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SUMMARY:EQUALITY-BASED FORMULATION FOR NON-SMOOTH VIBRATING SYSTEMS - Prof
 . Christopher Pierre\, Stevens Institute of Technology
DTSTART:20240524T130000Z
DTEND:20240524T140000Z
UID:TALK213340@talks.cam.ac.uk
CONTACT:46601
DESCRIPTION:A new approach is presented for the vibration of non-smooth st
 ructural systems with dry friction and unilateral contact. These nonlinear
 ities are ubiquitous in engineering\, and turbomachinery rotors are a prim
 e example of industrial systems subject to a variety of intermittent conta
 ct and frictional occurrences. While non-smooth nonlinearities are commonl
 y expressed as a complementarity system of equalities and inequalities\, t
 he key idea here is to formulate them as non-smooth equality-only conditio
 ns\, which together with the equations of motion are then satisfied in a w
 eak integral sense through a weighted residual formulation. The resulting 
 algebraic nonlinear equations are solved numerically using an adapted trus
 t region nonlinear solver and basic integral quadrature schemes. The appro
 ach is developed for one-dimensional friction\, extended to two-dimensiona
 l friction and contact\, and applied to the fir-tree blade attachment of a
  helicopter engine bladed disk. The method is shown to be compact\, effect
 ive\, and computationally efficient. Periodic solutions with intricate sti
 cking\, sliding and separation phases are found with a high degree of accu
 racy for large numbers of Fourier harmonics. Importantly\, the equality-ba
 sed formulation does not suffer from the typical limitations or hypotheses
  of existing frequency-time domain methods for non-smooth systems\, such a
 s regularization\, penalization\, or massless frictional interfaces.
LOCATION:Department of Engineering - LT6
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