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Research Papers

Active Vibration Control of a Doubly Curved Composite Shell Stiffened by Beams Bonded With Discrete Macro Fiber Composite Sensor/Actuator Pairs

[+] Author and Article Information
Ali H. Daraji

Mem. ASME
Faculty of Engineering,
Environment and Computing,
Coventry University, Coventry, CV1 2JH UK
e-mail: ac7202@coventry.ac.uk

Jack M. Hale

School of Engineering,
Newcastle University,
Newcastle upon Tyne, NE1 7RU UK
e-mail: jack.hale@ncl.ac.uk

Jianqiao Ye

Engineering Department,
Lancaster University
Lancaster, LA1 4YW UK
e-mail: j.ye2@lancaster.ac.uk

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received September 21, 2017; final manuscript received June 22, 2018; published online July 23, 2018. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 140(12), 121009 (Jul 23, 2018) (11 pages) Paper No: DS-17-1479; doi: 10.1115/1.4040669 History: Received September 21, 2017; Revised June 22, 2018

Doubly curved stiffened shells are essential parts of many large-scale engineering structures, such as aerospace, automotive and marine structures. Optimization of active vibration reduction has not been properly investigated for this important group of structures. This study develops a placement methodology for such structures under motion base and external force excitations to optimize the locations of discrete piezoelectric sensor/actuator pairs and feedback gain using genetic algorithms for active vibration control. In this study, fitness and objective functions are proposed based on the maximization of sensor output voltage to optimize the locations of discrete sensors collected with actuators to attenuate several vibrations modes. The optimal control feedback gain is determined then based on the minimization of the linear quadratic index. A doubly curved composite shell stiffened by beams and bonded with discrete piezoelectric sensor/actuator pairs is modeled in this paper by first-order shear deformation theory using finite element method and Hamilton's principle. The proposed methodology is implemented first to investigate a cantilever composite shell to optimize four sensor/actuator pairs to attenuate the first six modes of vibration. The placement methodology is applied next to study a complex stiffened composite shell to optimize four sensor/actuator pairs to test the methodology effectiveness. The results of optimal sensor/actuator distribution are validated by convergence study in genetic algorithm program, ANSYS package and vibration reduction using optimal linear quadratic control scheme.

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References

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Figures

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Fig. 1

Doubly curved shell stiffened by beams and bonded with sensor/actuator pair

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Fig. 2

Simulink design based on the optimal linear quadratic control scheme

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Fig. 3

Doubly curved composite shell

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Fig. 4

Doubly curved composite shell stiffened by four beams located symmetrically

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Fig. 5

Population fitness progression over 50 generations. Each individual is represented as one of the points distributed around the circle, with its fitness values, obtained from its chromosome, defining its distance from the center with large radius indication high fitness.

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Fig. 6

Sensor/actuator placement for the cantilever composite shell. Each dot shows the location of a s/a pair in one of the 100 breeding individuals in each generation. Initially they are randomly distributed. After Ten generations, they have begun to group in efficient locations. After 50 generations, they have completely converged on four optimal sites at the root of the cantilever shell.

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Fig. 7

Fitness value for the best individual in each generation repeated for seven times for the cantilever composite shell

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Fig. 8

Population fitness progression over 100 generations for the composite stiffened shell. Each individual is represented as one of the points distributed around the circle, with its fitness values, obtained from its chromosome, defining its distance from the center.

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Fig. 9

Sensor/actuator placement for the stiffened composite shell mounted rigidly from the four side edges. Each dot shows the location of a s/a pair in one of the 100 breeding individuals in each generation. Initially, they are randomly distributed. After 20 generations, they have begun to group in efficient locations. After 100 generations, they have completely converged on four optimal sites.

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Fig. 10

Fitness value for the best individual in each generation repeated for seven times for the stiffened composite shell

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Fig. 11

Electric field distribution at the first and third modes for the stiffened composite shell bonded with full coverage of single sensor

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Fig. 12

Sensor voltage distribution at the first and third modes for the stiffened composite shell bonded with full coverage of single sensor

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Fig. 13

Sensor voltage distribution at the first and third modes for the stiffened composite shell bonded with full coverage discrete 225 sensors

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Fig. 14

Cas1 and 2 are optimized and nonoptimized, respectively, a location of an actuator (05) excited by an external sinusoidal voltage disturbance at first six modes of the stiffened composite shell

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Fig. 15

Transient and steady-state voltage time responses of the s/a at the optimal location 01 as a result of applied external sinusoidal voltage on actuator at location 05 at the first mode for the stiffened shell

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Fig. 16

Transient and steady-state voltage time responses of the s/a at the optimal location 01 as a result of applied an external sinusoidal voltage on actuator at location 05 at the third mode for the stiffened shell

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Fig. 17

Transient and steady-state voltage time responses of the s/a at the optimal location 01 as a result of applied an external sinusoidal voltage on actuator at location 05 at the fifth mode for the stiffened shell

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