The current paper presents the reliability-based optimization of the location and feedback gains of active bar in a closed-loop control system for random smart truss structures under stationary random excitation. The mathematical model with reliability constraints on the root mean square value of the structural random dynamic displacement and stress response is developed based on maximization of dissipation energy due to the control action. The randomness of the structural physical materials, geometry, and damping are included in the analysis, and the applied forces are considered as stationary random excitation. The numerical characteristic corresponding to mean values and standard deviations of the stationary random responses of random smart structures is developed by the random factor method. Numerical examples of truss structures are presented to demonstrate the rationality and validity of the active control model.
HurlebausS.GaulL.Smart structure dynamics. Mech. Syst. Signal Process., 2006, 20(1), 255–281.
2.
ChopraI.Status of application of smart structures technology to rotorcraft systems. J. Am. Helicopter Soc., 2000, 45(4), 228–252.
3.
DiwekarA.M.YedavalliR. K.Smart structure control in matrix second-order form. Smart Mater. Struct., 1996, 5(4), 429–436.
4.
WangQ.WangC. M.Controllability Index for optimal design of piezoelectric actuators in vibration control of beam structures. J. Sound Vibr., 2001, 242(3), 507–518.
5.
SukJ.BooS.KimY.Lyapunov control law for slew maneuver using time finite element analysis. J. Guid. Control Dyn., 2001, 24(1), 87–94.
6.
QuekS. T.WangS. Y.AngK. K.Vibration control of composite plates via optimal placement of piezoelectric patches. J. Intell. Mater. Syst. Struct., 2003, 14(4–5), 229–245.
7.
ChenC. C.LinC. C.An impedance approach for determining optimal locations and shapes of multiple induced strain actuators. Smart Mater. Struct., 2005, 14(6), 1120–1126.
8.
PengF. J.NgA.HuY. R.Actuator placement optimization and adaptive vibration control of plate smart structures. J. Intell. Mater. Syst. Struct., 2005, 16(3), 263–271.
9.
PapadrakakisM.KotsopulosA.Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation. Comput. Methods Appl. Mech. Eng., 1999, 168(1–4), 305–320.
10.
HurtadoJ. E.BarbatA.H.Monte Carlo techniques in computational stochastic mechanics. Arch. Comput. Methods Eng., 1998, 5(1), 3–29.
11.
SinghB. N.YadavD.IyengarN. G. R.Natural frequencies of composite plates with random material properties using higher-order shear deformation theory. Int. J. Mech. Sci., 2001, 43(10), 2193–2214.
12.
SachdevaS. K.NairP. B.KeaneA. J.Comparative study of projection schemes for stochastic finite element analysis. Comput. Methods Appl. Mech. Eng., 2006, 195(19–22), 2371–2392.
13.
GhanemR. G.SpanosP. D.Spectral stochastic finite-element formulation for reliability-analysis. J. Eng. Mech. ASCE, 1991, 117(10), 2351–2372.
14.
ElishakoffI.RenY. J.ShinozukaM.New formulation of FEM for deterministic and stochastic beams through generalization of Fuchs' approach. Comput. Methods Appl. Mech. Eng., 1997, 144(3–4), 235–243.
15.
GrahamL. L.DeodatisG.Response and eigenvalue analysis of stochastic finite element systems with multiple correlated material and geometric properties. Probab. Eng. Mech., 2001, 16(1), 11–29.
16.
ZhaoL.ChenQ.Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation. Comput. Struct., 2000, 77(6), 651–657.
17.
LiJ.LiaoS. T.Dynamic response of linear stochastic structures under random excitation. Acta Mech. Sin., 2002, 34(3), 416–424.
18.
MaX. P.LengX. L.MengG.FangT.Evolutionary earthquake response of uncertain structure with bounded random parameter. Probab. Eng. Mech., 2004, 19(3), 239–246.
19.
LiJ.ChenJ. B.Dynamic response and reliability analysis of structures with uncertain parameters. Int. J. Numer. Methods Eng., 2005, 62(2), 289–315.
20.
BatheK. J.Finite element procedures in engineering analysis, 1995 (Prentice-Hall, Inc., New Jersey).
21.
GaoW.ChenJ. J.MaH. B.MaX. S.Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters. Comput. Struct., 2003, 81(1), 53–60.
22.
AbdullahM. M.Optimal location and gains of feedback controllers at discrete locations, AIAA J., 1998, 36(11), 2109–2116.
23.
ChenJ. J.DuanB. Y.Structural optimization by displaying the reliability constraints. Comput. Struct., 1994, 50(6), 777–783.
24.
GaoW.ChenJ. J.ZhouY. B.CuiM. T.Dynamic response analysis of closed loop control system for random intelligent truss structure under random forces. Mech. Syst. Signal Process., 2004, 18(4), 947–957.
25.
GaoW.ChenJ. J.CuiM. T.ChengY.Dynamic response analysis of linear stochastic truss structures under stationary random excitation. J. Sound Vibr., 2005, 281(1–2), 311–321.
26.
GaoW.ChenJ. J.MaJ.LiangZ. T.Dynamic response analysis of stochastic frame structures under non-stationary random excitation. AIAA J., 2004, 42(9), 1818–1822.
