Free Vibration of Thick Quadrilateral Laminates Using Third-Order Shear-Normal Deformation Theory

AIAA Journal ◽  
2020 ◽  
Vol 58 (10) ◽  
pp. 4580-4594
Author(s):  
Berkan Alanbay ◽  
Rakesh K. Kapania ◽  
Romesh C. Batra
Keyword(s):  
Free Vibration ◽  
Deformation Theory ◽  
Third Order ◽  
Normal Deformation

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

scholarly journals Lowest Twelve Frequencies of Sandwich Plates Using Third-Order Shear-Normal Deformation Theory

AIAA Journal ◽  
2020 ◽  
Vol 58 (4) ◽  
pp. 1821-1835
Author(s):  
Berkan Alanbay ◽  
Romesh C. Batra ◽  
Rakesh K. Kapania
Keyword(s):  
Deformation Theory ◽  
Sandwich Plates ◽  
Third Order ◽  
Normal Deformation

FREE VIBRATION OF FUNCTIONALLY GRADED PLATES WITH A HIGHER-ORDER SHEAR AND NORMAL DEFORMATION THEORY

2013 ◽  
Vol 13 (01) ◽  
pp. 1350004 ◽  
Author(s):  
D. K. JHA ◽  
TARUN KANT ◽  
R. K. SINGH
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Normal Deformation ◽  
Fg Plates

Free vibration analysis of functionally graded elastic, rectangular, and simply supported (diaphragm) plates is presented based on a higher-order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson ratios of the FG plates are assumed to be constant, but their Young's modulii and densities vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modeled as a power law function. The equations of motion are derived using Hamilton's principle for the FG plates on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of Navier solution method. The accuracy of the numerical solutions is first established through comparison with the exact three-dimensional (3D) elasticity solutions and the present solutions are then compared with available solutions of other models.

The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate

2019 ◽  
Vol 50 (9-11) ◽  
pp. 267-290
Author(s):  
Ali Bakhsheshy ◽  
Hossein Mahbadi
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Scale Parameter ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
The Third

This article develops the modified couple stress theory to study the free vibration of bi-directional functionally graded microplates subjected to multidimensional temperature distribution. Third-order shear deformation and classical theories of plates are adapted for free vibration analysis of thick and thin microplates, respectively. Employing the third-order shear deformation theory, both normal and shear deformations are considered without the need for shear correction factor. Material of the bi-directional functionally graded microplate is graded smoothly through the length and thickness of the microplate. Gradient of the material is assumed to obey from the power law in terms of the volume fraction of the constituents. Assuming the uniform and nonuniform temperature distributions, the effect of thermal environment on dynamic behavior of the microplate is discussed in detail. Applying the Ritz method, the displacement field is expanded by admissible functions which satisfy the essential boundary conditions, and Hamilton principle is employed to determine the natural frequencies of the microplate. Developed model has been applied to determine the natural frequencies in problems of thin/thick, one-directional/bi-directional functionally graded, and homogeneous/nonhomogeneous microplates. Effects of parameters such as the thermal environment, power law indexes [Formula: see text] and length scale parameter on free vibration of these problems are studied in detail. The results show that higher values of length scale parameter and temperature rise decrease the natural frequency of the bi-directional functionally graded microplate. According to results obtained by classical and third-order shear deformation theories, the third-order shear deformation theory is proposed for vibration analysis of microplates with thickness-to-length ratio less than five.

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