Active Control And Design Optimization Of Vibration And Sound Radiation Of Piezoelectric Curved Shell Structures

Curved shell structures have been widely used in aerospace,transportation,machinery and other fields,with the characteristics of thin-walled and low damping.Therefore,it is of great engineering significance to control the vibration and radiated noise of the curved shells.Piezoelectric smart materials are widely used in the control field of structural vibration and noise due to their light weight,high sensitivity,high precision and convenient application.Then active control technology based on the piezoelectric material has gained ever-increasing attention.Structural configuration(such as size,location and number)and control parameter(control voltage or control gain)are important factors that affect the control performance.To achieve the best control performance and meet the needs of economic benefits,the study on the concurrent design of piezoelectric sensors/actuators and their corresponding control parameter become highly important.This dissertation presents investigations into active control of structural vibration and sound radiation of curved shells with piezoelectric curved shell actuators under different types of loads,integrated design optimization of the piezoelectric curved shell structure and control system,topology optimization of electrode coverage of the piezoelectric curved shell structures.The main contents and results are given as follows:(1)Time domain optimal vibration control of piezoelectric curved shell structures.A piezoelectric curved shell element is derived,and the finite element formulation of piezoelectric curved shell structure is presented.The displacement constraint equations are used to couple the base structure and piezoelectric patches,which reduces the degree of freedom and improves the computation efficiency.Then the space state equation of the system is created.The optimal control can be obtained using the optimal controller for minimizing the linear quadratic performance index.Numerical examples show that the number of curved shell actuators required is much less than that of flat shell actuators in achieving the same control effect when the vibration of the curved shell is controlled.(2)Integrated design optimzation of control parameters and configurations of actuators in optimal vibration control.The number,location and size of actuators and control voltage are the important factors that affect the control performance.In this dissertation,the locations and sizes of piezoelectric actuators and control voltages are treated as design variables.Integrated design optimization model of the location and size of actuators and control voltages for structural vibration control simultaneously considering the number of actuators,piezoelectric material used,the work voltage range as well as the control effect are proposed.To deal with the optimization problem with continuous variables and discrete variables coexisted,a two-layer optimization scheme based on simulated annealing algorithm is developed.Numerical examples show that the proposed optimization scheme can achieved the optimal design of the limited number of actuators in the safe work voltage range,which not only reduces the control cost and the complexity of the control system,but also obtains the best control performance.(3)Control and design optimization of sound radiation of vibrating piezoelectric curved shell structures under harmonic excitation.Based on the structural harmonic response solved by the finite element method,the sound radiation problem caused by the vibrating structure is solved by the acoustic Helmholtz equation and the boundary element method.Piezoelectric sensors and actuators are attached to both sides of the curved shell structures and have the same configuration.The negative speed feedback control strategy is used to obtain the voltages applied to the actuators,which realizes the active structural acoustic control of the piezoelectric curved shell structure.Integrated design optimization model of structure and control for reducing the sound radiation is proposed.Therein,the design variables include the locations of sensor/actuator and control gains as well as base structure thicknesses.In the optimization model,two kinds of objective functions are carried out,which are the sound power and the sound pressure at the reference field points under the specified excitation frequency or in the given excitation frequency range.Meanwhile,the base structure mass and the number of the sensors/actuators are constrained.Simulated annealing algorithm is employed to solve the optimization problem.The influence of excitation frequency,structural damping and natural frequency on the optimized results are discussed in the numerical examples.(4)Active control and design optimization of sound radiation of vibrating piezoelectric structures under random excitation.Based on the theory of pseudo excitation method for random vibration analysis,it is extended to active structural acoustic control of piezoelectric coupled system.The calculation formulas of random sound radiation are derived by combining the pseudo excitation method with the bound element method.Then design optimization model of piezoelectric structures based on active structural acoustic control under random excitation is presented.In the optimization model,the power spectral density of sound pressure at reference point or in the reference surface is taken as the objective function.The locations of piezoelectric sensors/actuators and the control gains are simultanously chosen as design variables.The number of sensors/actuators and the control power are constrained.The best control performance with given control cost is achieved and the control system is simplified.Numerical examples show that the optimized placement of sensors/actuators can more efficiently control sound radiation caused by random vibrating structure.(5)Topology optimization and sensitivity analysis of electrode coverage of piezoelectric curved shell structures with active vibration control under random excitation.The pseudo excitation method is introduced into the analysis of random vibration of the curved shell structures and on the basis,the active control of random vibration of the curved shell structure is carried out by using piezoelectric sensor/actuator and the negative speed feedback control law.In this context,the elemental pseudo density variables are introduced for indicating presence and absence of electrodes of piezoelectric elements.The average displacement power spectral density in the excitation frequency range is taken as the objective function.The topology optimization model of electrode coverage of piezoelectric curved shell structures is presented.Active damping model with penalization on intermediate values is presented for acquiring a clear black-and-white electrode layout.A scheme combining the pseudo excitation method and the adjoint variable is developed for the sensitivity analysis of displacement power spectral density with respect to topological design variables.GCMMA is used to solve the optimization problem.Numerical examples demonstrate the accuracy of the sensitivity analysis and the effectiveness of the proposed method.