A. Mahieddine  , M. Ouali  , 
    Finite Element Formulation of a Beam with Piezoelectric Patch,
    Journal of Engineering and Applied Sciences,
    Volume 3,Issue 10,
    2008,
    Pages 803-807,
    ISSN 1816-949x,
    jeasci.2008.803.807,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2008.803.807)
    Abstract: A finite element model is used to analyze beams with piezoelectric sensors and actuators. The formulation is based on first order Kirchoff theory and accounts for lateral strains. Various parametric studies are conducted to demonstrate the effectiveness of piezoelectrics in actively controlling the vibration of beams.
    Keywords: Piezoelectric materials;beams;vibration control;lateral strain;sensors;actuators