In　this　paper,　we　investigate　the　vibration　characteristics　of　a　Z-shaped　beam　with　variable　folding　angles　which　is　used　to　model　a　folding　wing　of　a　morphing　aircraft　under　the　condition　of　a　fixed　structure.　The　governing　equations　of　motions　for　the　Z-shaped　beam　are　formulated.　For　a　specific　set　of　material　and　geometrical　parameters,　the　first　three　in-plane　and　the　first　two　out-of-plane　linear　frequencies　of　the　Z-shaped　beam　are　theoretically　calculated,　and　validated　by　the　experiments　and　numerical　simulations.　Additionally,　the　theoretical　mode　shapes　at　a　fixed　folding　angle　are　compared　to　the　experimental　results　and　the　finite　element　simulations.　The　theoretical　results　agree　well　with　numerical　simulations　and　experiments.　The　results　obtained　in　this　paper　are　helpful　for　designing　and　controlling　Z-shaped　beam　structures,　and　can　also　be　used　as　a　basis　to　study　the　nonlinear　dynamics　of　these　structures.