Free vibration of functionally graded viscoelastic foam plates using shear- and normal-deformation theories

In this paper, various shear- and normal-deformation theories with polynomial, hyperbolic and integral functions of displacements are applied to examine thickness-stretching effects on the free vibration of thick open-cell foam plates. Displacement functions include bending, shear and thickness stre...

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Bibliographic Details
Published in:Mechanics of time-dependent materials 2023-12, Vol.27 (4), p.1273-1294
Main Author: Zamani, H. A.
Format: Article
Language:English
Subjects:
Algorithms
Characterization and Evaluation of Materials
Classical Mechanics
Constitutive relationships
Deformation effects
Differential equations
Engineering
Equations of motion
Free vibration
Functions (mathematics)
Hamilton's principle
Iterative methods
Plates
Polymer Sciences
Polynomials
Porosity
Resonant frequencies
Shear
Solid Mechanics
Stretching
Thickness
Viscoelasticity
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Summary:In this paper, various shear- and normal-deformation theories with polynomial, hyperbolic and integral functions of displacements are applied to examine thickness-stretching effects on the free vibration of thick open-cell foam plates. Displacement functions include bending, shear and thickness stretching of transverse deflection. The distribution of porosity through the thickness is considered by a power-law relationship, while the separable kernel framework and Boltzmann–Volterra superposition principles are used to describe the constitutive relations. Also, a standard solid viscoelastic model is investigated as a special case. The integropartial differential equations of motion with frequency-dependent coefficients based on different deformation theories are derived using the Hamilton principle in the complex domain, and they are solved via semianalytical and iterative numerical algorithms in the spatial and frequency domains. The solution procedure is assessed for elastic functionally graded plates and viscoelastic laminated plates. The effects of porosity distribution, thickness stretching, different deformation theories and geometrical parameters on natural frequencies and loss factors are investigated through parametric studies and it is revealed that the results obtained from deformation theories with integral functions give the nearest loss factors to the layerwise theory, the highest vibrational characteristics and are most affected by the power index in comparison with other theories.
ISSN:1385-2000
1573-2738
DOI:10.1007/s11043-021-09533-w