Elastic beams as popular structural elements have broad engineering applications with a long history of indispensable functions and simple configuration, but recent popular applications as flexible components demand a thorough examination of the functions and properties in emerging and novel roles such as with wearable technology and products.  As it is generally known, the flexible elements can easily deform under various loadings, then the functions and properties related to changes of configuration can also vary with the deformation in almost all situations.  For this reason, applications and functions of flexible elements should be carefully chosen and evaluated to ensure the properties are in the specified range to guarantee essential functions are performed accurately as designed.  To this objective, a flexible beam element is studied by starting with a specified deformation in a vibrating Timoshenko beam, representing a class of dynamic structures widely used in wearable technology and products today.  With the initial deformation known and consequently the specification of the flexibility of the elastic element, vibrations of the deformed Timoshenko beam are analyzed for essential properties such as frequency and the corresponding mode shapes.  The equations of motion of a deformed beam can have different forms such as the curved beam equations or an integral equation with the inclusion of deformation.  For solutions of the nonlinear equations with existing deformation, the extended Galerkin method (EGM) is utilized for approximate solutions in trigonometric function series asymptotically.  The approximate results are validated by earlier results from the approximate analysis of curved beams.  Consequently, the equation and procedure can be used for the assessment of properties of the Timoshenko beam, or other flexible elements, with accurate estimation for functions under possible deformation.  This will be an important step in the analysis and development of flexible components and devices in future applications.

Professor Ji Wang has been a Qianjiang Fellow Professor of Zhejiang Province at Ningbo University since 2002.  He also served as Associate Dean for Research and Graduate, School of Mechanical Engineering and Mechanics, Ningbo University, from 2013 to 2019.  Professor Ji Wang is the founding director of the Piezoelectric Device Laboratory, which is a designated Key Laboratory of City of Ningbo.  Professor Ji Wang was employed at SaRonix, Menlo Park, CA, as a senior engineer from 2001 to 2002; NetFront Communications, Sunnyvale, CA, as senior engineer and manager from 1999 to 2001; Epson Palo Alto Laboratory, Palo Alto, CA, as Senior Member of Technical Staff from 1995 to 1999.  Professor Ji Wang also held visiting positions at Chiba University, University of Nebraska-Lincoln, and Argonne National Laboratory.  He received his PhD and Master degrees from Princeton University in 1996 and 1993 and bachelor from Gansu University of Technology in 1983.  

Professor Wang has been working on acoustic waves and high frequency vibrations of elastic and piezoelectric solids for resonator design and analysis with several US and Chinese patents, over 200 journal papers, and frequent invited, keynote, and plenary presentations in major conferences around world.  He has been board members, advisors, and consultants to many leading companies in acoustic wave device industry.  Professor Wang has been a member of many international conference committees and currently serving the IEEE UFFC Technical Program Committees of the Frequency Control and Ultrasonics Symposia, the IEEE MTT-S, and the IEC TC-49.  He is also the funding chair of Committee on Mechanics of Electronic and Magnetic Devices, CSTAM, and the SPAWDA.  From 2015, Profess Wang is the editor-in-chief of Structural Longevity and members of the editorial boards of several international journals.