TY - JOUR ID - 15883 TI - Forced Vibration Responses of Axially Functionally Graded ‎Beams by using Ritz Method JO - Journal of Applied and Computational Mechanics JA - JACM LA - en SN - AU - Akbaş, Şeref Doğuşcan AD - Bursa Technical University, Department of Civil Engineering, Yıldırım Campus, 16330, Yıldırım/Bursa, Turkey Y1 - 2021 PY - 2021 VL - 7 IS - 1 SP - 109 EP - 115 KW - Axially Functionally Graded Material KW - Forced Vibration Analysis KW - Timoshenko Beams KW - Ritz method DO - 10.22055/jacm.2020.34865.2491 N2 - This work presents forced vibration responses of a cantilever beam made of functionally graded material under a harmonic load. The material properties of beam vary along the axial direction. The kinematics of the beam are considered within Timoshenko beam theory. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method is used in the time history. In this study, free and forced vibration responses of the axially functionally graded beam are investigated in detail. In the numerical examples, the effects of material graduation, geometric and dynamic parameters on the free and forced vibration response of axially graded beam are investigated. UR - https://jacm.scu.ac.ir/article_15883.html L1 - https://jacm.scu.ac.ir/article_15883_33359952593ce5446e2c3dc659a1ec6b.pdf ER -