SYSTEM IDENTIFICATION OF ADAPTIVE TRUSS STRUCTURES USING PIEZOELECTRIC ACTIVE MEMBERS

Adaptive truss structures are a new kind of structures with integrated active members,whose dynamic characteristies can be beneficially modified to meet mission requirements.Active members containing actuating and sensing units are the major components of adaptive truss structures.Modeling of adaptive truss structures is a key step to analyze the structural dynamic characteristics.A new experimental modal analysis approach,in which active members are used as excitatiDn sources for modal test,has been proposed in this paper.The excitation forces generated by the active members, which are different from the excitation forces exerted on structures in the conventional modal test,are internal forces for the truss structures.The relation between internal excitation forces and external forces is revealed such that the traditional identification method can be adopted to obtain modal parameters of adaptive structures.Placement problem of the active member in adaptive truss structures is also discussed in this work. Modal test and analysis are conducted with a planar adaptive truss structure by using piezoelectric active members in order to verify the feasibility and effectiveness of the proposed method.

Dynamic Response of Truss Adaptive Structures

It is pointed out that the damping matrix deduced by active members in the finite element vibration equation of a truss adaptive structure generally can not be decoupled, which leads to the difficulty in the process of modal analysis by classical superposition method. This paper focuses on the computational method of the dynamic response for truss adaptive structures. Firstly, a new technique of state vector approach is applied to study the dynamic response of truss adaptive structures. It can make the coeffic lent matrix of first derivative of state vector a symmetric positive definite matrix, and particularly a diagonal matrix provided that mass matrix is derived by lumped method, so the coefficient matrix of the first derivative of state vector can be exactly decomposed by CHOLESKY method. In this case, the proposed technique not only improves the calculation accuracy, but also saves the computing time. Based on the procedure mentioned above, the mathematical formulation for the system response of truss adaptive structures is systematically derived in theory. Thirdly, by using FORTRAN language, a program system for computing dynamic response of truss adaptive structures is developed. Fourthly, a typical 18 bar space truss adaptive structure has been chosen as test numerical examples to show the feasibility and effectiveness of the proposed method. Finally, some good suggestions, such as how to choose complex mode shapes practically in determining the dynamic response are also given. The new approach can be extended to calculate the dynamic response of general adaptive structures.

Optimal Placement of Active Members in Truss Adaptive Structures

The mathematical model of optimal placement of active members in truss adaptive structures is essentially a nonlinear multi-objective optimization problem with mixed variables. It is usually much difficult and costly to be solved. In this paper, the optimal location of active members is treated in terms of （0, 1） discrete variables. Structural member sizes, control gains, and （0, 1） placement variables are treated simultaneously as design variables. Then, a succinct and reasonable compromise scalar model, which is transformed from original multi-objective optimization, is established, in which the （0, 1） discrete variables are converted into an equality constraint. Secondly, by penalty function approach, the subsequent scalar mixed variable compromise model can be formulated equivalently as a sequence of continuous variable problems. Thirdly, for each continuous problem in the sequence, by choosing intermediate design variables and temporary critical constraints, the approximation concept is carried out to generate a sequence of explicit approximate problems which enhance the quality of the approximate design problems. Considering the proposed method, a FORTRAN program OPAMTAS2.0 for optimal placement of active members in truss adaptive structures is developed, which is used by the constrained variable metric method with the watchdog technique （CVMW method）. Finally, a typical 18 bar truss adaptive structure as test numerical examples is presented to illustrate that the design methodology set forth is simple, feasible, efficient and stable. The established scalar mixed variable compromise model that can avoid the ill-conditioned possibility caused by the different orders of magnitude of various objective functions in optimization process, therefore, it enables the optimization algorithm to have a good stability. On the other hand, the proposed novel optimization technique can make both discrete and continuous variables be optimized simultaneously.