The electromechanical characteristics of a heterogeneous piezoelectric bender subjected to various electrical and mechanical boundary conditions are discussed based on the results of the free bender analysis. The mechanical boundary conditions considered are: a mechanical moment at the end of the bender, a force applied perpendicularly to the tip of the bender, and a uniform load applied over the entire length of the bender. The constituent equations of the bender under these electromechanical influences are derived by calculating the internal energy assuming thermodynamic equilibrium. >

The constituent equations of piezoelectric heterogeneous bimorphs

A brief review of applications of piezoelectric bimorphs is presented. The constituent equations which describe the behavior of piezoelectric bimorphs for various mechanical boundary conditions are derived. The internal energy density of infinitesimally small volume elements in thermodynamic equilibrium is calculated in the presence of a voltage on the electrodes, a clamped cantilever beam condition on one side of the beam and a set of three different classical boundary conditions on the other side of the beam. These are a mechanical moment M at the end of the beam, a force F perpendicular to the beam, applied at its tip, and a uniformly distributed body force p.

The total internal energy content is calculated by integrating over the entire volume of the beam. Two different beam configurations are considered: parallel polarizations of the two adjoining elements of the beam with an internal electrode; and antiparallel orientation without an internal electrode.

The canonical conjugate of the moment is calculated as the angular deflection at the tip of the beam α, while that of the force at the tip is the local vertical deflection δ. The canonical conjugate of the uniform load on the beam is found to be the volume displacement V of the beam. The canonical conjugate of the voltage across the electrodes is the charge on the electrodes. The equations are given in the direct form, with external parameters (M, V), (F, V), and (p, V) as independent variables and also in a linear combination with (M, F, p, V) as variables.

These constituent equations can be used to calculate the behavior of the bimorph under any condition that can be described as a linear combination of forces at the tip, moments at the tip and uniform loads on the entire beam. This allows us to use the bimorph as a black box, without having to consider its internal movement or charges.

The constituent equations of piezoelectric bimorphs

This article presents in a unified way, the various optimization criteria used by researchers for optimal placement of piezoelectric sensors and actuators on a smart structure. The article discusses optimal placement of piezoelectric sensors and actuators based upon six criteria: (i) maximizing modal forces/moments applied by piezoelectric actuators, (ii) maximizing deflection of the host structure, (iii) minimizing control effort/maximizing energy dissipated, (iv) maximizing degree of controllability, (v) maximizing degree of observability, and (vi) minimizing spill-over effects. Optimal piezoelectric sensor and actuator locations on beam and plate structures for each criterion and modes of interest are presented in a tabular form. This technical review has two objectives: (i) practicing engineers can pick the most suitable philosophy for their end application and (ii) researchers can come to know about potential gaps in this area.

Optimization Criteria for Optimal Placement of Piezoelectric Sensors and Actuators on a Smart Structure: A Technical Review

A finite element formulation is presented for modeling the behavior of laminated composites with integrated piezoelectric sensors and actuators. This model is valid for both con tinuous and segmented piezoelectric elements that can be either surface bonded or embedded in the laminated plate. The present model takes into account the mass and the stiffness of the piezoelectric patches. The formulation is based on the first-order shear deformation theory, which is applicable for both thin and moderately thick plates. An additional feature of the present model is that it does not introduce the voltage as an additional degree of freedom. The charge/current generated by the sensor and the response of the plate to an actuator voltage can be computed independently. These features are then coupled with a constant-gain negative-velocity/positive-position feedback control algorithm to actively control the transient response of the plate in a closed loop. Numerical results are presented which indicate the increase in...

S. Poh

Papers

Performance of an active control system with piezoelectric actuators

Control of the natural frequencies of nitinol-reinforced composite beams

Experimental implementation of the modified independent modal space control method

A Multi-Mode Distributed Sensor for Vibrating Beams