Study On Active Vibration Control Of Random FG-CNTRC Structures With Piezoelectric Layers

Functionally graded carbon nanotube reinforced composite material is a new type of composite material that uses carbon nanotubes as a reinforcing material to add matrix materials with different functional gradients to make the composition and structure show a continuous gradient change.A new type of functional material developed to meet the structure's ability to work normally and repeatedly in extreme environments.Carbon nanotubes have good mechanical properties,electrical conductivity,heat transfer properties,and high thermal conductivity.In addition,carbon nanotubes have the highest melting points among known materials;functionally graded composite materials continuously change the composition of these two materials and structure,so that the interface disappears,and there is no sudden change in physical properties,which can better avoid or reduce the phenomenon of stress concentration.From the existing literature,the research on the structure of traditional functionally graded composite materials is relatively mature,and the research on carbon nanotubes as reinforcing materials is not comprehensive.Therefore,this article is based on the predecessors,and focuses on functionally graded carbon nanotubes reinforced composites.The structure has been studied in the following areas:(1)In order to examine the influence of carbon nanotubes on the dynamic characteristics of the structure,the relationship between stress,strain,and displacement field was derived using high-order shear deformation theory and general mixed law;mathematical modeling was performed using the finite element method,and the Hamilton principle establishes the structural dynamics equations,and derives the equations for the cantilever beam natural frequencies and modal modes.The research shows that the functional gradient arrangement of carbon nanotubes with more volume content and higher surface density can be further improved the dynamic characteristics of the structure.(2)In order to examine the influence of piezoelectric materials on the natural frequency of the structure,the piezoelectric constitutive equation was introduced and integrated into the finite element model.The dynamic equations related to the electromechanical coupling were derived,and the natural frequency of the piezoelectric functionally gradient carbon nanotube reinforced composite cantilever beam was derived.Studies have shown that the piezoelectric material makes the average of the first three-order modal frequency of the structure decrease.(3)In order to examine the contribution of randomness to the dispersion of the natural frequency of the structure,the perturbation finite element model was established by introducing random variable parameters using the first-order perturbation method,and the digital characteristics relationship between the natural frequency and the random of physical parameters of component materials and component distribution are derived.The results show that the contribution of the randomness of physical parameters of component materials to the scattering of the natural frequency is much greater than the component distribution.When the volume fraction of carbon nanotubes increases to a certain value,the frequency dispersion of carbon nanotubes under X-type functional gradient arrangement first decreases and then increases rapidly.The frequency dispersion of carbon nanotubes under O-type functional gradient arrangement is still attenuating.(4)In order to examine the influence of model uncertainty on the structure's active vibration control performance,the model uncertainty was introduced,and the output feedback robust control theory based on the linear matrix inequality processing method and the linear quadratic classical optimal control theory were used to establish the uncertainty robust control system for suppressing active vibration of random piezoelectric functionally graded carbon nanotube reinforced composite cantilever structures.Research shows that model uncertainty has great significance for structural modeling and vibration control in practical engineering,and the output feedback robust controller of linear matrix inequality processing method has better control performance than linear quadratic controller.