Semnan University Press Journal of Modeling in Engineering 2008-4854 17 58 2019 09 23 Free vibration analysis of semi-rigid frames with elastic rotational restraints and inhomogeneous members Free vibration analysis of semi-rigid frames with elastic rotational restraints and inhomogeneous members 187 202 4011 10.22075/jme.2019.15906.1577 FA Mohsen Bambaeechee Dept. of Civil Engineering, Faculty of Engineering, Quchan University of Technology, P. Box 94771-67335 Quchan, Iran. Morteza Hoseinalizadeh Toni M. Sc. Student of Structural Eng., Faculty of Civil Eng., Quchan University of Technology, Quchan, Iran Journal Article 2018 09 11 The present research deals with the free vibration analysis of functionally graded (FG) frames with semi-rigid connection and elastic supports. Flexibility of elastic supports and semi-rigid connection are modeled with linear rotational springs. Moreover, inhomogeneous members (FGM) are modeled as a power function. Accordingly, based on the Euler–Bernoulli beam theory an exact formulation for free vibration analysis of FGM frames with various boundary conditions is obtained in terms of the Bessel functions. In other words, explicit relations are available to find the natural frequency and vibrational modes of semi-rigid frames with inhomogeneous members and elastic rotational restraints. In this way, dynamic properties such as the natural frequency and vibrational modes of these structures with various boundary conditions can be found. Comparing the outcomes with other research demonstrating the accuracy and efficiency of the proposed formulation. Finally, the effects of various parameters such as flexibility of connection and elastic supports, and the functionally graded material on the free vibration response of the structures are investigated. The present research deals with the free vibration analysis of functionally graded (FG) frames with semi-rigid connection and elastic supports. Flexibility of elastic supports and semi-rigid connection are modeled with linear rotational springs. Moreover, inhomogeneous members (FGM) are modeled as a power function. Accordingly, based on the Euler–Bernoulli beam theory an exact formulation for free vibration analysis of FGM frames with various boundary conditions is obtained in terms of the Bessel functions. In other words, explicit relations are available to find the natural frequency and vibrational modes of semi-rigid frames with inhomogeneous members and elastic rotational restraints. In this way, dynamic properties such as the natural frequency and vibrational modes of these structures with various boundary conditions can be found. Comparing the outcomes with other research demonstrating the accuracy and efficiency of the proposed formulation. Finally, the effects of various parameters such as flexibility of connection and elastic supports, and the functionally graded material on the free vibration response of the structures are investigated. https://modelling.semnan.ac.ir/article_4011_ed80d96ef2017ecb8fed33d6e2d5ec96.pdf