# Mathematical Model of Cantilever Plate Using Finite Element Technique Based on Hamilton’s Principle

• Behrouz Kheiri Sarabi
• Manu Sharma
• Damanjeet Kaur
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 490)

## Abstract

In this work, the finite element model of a cantilevered plate is derived using Hamilton’s principle. A cantilevered plate structure instrumented with one piezoelectric sensor patch and one piezoelectric actuator patch is taken as a case study. Quadrilateral plate finite element having three degrees of freedom at each node is employed to divide the plate into finite elements. Thereafter, Hamilton’s principle is used to derive equations of motion of the smart plate. The finite element model is reduced to the first three modes using orthonormal modal truncation, and subsequently, the reduced finite element model is converted into a state-space model.

## Keywords

Mathematical model Cantilevered plate Finite element Hamilton’s principal State-space

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© Springer Nature Singapore Pte Ltd. 2018

## Authors and Affiliations

• Behrouz Kheiri Sarabi
• 1
• Manu Sharma
• 1
• Damanjeet Kaur
• 1
1. 1.UIET, Panjab UniversityChandigarhIndia