In　this　paper,　a　z-shaped　planar　inextensible　beam　with　harmonic　foundation　excitations　is　considered.　The　linear　frequencies　and　modes　of　the　beam　with　various　folding　angles　are　obtained　through　analytical　formulations,　and　validated　by　numerical　simulations.　The　continuous　system　is　truncated　into　a　system　of　ordinary　differential　equations　with　quadratic　nonlinear　terms　by　using　the　Galerkin　method　based　on　the　modes　obtained　under　a　special　folding　angle,　which　may　bring　about　modal　interactions.　The　nonlinearities　of　the　system　are　researched　under　the　combined　resonances,　such　as　primary　and　internal　resonances.