The active vibration control of smart plate equipped with patched piezoelectric sensors and actuators is presented in this study. An equivalent single layer third order shear deformation theory is employed to model the kinematics of the plate and to obtain the shear strains. The governing equations of motion are derived using extended Hamilton's principle. Linear variation of electric potential across the piezoelectric layers in thickness direction is considered. The electrical variable is discretized by Lagrange interpolation function considering two-noded line element. Undamped natural frequencies and the corresponding mode shapes are obtained by solving the eigen value problem with and without electromechanical coupling. The finite element model in nodal variables are transformed into modal model and then recast into state space. The dynamic model is reduced for further analysis using Hankel norm for designing the controller. The optimal control technique is used to control the vibration of the plate.
Vibration suppression of smart beams using the piezoelectric patch structure is presented in the present work. The smart system consists of a beam as the host structure and piezoceramic patches as the actuation and sensing elements. An experimental set-up has been developed to obtain the active vibration suppression of smart beam. The set-up consists of a smart cantilever beam, the data acquisition system and a LabView based controller. Experiments are performed for different beam specimen. The coupled efficient layerwise (zigzag) theory is used for theoretical finite element modeling. The finite element model is free of shear locking. The beam element has two nodes with four mechanical and a variable number of electric degrees of freedom at each node. In the thickness direction, the electric field is approximated as piecewise linear across an arbitrary number of sub-layers in the piezoelectric layers. Cubic Hermite interpolation is used for the deflection, and linear interpolation is used for the axial displacement and the shear rotation. Undamped Natural Frequencies are obtained by solving the Eigen Value problem using Subspace Iteration method for cantilever beam. A state space model characterizing the dynamics of the physical system is developed from experimental results using PID approach for the purpose of control law design. The experimental results obtained by using the active vibration control system have demonstrated the validity and efficiency of PID controller. Experiments are conducted to compare the controlling of various cantilever beams of different sizes. It shows that the present actuator and sensor based control method is effective and the LabView control plots for various beams can be used as a benchmark for analytical work. The results are compared with ABAQUS software and 1D Finite element formulation based on zigzag theory.
A 1D Finite Element model for static response and free vibration analysis of functionally graded material (FGM) beam is presented in this work. The FE model is based on efficient zig-zag theory (ZIGT) with two noded beam element having four degrees of freedom at each node. Linear interpolation is used for the axial displacement and cubic hermite interpolation is used for the deflection. Out of a large variety of FGM systems available, Al/SiC and Ni/Al2O3 metal/ceramic FGM system has been chosen. Modified rule of mixture (MROM) is used to calculate the young's modulus and rule of mixture (ROM) is used to calculate density and poisson's ratio of FGM beam at any point. The MATLAB code based on 1D FE zigzag theory for FGM elastic beams is developed. A 2D FE model for the same elastic FGM beam has been developed using ABAQUS software. An 8-node biquadratic plane stress quadrilateral type element is used for modeling in ABAQUS. Three different end conditions namely simply-supported, cantilever and clamped-clamped are considered. The deflection, normal stress and shear stress has been reported for various models used. Eigen Value problem using subspace iteration method is solved to obtain un-damped natural frequencies and the corresponding mode shapes. The results predicted by the 1D FE model have been compared with the 2D FE results and the results present in open literature. This proves the correctness of the model. Finally, mode shapes have also been plotted for various FGM systems.
Active vibration control of smart composite shallow shells with distributed piezoelectric sensors and actuators is presented in this work. An integrated approach is used for recording the uncontrolled and controlled vibration response under pressure impulse load. The FE model developed in ABAQUS is utilized to generate the global mass, stiffness and load matrices of the system. The system matrices are arranged in statespace format and the dynamic equations of the system are obtained. The controlled responses are achieved using the inputs from FE model in ABAQUS in conjunction with the developed MATLAB codes for Constant Gain Velocity Feedback (CGVF) and Linear Quadratic Regulator (LQR) control strategies. The method is first validated by comparing the natural frequencies obtained using the ABAQUS generated matrices with that obtained using an FE model with four noded quadrilateral shallow shell element based on efficient zigzag theory. The shell element uses the concept of electric nodes to satisfy the equipotential condition of electrode surface. An 8-noded linear piezoelectric brick element is used for piezoelectric layers and an 8-noded quadrilateral continuum shell element is used for the elastic layers of hybrid shells for making the finite element mesh in ABAQUS. The non-dimensional natural frequencies and active vibration control responses for hybrid composite cylindrical and spherical shells are presented for clamped-clamped and cantilever boundary conditions. Boundary conditions have significant effect on vibration amplitude, control voltage and settling time. In comparison to CGVF controller, a better control in lesser time is achieved with LQR controller for a shell with similar boundary conditions. Larger gain values (G) are required for vibration control of thick shells.
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