Effects of all-over part-through cracks on the aeroelastic characteristics of rectangular panels

Abstract

In this study, flutter, limit cycle oscillation, and different nonlinear oscillations analyses of rectangular panels with all-over part-through crack are presented. These analyses are carried out for panels in according to first order shear deformation or Mindlin plate theory. The effects of crack's depth and location on various aeroelastic characteristics of moderately thick rectangular panels are accurately studied. These analyses show that for much of crack's depths and locations, the amplitude of nonlinear vibrations are increased. But there are some crack's locations, for them panel has lower amplitude of vibrations with respect to its intact counterpart. With changing the location and depth of crack, the maximum limit cycle oscillation amplitude will be different from intact counterpart. Also cracked panel may exhibit complex oscillations, other than limit cycle oscillation of intact panel. From these analyses, it can be shown that crack has significant influence on flutter boundary, and amplitude of limit cycle oscillation. Nomenclatureܽ Panel chord-wise length ܷ elastic energy ܾ Panel span-wise length ‫,ݔ‬ ‫,ݕ‬ ‫ݖ‬ Coordinates ‫ܦ‬ Plate bending flexible ߫, ߟ, ‫ݓ‬ ഥ non-dimensional coordinates ‫ܧ‬ Panel module of elasticity ߛ Shear strains ‫ܪ‬ Panel thickness ߝ Tensile strain components ℎ Crack thickness ߢ Shear correction factor ݉, ݊ Number of modes shapes for chord-wise and span-wise direction ߣ ி Dimensionless flutter (critical) aerodynamic pressure ‫ܯ‬ Mass matrix ߩ, ߩ Panel and air densities ‫ܭ‬ Stiffness matrix ߥ Poisson's ratio ‫ܮܰ‬ Nonlinear matrix ߱ Dimensionless frequency ‫ܣ‬ cross-sectional area ߱ Dimensionless i'th transverse frequency ‫ܭ‬ Crack stiffness coefficient ߫ Chord wise dimensionless crack location

Bifurcation Study of Thin Plate with an All-Over Breathing Crack

“…The coefficients given in (16a), (16b), and (16c) can be written as 13) cos ( 2 ) cos ( ) cosh ( ) + (13) cos ( 2 ) sin ( ) sinh ( ) + (13) cos ( ) cosh ( ) + (13) sin ( ) sinh ( ) + (13) cos 2+ (13) cos ( 2 ) + (13) cosh ( 2 )) ,…”

“…In 2013, Bose and Mohanty [12] studied the vibration of a rectangular thin isotropic plate with a part-through surface crack of arbitrary orientation and position by using the Kirchhoff plate theory, and the problem of [11] was reconsidered and rigorously modified. AsadiGorgi et al [13] investigated the flutter, limit cycle oscillation, and different nonlinear oscillations of rectangular panels with an all-over part-through crack in 2015. They performed these analyses for panels according to the first-order shear deformation or Mindlin plate theory and accurately studied the effects of the depths and locations of cracks on various aeroelastic characteristics of moderately thick rectangular panels.…”