Dynamic modelling and active vibration controller design for a cylindrical shell equipped with piezoelectric sensors and actuators

Abstract

This paper is concerned with the dynamic modelling, active vibration controller design and experiments for a cylindrical shell equipped with piezoelectric sensors and actuators. The dynamic model was derived by using Rayleigh–Ritz method based on the Donnel–Mushtari shell theory. The actuator equations which relate the applied voltages to the generalized force and sensor equations which relate the generalized displacements to the sensor output voltages for the piezoelectric wafer were derived based on the pin-force model. The equations of motion along with the piezoelectric sensor equations were then reduced to modal forms considering the modes of interest. An aluminium shell was fabricated to demonstrate the effectiveness of the modelling and control techniques. The boundary conditions at both ends of the shell were assumed to be a shear diaphragm in the numerical analysis. Theoretical natural frequencies of the aluminium shell were then calculated and compared to experimental result. They were in good agreement with experimental result for the first two free-vibration modes. The multi-input and multi-output positive position feedback controller, which can cope with the first two vibration modes, was designed based on the block-inverse theory and was implemented digitally using the DSP board. The experimental results showed that vibrations of the cylindrical shell can be successfully suppressed by the piezoelectric actuator and the proposed controller.