Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution

Purpose: This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.

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Free Vibration Analysis of Functionally Graded Plates on Two-Parameter Elastic Supports and in Contact With Stationary Fluid

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4038031 ◽

2017 ◽

Vol 140 (2) ◽

Cited By ~ 1

Author(s):

Arash Shahbaztabar ◽

Ahmad Rahbar Ranji

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Volume Fraction ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Rectangular Plates ◽

Power Law Distribution ◽

Fg Plates ◽

The Impact ◽

Two Parameter

Free vibration analysis of functionally graded (FG) rectangular plates on two-parameter elastic foundation and vertically coupled with fluid is the objective of this work. The fluid domain is considered to be infinite in length, but it is bounded in depth and width directions, and the effects of hydrostatic pressure and free surface waves are not taken into account. The mechanical properties of the FG plates are assumed to vary continuously through the thickness direction according to a power-law distribution of the volume fraction of the constituents. The accuracy and applicability of the formulation is illustrated by comparison studies with those reported in the open literature. At the end, parametric studies are carried out to examine the impact of different parameters on the natural frequencies.

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Elasticity solution for the free vibration analysis of functionally graded cylindrical shell bonded to thin piezoelectric layers

International Journal of Pressure Vessels and Piping ◽

10.1016/j.ijpvp.2011.10.020 ◽

2012 ◽

Vol 89 ◽

pp. 98-111 ◽

Cited By ~ 38

Author(s):

A. Alibeigloo ◽

A.M. Kani ◽

M.H. Pashaei

Keyword(s):

Cylindrical Shell ◽

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Elasticity Solution ◽

Piezoelectric Layers

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Free vibration analysis of four parameter functionally graded plates accounting transverse shear mode

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/36/2/3312 ◽

2014 ◽

Vol 36 (2) ◽

pp. 145-160

Author(s):

Gulshan Taj M. N. A. ◽

Anupam Chakrabarti ◽

Mohammad Talha

Keyword(s):

Free Vibration ◽

Power Law ◽

Transverse Shear ◽

Vibration Analysis ◽

Effective Properties ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Shear Mode ◽

Shear Stresses ◽

Element Formulation

In the present investigation, free vibration analysis of functionally graded material (FGM) plate is performed incorporating higher order shear deformation theory in conjunction with C0 based finite element formulation. The cubic component of thickness term is incorporated in in-plane fields and constant variation of thickness is assumed for transverse component. The theory incorporates the realistic parabolic variation of transverse shear stresses thus eliminates the use of shear correction factor. Aluminium/Zirconia plate is considered for the analysis and the effective properties are assumed to have smooth and gradual variation in the thickness direction and remain constant in in-plane direction. The spatial variation of properties pertaining to homogeneous and FGM plate is estimated by means of power law, which is described by the four parameters. With respect to dynamic analysis, it is vital for an analyst to know whether the top of the plate is ceramic or metal rich, and inversely bottom of the plate is ceramic or metal rich. This phenomenon can be described by choosing the appropriate values of the parameters appears in the power law. In the study, prominence has been given to study the influence of power law parameters on frequency response of FGM plates so as to accomplish different combination of FGM profiles. Thin and moderately thick FGM plates are analyzed to generate the frequency values of the FGM plate. The imperative conclusions presented regarding the choice of parameter in the power law could be useful for designer to arrive for particular material profile of FGM plate.

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