Free vibration analysis of axially functionally graded linearly taper beam on elastic foundation

International Conference on Advances in Materials and Manufacturing Applications 2016

Lohar, H.^1 ; Mitra, A.^2 ; Sahoo, S.^3

Mechanical Engineering Department, Heritage Institute of Technology, Kolkata

700107, India^1

Mechanical Engineering Department, Jadavpur University, Kolkata

7000032, India^2

Civil Engineering Department, Heritage Institute of Technology, Kolkata

700107, India^3

关键词: Beam on elastic foundation;    Different boundary condition;    Dimensionless frequency;    Eigen-value problems;    Foundation stiffness;    Free-vibration analysis;    Minimum potential energy principle;    Non-linear free vibration;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/149/1/012130/pdf
DOI  :  10.1088/1757-899X/149/1/012130

来源: IOP

【 摘 要 】

In the present study non-linear free vibration analysis is performed on a linearly tapered Axially Functionally Graded (AFG) beam resting on an elastic foundation with different boundary conditions. Firstly the static problem is carried out through an iterative scheme using a relaxation parameter and later on the subsequent dynamic problem is solved as a standard eigen value problem. Minimum potential energy principle is used for the formulation of the static problem and for the dynamic problem Hamilton's principle is utilized. The free vibrational frequencies are tabulated for different taper parameter and different foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane.