document: An analytical model for a composite adaptive rectangular structure using the Heaviside function The objective of this article is to describe a mathematical model , based on the Heaviside function and on the delta - Dirac distribution , for a composite adaptive rectangular structure with embedded and/or bonded piezoelectric actuators and sensors . In the adopted structure model , the laminae are made up a configuration of rectangular nonpiezoelectric and piezoelectric patches . The laminae do not all have the same area nor do they present the same configuration , such that there are points where there is no material . The equations of motion and the boundary conditions , which describe the electromechanical coupling , are based on the Mindlin displacement field , on the linear theory of piezoelectricity , and on the Hamilton principle
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extractive_keyphrases: composite adaptive rectangular structure mathematical model heaviside function piezoelectric actuators piezoelectric patches equations of motion boundary conditions electromechanical coupling mindlin displacement field hamilton principle
abstractive_keyphrases: delta-dirac distribution embedded actuators embedded sensors bonded actuators bonded sensors piezoelectric sensors nonpiezoelectric patches closed-form solution lagrangian functions linear piezoelectricity constitutive relations virtual kinetic energy rectangular composite plate finite-element method