Abstract
A rotating thin-walled beam with piezoelectric element is analysed. The beam is considered to vibrate in space, hence the longitudinal, transverse and torsional deformations are taken into account. The bending deformations of the beam are modelled by assuming Timoshenko's theory. Torsion is included by considering that the cross section rotates as a rigid body but can deform in longitudinal direction due to warping. The warping function is computed preliminary by the finite element method. The equation of motion is derived by the principle of virtual work and discretized in space by the Ritz method. Electro-mechanical coupling is included in the model by considering the internal electrical energy and the electric charge output. The piezo-electric constitutive relations are used in reduced form. The beam is assumed to rotate about a fixed axis with constant speed. The equation of motion is derived in rotating coordinate system, but the influence of the rotation of the coordinate system is taken into account through the inertia forces. Results in time domain are presented for different speeds of rotation and frequencies of vibration. The influence of the speed of rotation and of the frequency of vibration on the electrical output is presented and analysed.
Highlights
In the last decades, the need of independent energy sources for small devices has increased significantly
The most popular devices that convert kinetic energy into electrical energy are the devices composed of piezoelectric elements [1]
Three-dimensional displacement field is considered, i.e. the beam can vibrate in both transverse directions and it can perform longitudinal and torsional deformations
Summary
The need of independent energy sources for small devices has increased significantly Small devices, such as sensors, have application in health monitoring and control of structures. A rotating thin-walled beam with piezoelectric element is analysed. Three-dimensional displacement field is considered, i.e. the beam can vibrate in both transverse directions and it can perform longitudinal and torsional deformations. The beam equation of motion is derived by Timoshenko’s beam assumption and it is considered that under torsion the cross section rotates as a rigid body but it can deform in longitudinal direction due to warping. The piezoelectric element is considered to be close to the clamped end. Geometrical nonlinearity is considered and electro-mechanical coupling is introduced into the model through the piezoelectric constitutive equations, used in reduced form. The responses of the beam due to harmonic force and different speeds of rotation are compared
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