341-353.

Figures/Tables 12

Fig.1 Motion description based on Descartes coordinates

Fig.2 Forces and moments acted on the rigid body

Fig.3 Constraint relationship of rigid connecting deformable bodies

Fig.4 Constraint relationship of elastic connection deformable bodies

Fig.5 Motion description of the Euler-Bernoulli beam

Fig.6 Piezoelectric multi-beam structure connected with joints

Fig.7 The model of the joint

Fig.8 (a) Geometric and (b) natural matching conditions at the joint${S}_{2}$

Fig.9 (a) Geometric and (b) natural matching conditions on the rigid body

Table 1 Geometric and material parameters of the multi-beam structure connected with joints

l/m	E/GPa	b/mm	h"mm
0.15	210	50	5
p/(kg.m^-1)	kL/(Nm.rad^-1)	mr /kg	J"(kg.m²)
1.962 5	1000	0.353 3	1.33 x 10^-4

Fig.10 The first eight natural frequencies and mode shapes of the structure from Ansys

Fig.11 The first eight natural frequencies and mode shapes of the structure from the analytic method

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