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

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Hareram Lohar ◽  
Anirban Mitra ◽  
Sarmila Sahoo
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Dynamic Problem ◽  
Free Vibration Analysis ◽  
Static Problem ◽  
Functionally Graded ◽  
Dimensionless Frequency ◽  
Energy Principle ◽  
Eigen Value ◽  
Minimum Potential Energy Principle

AbstractIn 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 dimensionless frequency-amplitude plane.

scholarly journals Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

2016 ◽  
Vol 9 ◽  
pp. 9-25 ◽  
Author(s):  
Hareram Lohar ◽  
Anirban Mitra ◽  
Sarmila Sahoo
Keyword(s):  
Elastic Foundation ◽  
Static Problem ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Dimensionless Frequency ◽  
Energy Principle ◽  
Various Boundary Conditions ◽  
Non Linear ◽  
Beams On Elastic Foundation ◽  
Minimum Potential Energy Principle

A displacement based semi-analytical method is utilized to study non-linear free vibration and mode shapes of an exponential tapered axially functionally graded (AFG) beam resting on an elastic foundation. In the present study geometric nonlinearity induced through large displacement is taken care of by non-linear strain-displacement relations. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. In the present paper at first the static problem is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic analysis is carried out as a standard eigen value problem. Energy principles are used for the formulation of both the problems. The static problem is solved by using minimum potential energy principle whereas in case of dynamic problem Hamilton’s principle is employed. The free vibrational frequencies are tabulated for exponential taper profile subject to various boundary conditions and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane and in some particular case the mode shape results are furnished.

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

scholarly journals Free vibration analysis of sandwich beams with FG porous core and FGM faces resting on Winkler elastic foundation by various shear deformation theories

2018 ◽  
Vol 12 (3) ◽  
pp. 23-33 ◽  
Author(s):  
Dang Xuan Hung ◽  
Huong Quy Truong
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Porous Core ◽  
Winkler Elastic Foundation ◽  
Beam Theories ◽  
Good Agreement

This paper studies the free vibration behavior of a sandwich beam resting on Winkler elastic foundation. The sandwich beam is composed of two FGM face layers and a functionally graded (FG) porous core. A common general form of different beam theories is proposed and the equations of motion are formulated using Hamilton's principle. The result of the general form is validated against those of a particular case and shows a good agreement. The effect of different parameters on the fundamental natural frequency of the sandwich beam is investigated. Article history: Received 02 March 2018, Revised 26 March 2018, Accepted 27 April 2018

Free Vibration Analysis of Functionally Graded Beams Resting on Elastic Foundation in Thermal Environment

2016 ◽  
Vol 16 (07) ◽  
pp. 1550029 ◽  
Author(s):  
P. Zahedinejad
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Various Boundary Conditions

The free vibration of functionally graded (FG) beams with various boundary conditions resting on a two-parameter elastic foundation in the thermal environment is studied using the third-order shear deformation beam theory. The material properties are temperature-dependent and vary continuously through the thickness direction of the beam, based on a power-law distribution in terms of the volume fraction of the material constituents. In order to discretize the governing equations, the differential quadrature method (DQM) in conjunction with the Hamilton’s principle is adopted. The convergence of the method is demonstrated. In order to validate the results, comparisons are made with solutions available for the isotropic and FG beams. Through a comprehensive parametric study, the effect of various parameters involved on the FG beam was studied. It is concluded that the uniform temperature rise has more significant effect on the frequency parameters than the nonuniform case.

scholarly journals A Finite Element Formulation and Nonlocal Theory for the Static and Free Vibration Analysis of the Sandwich Functionally Graded Nanoplates Resting on Elastic Foundation

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Van-Ke Tran ◽  
Thanh-Trung Tran ◽  
Minh-Van Phung ◽  
Quoc-Hoa Pham ◽  
Trung Nguyen-Thoi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Material Properties ◽  
Free Vibration Analysis ◽  
Nonlocal Theory ◽  
Functionally Graded ◽  
Element Formulation ◽  
Proposed Model ◽  
Homogeneous Core

This article presents a finite element method (FEM) integrated with the nonlocal theory for analysis of the static bending and free vibration of the sandwich functionally graded (FG) nanoplates resting on the elastic foundation (EF). Material properties of nanoplates are assumed to vary through thickness following two types (Type A with homogeneous core and FG material for upper and lower layers and Type B with FG material core and homogeneous materials for upper and lower layers). In this study, the formulation of the four-node quadrilateral element based on the mixed interpolation of tensorial components (MITC4) is used to avoid “the shear-locking” problem. On the basis of Hamilton’s principle and the nonlocal theory, the governing equations for the sandwich FG nanoplates are derived. The results of the proposed model are compared with published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and material properties on the static and free vibration behaviors of nanoplates are investigated in detail.

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