scholarly journals FREQUENCY ANALYSIS OF CRACKED FUNCTIONALLY GRADED CANTILEVER BEAM

2017 ◽  
Vol 55 (2) ◽  
pp. 229
Author(s):  
Nguyen Ngoc Huyen ◽  
Nguyen Tien Khiem
Keyword(s):  
Cantilever Beam ◽  
Edge Crack ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Frequency Equation ◽  
Functionally Graded ◽  
Neutral Axis ◽  
Open Crack ◽  
Graded Material ◽  
Fgm Beam

In this paper, a functionally graded cantilever beam with an open crack is investigated on the base of Timoshenko beam theory; power law of functionally graded material (FGM) and taking into account actual position of neutral axis instead of the central one. The open and edge crack is modeled by coupled translational and rotational springs stiffness of which is calculated by the formulas conducted accordingly to fracture mechanics. Using the frequency equation obtained in the framework of the theory natural frequencies of the beam are examined along the crack parameters and material properties. This analysis demonstrates that sensitivity of natural frequencies of FGM beam to crack is strongly dependent on the material constants of FGM

The Vibration and Modal Power Flow Analysis of a Functionally Graded Material Beam With an Open Crack

2019 ◽  
Author(s):  
Xiaotian Liang ◽  
Tianyun Li ◽  
Xing Heng ◽  
Xiaofang Hu ◽  
Xiang Zhu
Keyword(s):  
Functionally Graded Material ◽  
Power Flow ◽  
Crack Depth ◽  
Flow Analysis ◽  
Damage Index ◽  
Functionally Graded ◽  
Open Crack ◽  
Modal Power ◽  
Graded Material ◽  
Fgm Beam

Abstract The free vibration and modal power flow of a functionally graded material (FGM) beam with an open crack are studied. The crack is simulated by using the massless-rotational spring model. The natural frequencies and corresponding modal shapes of the cracked beam are obtained by the wave propagation method. A modal power flow formula of the FGM beam is deduced by Bernoulli-beam theory. A detailed parametric study is conducted to show the influences of crack location, crack depth, material property gradient, and boundary condition on the modal power flow characteristics based on a modal power flow damage index. Numerical examples show that the damage index based on the modal power flow can effectively identify the crack in the FGM beam, which provides the basis for the future study on the modal power flow based damage detection of functionally graded material structures.

Vibration characteristics and stable region of a parabolic FGM thin-walled beam with axial and spinning motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Baichuan Lin ◽  
Bo Chen ◽  
Yinghui Li ◽  
Jie Yang
Keyword(s):  
Natural Frequencies ◽  
Angular Speed ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Stable Region ◽  
Graded Material ◽  
Axially Moving ◽  
Fgm Beam ◽  
Spinning Speed ◽  
Axial Speed

Abstract This paper focuses on the vibration characteristics of the parabolic functionally graded material (FGM) beam considering the axially moving and spinning motion. Based on the Hamilton’s principle, the governing equation of the beam is derived. Then, the Galerkin’s method is employed to solve the equation. The combined influence of axial speed, spinning speed, and geometric parameters on natural frequencies of the beam are investigated. What’s more, the axially moving and spinning motion can lead to a critical axial speed and critical spinning angular speed, respectively. These two critical speeds and stable region affected by different parameters are also discussed.

scholarly journals Frequency Analysis for Functionally Graded Material Cylindrical Shells: A Significant Case Study

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rabia Anwar ◽  
Madiha Ghamkhar ◽  
Muhammad Imran Khan ◽  
Rabia Safdar ◽  
Muhammad Zafar Iqbal ◽  
...  
Keyword(s):  
Functionally Graded Materials ◽  
Natural Frequencies ◽  
Constitutive Relations ◽  
Cylindrical Shells ◽  
Frequency Equation ◽  
Functionally Graded ◽  
Graded Materials ◽  
Simply Supported ◽  
Love’S Shell Theory ◽  
Graded Material

Cylindrical shells play an important role for the construction of functionally graded materials (FGMs). Functionally graded materials are valuable in order to develop durable materials. They are made of two or more materials such as nickel, stainless steel, zirconia, and alumina. They are extremely beneficial for the manufacturing of structural elements. Functionally graded materials are broadly used in several fields such as chemistry, biomedicine, optics, and electronics. In the present research, vibrations of natural frequencies are investigated for different layered cylindrical shells, those constructed from FGMs. The behavior of shell vibration is based on different parameters of geometrical material. The problem of the shell is expressed from the constitutive relations of strain and stress with displacement, as well as it is adopted from Love’s shell theory. Vibrations of natural frequencies (NFs) are calculated for simply supported-simply supported (SS-SS) and clamped-free (C-F) edge conditions. The Rayleigh–Ritz technique is employed to obtain the shell frequency equation. The shell equation is solved by MATLAB software.

Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory

2017 ◽  
Vol 24 (17) ◽  
pp. 3809-3818 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati ◽  
Parisa Haghi
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Wave Number ◽  
Graded Material ◽  
Fg Nanobeam

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc.

scholarly journals UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM

2016 ◽  
Vol 54 (6) ◽  
pp. 785 ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Nguyen Ngoc Huyen
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Power Law Distribution ◽  
Material Parameters ◽  
Flexural Vibrations ◽  
Fgm Beam

Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slendernes

Vibration of a Cracked Cantilever Beam

1998 ◽  
Vol 120 (3) ◽  
pp. 742-746 ◽  
Author(s):  
T. G. Chondros ◽  
A. D. Dimarogonas
Keyword(s):  
Cantilever Beam ◽  
Edge Crack ◽  
Beam Theory ◽  
Experimental Results ◽  
Crack Model ◽  
Cracked Beam ◽  
Lateral Vibrations ◽  
Vibration Model ◽  
Cantilevered Beam ◽  
Continuous Crack

A continuous cracked bar vibration model is developed for the lateral vibration of a cracked Euler-Bernoulli cantilevered beam with an edge crack. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions for the cracked beam as an one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of lateral vibrations of an aluminum cantilever beam with a single-edge crack are presented: the continuous cracked beam vibration model, the lumped crack model vibration analysis, and experimental results. Experimental results fall very close to the values predicted by the continuous crack formulation. Moreover, the continuous cracked beam theory agrees better with the experimental results than the lumped crack flexibility theory.

A third-order shear deformation theory for nonlinear vibration analysis of stiffened functionally graded material sandwich doubly curved shallow shells with four material models

2017 ◽  
Vol 21 (4) ◽  
pp. 1316-1356 ◽  
Author(s):  
Dang T Dong ◽  
Dao Van Dung
Keyword(s):  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Shallow Shells ◽  
Graded Material ◽  
Doubly Curved

This study presents a nonlinear vibration analysis of function graded sandwich doubly curved shallow shells, which reinforced by functionally graded material stiffeners and rested on the Pasternak foundation. The shells are subjected to the combination of mechanical, thermal, and damping loading. Four models of the sandwich shells with general sigmoid and power laws distribution are considered. The governing equations are established based on the third-order shear deformation theory. Von Kármán-type nonlinearity and smeared stiffener technique are taken into account. The explicit expressions for determining natural frequencies, nonlinear frequency–amplitude relation, and time–deflection curves are obtained by employing the Galerkin method. Finally, the fourth-order Runge–Kutta method is applied to investigate the influences of functionally graded material stiffeners, the boundary conditions, the models of the shells, thermal environment, foundation and geometrical parameters on the natural frequencies and dynamic nonlinear responses of the sandwich shells.

Flap wise bending vibration and dynamic stability of rotating functionally graded material plates in thermal environments

2016 ◽  
Vol 231 (2) ◽  
pp. 203-217
Author(s):  
Ramu Inala ◽  
SC Mohanty
Keyword(s):  
Dynamic Stability ◽  
Functionally Graded Material ◽  
Rotational Speed ◽  
Natural Frequencies ◽  
Functionally Graded ◽  
Bending Vibration ◽  
Thermal Environments ◽  
Graded Material ◽  
Instability Regions ◽  
Rotating Plate

This paper deals with the study of the flapwise bending vibration and dynamic stability of rotating functionally graded material plates in thermal environments. A finite element formulation is derived for modal and dynamic stability analyses of rotating functionally graded material plates using first-order shear deformation theory. Temperature-dependent material properties of the plates are considered in the analysis and a simple power law is assumed for composition of constituent materials to vary along the thickness direction. The same power law is also proposed in thermal environments for temperature variation across the thickness of the plate. Some numerical results obtained from the present method are compared with numerical results available in the literature and are found to be in good agreement. Parametric investigation is carried out thoroughly to study the effect of the temperature rise, hub radius, and rotational speed on vibration and the dynamic stability of rotating plate in thermal environment. Bolotin’s method is used to generate the boundaries of stability and instability regions. These instability regions are plotted in the parameter space with the nondimensional dynamic load and excitation frequency. It is observed that the natural frequencies reduce with an increase in temperature rise. Increase in rotational speed and hub radius results in increase of natural frequencies of vibration. The rise in temperature leads to reduction in the dynamic stability of plate. Increase in rotational speed and hub radius enhances the dynamic stability of the rotating plate.

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