טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKogan Grigory
SubjectNonlinear Dynamics and Orbital Stability of a Two-Field
Viscoelastic Whirling Structure Subject to
Periodic Excitation
DepartmentDepartment of Mechanical Engineering
Supervisors Professor Oded Gottlieb
Dr. Shlomo Jersey
Full Thesis textFull thesis text - English Version


Abstract

Airborne optical systems are sensitive to excessive levels of vibration which in-turn cause poor line-of-sight (LOS) stabilization, culminating with significant degradation in image quality. Motivated by excessive finite amplitude response obtained from controlled forced vibration experiments of a stabilized seeker near internal resonance, we formulate a theoretical model for an equivalent two-field, beam based whirling structure and investigate its nonlinear spatio-temporal response. The selected two-field visco-elastic structure has different cross-sections and end masses that can be calibrated to mimic the experimentally determined in-plane and out-of plane frequency ratios near a 3:3:1 internal resonance. We formulate an initial-boundary-value-problem, accurate to cubic order, which is then reduced to a low-order modal dynamical system consisting of two in-plane and one out-of-plane flexural modes. The dynamical system is solved via multiple-scale asymptotics and integrated numerically in both weakly and strongly nonlinear domains, respectively. This combined approach enables construction of an approximate analytical bifurcation structure, it's numerical validation and determination of orbitally unstable solutions. Results reveal coexisting finite amplitude periodic solutions, and periodic and quasiperiodic energy transfer between the directly excited in-plane mode to the nonlinearly coupled out-of-plane mode. Analysis of the equivalent two-field structure with passive appendages will enable a consistent comparison of stabilization strategies for suppression of excessive and undesired system vibration.