The next chapter presents an analytical solution for a nano-plate with Levy boundary conditions. The free vibration analysis is based on a first order shear deformation theory which includes the small scale effect. The governing equations of motion, reformulated as two new equations called the edge-zone and interior equations, are based on the nonlocal constitutive equations of Eringen. | X-RAY SPECTROSCOPY Edited by Shatendra K. Sharma X-Ray Spectroscopy Edited by Shatendra K. Sharma Published by InTech Janeza Trdine 9 51000 Rijeka Croatia Copyright 2011 InTech All chapters are Open Access distributed under the Creative Commons Attribution license which allows users to download copy and build upon published articles even for commercial purposes as long as the author and publisher are properly credited which ensures maximum dissemination and a wider impact of our publications. After this work has been published by InTech authors have the right to republish it in whole or part in any publication of which they are the author and to make other personal use of the work. Any republication referencing or personal use of the work must explicitly identify the original source. As for readers this license allows users to download copy and build upon published chapters even for commercial purposes as long as the author and publisher are properly credited which ensures maximum dissemination and a wider impact of our publications. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials instructions methods or ideas contained in the book. Publishing Process Manager Anja Filipovic Technical Editor Teodora Smiljanic Cover Designer InTech Design Team First published January 2012 Printed in Croatia A free online edition of this book is available at Additional hard copies can be obtained from orders@ X-Ray Spectroscopy Edited by Shatendra K. Sharma p. cm. ISBN 978-953-307-967-7 ikrrr iJ OPEN ACCESS INI Cvn PUBLISHER INTECH open free online editions of InTech Books and Journals can be found at .