In　this　paper,　the　parametric　dynamics　of　bidirectional　functionally　graded　(BDFG)　beams　subjected　to　a　time-dependent　axial　force　are　studied.　The　material　properties　of　beam　which　vary　along　both　thickness　and　axial　directions　follow　the　power　law,　and　four　different　distribution　patterns　are　considered.　The　coupled　nonlinear　partial　differential　equations　describing　the　longitudinal-transverse　displacements　and　the　shear　deformation　are　derived　using　Hamilton＇s　principle　based　on　Timoshenko　beam　theory.　The　Galerkin　scheme　is　employed　to　discrete　the　continuous　model　resulting　in　a　multiple　degree-of-freedom　system,　namely,　the　reduced　order　model.　The　nonlinear　parametric　response　of　the　beam　is　obtained　by　solving　the　discrete　system　numerically,　and　the　frequency-　and　force-response　curves　are　constructed　by　tracing　the　period　motion　using　the　pseudoarclength　continuation　technique.　Numerical　results　are　presented　to　examine　the　effects　of　system　parameters,　e.g.,　gradient　parameters,　magnitude　and　frequency　of　external　excitation,　and　damping　coefficients.　Cyclic-fold　bifurcation　and　branch　points　of　the　period　motion　are　spotted　in　parametric　resonance　of　the　BDFG　beam.　Results　show　that　the　asymmetrical　material　distribution　in　thickness　direction　of　beam　leads　to　the　asymmetry　of　dynamic　responses.　Moreover,　the　gradient　of　material　in　axial　direction　has　more　significant　effect　on　the　dynamic　features　of　BDFG　beam　than　that　in　the　thickness　direction.http://mts.hindawi.com/update/　©　2020　Yixin　Lu　and　Xiaochao　Chen.