Classical laminated plate theory (CLPT) is applied to a laminate plate with induced strain actuators, such as piezoceramic patch, bonded to its surface or embedded within the laminate to develop an induced strain actuation theory that allows for the actuator patch to be spatially distributed. When piezoceramic patches are subjected to voltage fields, the equivalent external forces induced by piezoceramic patches can be determined upon the assumption of free constraint for the expansion or contraction of piezoceramic patches. This assumption is generally done in thermal expansion problem. Several examples, including pure bending and pure extension, are illustrated. For the case of pure bending, a comparison between the current work and that of Dimitriadis et al. (1989) is given. In addition, an orthotropic angle-ply laminate with an embedded piezoceramic patch is presented to show the coupling of bending and extension.

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A model for laminate beams and plates with attached or embedded finitelength spatially-distributed induced strain actuators has been formulated and is presented. A conservation of strain-energy model was developed by equaling the applied moment on the cross section of the edges of actuators to determine the induced linear strain distribution and the equivalent axial force and bending moment induced by the actuators. Results show that the strain-energy model for a thin laminate beam agrees well with the pin-force madel. In addition, more general conditions were included in this work; for example, multiple actuators can be embedded in any layer of laminate. The concept of the conservation of strain-energy model for beams was also extended to a two-dimensional problemplates. Classical laminate plate theory for spatially-distributed induced strain actuators developed previously by the authors is revised here to include the use of the strain-energy model. This work also compares several developed models and a fnite element formulation. A simple approach to the application of induced strain actuators to the vibration and noise control of laminate beams and plates is provided. INTRODUCTIOÑ

This paper analytically demonstrates the use of multiple piezoelectric actuators bonded to the surface and point force actuators applied directly to a plate to reduce sound transmission through the plate. A harmonic plane wave incident on a simply supported, thin rectangular plate mounted in an infinite baffle was considered as the primary source. Both multiple piezoelectric and point force actuators are separately used as secondary (control) sources to attenuate the sound transmission through the plate. An optimal process was applied to obtain the input voltages of the piezoelectric actuators and the magnitude of the point forces, so that the radiated acoustic power can be minimized.

This paper presents a general formulation of the optimization problem for the placement and sizing of piezoelectric actuators in adaptive LMS control systems. The selection of objective function, design variables and physical constraints are separately discussed. A case study for the optimal placement of multiple fixed size piezoelectric actuators in sound radiation control is presented. A solution strategy is proposed to calculate the applied voltages to piezoelectric actuators with the use of linear quadratic optimal control theory which is to simulate the LMS feedforward control algorithm. The location of piezoelectric actuators is then determined by minimizing the objective function, which is defined as the sum of the mean square sound pressure measured by a number of error microphones. The optimal location of piezoelectric actuators for sound radiation control is determined and shown to be dependent on the excitation frequency. Particularly, the optimal placement of multiple piezoelectric actuators for on-resonance and off-resonance excitation is presented. The results show that the optimally located piezoelectric actuators perform far better sound radiation control than arbitrarily selected ones. This work leads to a design methodology for adaptive or intelligent material systems with highly integrated actuators and sensors. The optimization procedure also leads to a reduction in the number of control transducers.