Analytical Vibration

Piezoelectric beams are the most common energy converters for mechanical-to-electrical energy. In this paper, an analytical method is introduced and developed for modeling piezoelectric vibrationbased energy harvester, which is a strain energy method, and it is simple enough and straightforward than similar methods, such as finite element and FRFs approaches. Closed-form expressions have been extracted for the open-circuit natural frequencies, open-circuit voltage, generated current, and maximum output power which are important parameters of the energy harvesting system, therefore measurements don't need the experimental setup to take. Piezoelectric layers are also investigated in both parallel and series connections which produce equal power at optimum resistive load but cause different voltage and current in the resistive load. The maximum output power occurs when the equivalent capacitive reactance of piezoelectric layers is equal to the resistive load; in addition, the optimum load resistance in series connection is 4 times larger than the parallel connection. Depending on the type of generator's usage and its application, an appropriate decision regarding the parallel or series connection could be made. The maximum normalized power density in the fundamental natural frequency, at the optimum thickness and the optimum load resistance, was 18.717 . mW g cm 2 3 ( ) REVISED

A finite element formulation for active vibration control of thin plate laminated structures with integrated piezoelectric layers, acting as sensors and actuators is presented. The finite element model is a nonconforming single layer triangular plate/shell element with 18 degrees of freedom for the generalized displacements and one electrical potential degree of freedom for each piezoelectric element layer, and is based on the Kirchhoff classical laminated theory. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers, and Newmark method is used to calculate the dynamic response of the laminated structures. The model is applied in the solution of several illustrative cases, and the results are presented and discussed.

This paper presents a method for simulating low electrical power resulting from the transient vibration of a coupled piezosensor-plate structure using numerical finite element analysis. Love-Kirchhoff's plate theory, together with the piezoelectric constitutive equations were used to analyse the dynamic governing equations using the Lagrangian method. The piezoelectric direct mode effects generate polarity of the electric field due to an input transient force where the piezoelectric element was bonded onto the upper surface of the plate structure. Four node rectangular finite elements with twelve degrees of freedom per element were used for the coupled piezosensor-plate structure. The Newmark-β numerical differential equation solution techniques were used within the MATLAB environment to simulate the resulting transient displacement and electric voltage responses. In this case, Rayleigh's proportional damping was used with damping constants chosen based on experimental results. The results obtained from the numerical modelling are compared with experimental work.