TY - JOUR N2 - In this paper, a comprehensive study is carried out on the dynamic behaviour of Euler–Bernoulli and Timoshenko beams resting on Winkler type variable elastic foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying along the length direction. The free vibration problem is formulated using Rayleigh-Ritz method and Hamilton’s principle is applied to generate the governing equations. The results are presented as non-dimensional natural frequencies for different material gradation models and different foundation stiffness variation models. Two distinct boundary conditions viz., clamped-clamped and simply supported-simply supported are considered in the analysis. The results are validated with existing literature and excellent agreement is observed between the results. L1 - http://journals.pan.pl/Content/115032/PDF/AME_2020_131700.pdf L2 - http://journals.pan.pl/Content/115032 PY - 2020 IS - No 4 EP - 470 DO - 10.24425/ame.2020.131700 KW - free vibration KW - variable elastic foundation KW - axially functionally graded beam KW - Euler-Bernoulli beam KW - Timoshenko beam A1 - Kumar, Saurabh PB - Polish Academy of Sciences, Committee on Machine Building VL - vol. 67 DA - 28.10.2020 T1 - Dynamic behaviour of axially functionally graded beam resting on variable elastic foundation SP - 451 UR - http://journals.pan.pl/dlibra/publication/edition/115032 T2 - Archive of Mechanical Engineering ER -