This　work　addresses　the　vibration　characteristics　of　imperfect　bi-directional　functionally　graded　(BDFG)　beams　with　arbitrary　boundary　conditions.　Two　kinds　of　geometrical　imperfections　including　global　and　localized　types　are　considered,　which　are　simulated　using　hyperbolic,　exponential　and　trigonometric　functions.　Energy　equations　of　beam　are　formulated　on　basis　of　the　Timoshenko　beam　theory,　and　the　domain　decomposition　method　in　which　the　original　beam　structure　is　divided　to　several　beam　segments.　The　flexible　couplings　between　beam　segments　and　boundary　constraints　of　beam　are　modeled　employing　artificial　spring　technique.　By　choosing　the　Jacobi　polynomials　as　admissible　functions,　modal　characteristics　are　acquired　using　the　Ritz　method.　Convergence,　stability　and　reliability　of　presented　method　are　validated,　and　penalty　technique　for　artificial　springs　is　examined　for　the　classic　and　general　boundary　conditions.　Numerical　simulations　are　performed　to　probe　the　impact　mechanism　of　geometric　and　material　parameters　on　vibration　performance　of　BDFG　beam.　Results　show　that　imperfection　may　cause　appearance　of　mode　veering　phenomenon　where　modal　features　distort.　The　types　of　mode　veering　are　dominated　by　material　distribution　pattern,　boundary　constraints　and　kinds　of　geometrical　imperfection.　©　2022　Elsevier　Ltd