19 May 2005 Comparison of Laplace transform, integral equation, and assumed modes approaches for piezo-patch control of beams
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Abstract
Use of piezoelectric patches as sensors and actuators for the vibration control of beams is a well established technology. Various techniques developed to analyze these problems range from analytical to computational ones, each with a different level of complexity and accuracy. In the present paper three techniques, namely, Laplace Transform, integral equation and assumed modes are applied to the vibration control problem involving a cantilever beam with piezoelectric patches attached to the top and bottom surfaces. These patches act as sensors and actuators providing a feedback control mechanism for the damping of vibrations. The Laplace Transform involves the transform of the space part of the partial differential equation governing the motion of the beam and inverse transform to find the exact solution. The integral equation approach transforms the differential equation formulation to an integral equation formulation which, in turn, is replaced by an infinite system of equations. As such this method provides an approximate solution, the accuracy of which depends on the size of the system of linear equations involved. The assumed modes method is quite widely used because of its ease of application, and its accuracy depends on the number of terms in the series approximation used to express the solution. The above solution methods are summarized and difficulties, drawbacks and advantages associated with each method are discussed. The accuracy of each technique is compared and assessed in the context of a vibrating cantilever beam with patches. The results are given in a comparative manner which also includes the exact solutions.
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Oe. Kayacik, Oe. Kayacik, J. C. Bruch, J. C. Bruch, J. M. Sloss, J. M. Sloss, S. Adali, S. Adali, I. S. Sadek, I. S. Sadek, } "Comparison of Laplace transform, integral equation, and assumed modes approaches for piezo-patch control of beams", Proc. SPIE 5757, Smart Structures and Materials 2005: Modeling, Signal Processing, and Control, (19 May 2005); doi: 10.1117/12.599899; https://doi.org/10.1117/12.599899
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