טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBlotnick Guy
SubjectNonlinear Dynamics and Orbital Stability of Viscoelastic
Beams
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oded Gottlieb
Full Thesis textFull thesis text - English Version


Abstract

Vibration suppression of payload dynamics via viscoelastic supports is frequently employed to reduce violent system response that is subject to severe environmental conditions. To date, there is no comprehensive and systematic approach for theoretical based design of vibration suppression mechanisms that make use of viscoelastic materials. Thus, the goal of this research project was to investigate the nonlinear dynamics, instabilities, and vibration suppression performance of vibrating viscoelastic beams that operate near primary, secondary and internal resonant conditions.


The investigation included derivation and analysis of a theoretical continuum based model for a pretensioned viscoelastic beam made of a Voigt-Kelvin material that incorporates geometric nonlinearities truncated to cubic order. A reduced order modal nonlinear dynamical system near its primary and 3:1 internal resonances is investigated via an asymptotic averaging method and reveals a complex bifurcation structure including coexisting bi-stable and orbitally unstable solutions. The theoretical analysis is verified numerically culminating with quasiperiodic response obtained within the unstable regimes of operation. We also manufactured and tested an apparatus which enables controlled vibration measurements of a beam made of a viscoelastic Polyethylene Stratocell (PES). Experimental analysis reveals a high intensity damping mechanism in the PES material which can only be explained by a consistent model which incorporates nonlinear structural dissipation.