Geometric nonlinear free vibration of axially functionally graded non-uniform beams supported on elastic foundation

被引：12
|
作者：
Lohar, Hareram [1 ]
Mitra, Anirban [2 ]
Sahoo, Sarmila [3 ]
机构：
[1] Heritage Inst Technol, Dept Mech Engn, Kolkata 700107, India
[2] Jadavpur Univ, Dept Mech Engn, Kolkata 700032, India
[3] Heritage Inst Technol, Dept Civil Engn, Kolkata 700107, India
来源：
CURVED AND LAYERED STRUCTURES | 2016年 / 3卷 / 01期
关键词：
Axially functionally graded beam; Elastic foundation; Large amplitude; Energy principles; Geometric nonlinearity; Backbone curve;
D O I：
10.1515/cls-2016-0018
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
In the present study non-linear free vibration analysis is performed on a 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 whereas for the dynamic problem Hamilton's principle is utilized. The free vibrational frequencies are tabulated for different taper profile, taper parameter and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimension-less frequency-amplitude plane.
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页码：223 / 239
页数：17
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