Size-dependent analysis of homogeneous and functionally graded microplates using IGA and a non-classical Kirchhoff plate theory

2017 ◽  
Vol 172 ◽  
pp. 34-44 ◽  
Author(s):  
Shuo Liu ◽  
Tiantang Yu ◽  
Tinh Quoc Bui ◽  
Shifeng Xia
Keyword(s):  
Plate Theory ◽  
Functionally Graded ◽  
Kirchhoff Plate ◽  
Size Dependent ◽  
Kirchhoff Plate Theory

Analytical Solutions for Functionally Graded Sandwich Plates Bonded by Viscoelastic Interlayer Based on Kirchhoff Plate Theory

2020 ◽  
Vol 12 (06) ◽  
pp. 2050062
Author(s):  
Zhiyuan Yang ◽  
Peng Wu ◽  
Weiqing Liu ◽  
Hai Fang
Keyword(s):  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Time Dependent ◽  
Kirchhoff Plate ◽  
Time Step ◽  
Kirchhoff Plate Theory ◽  
Dependent Behavior ◽  
Present Solution ◽  
Viscoelastic Interlayer

In this paper, an analytical solution for functionally graded sandwich plate adhesively bonded by viscoelastic interlayer is proposed to research its time-dependent behavior. The Kirchhoff plate theory is employed to describe the mechanical property of each gradient layer with elastic modulus defined as the arbitrary function through the thickness direction. The standard linear solid model is applied to simulate the viscoelasticity of the interlayer with considering the strain memory effect. By the use of the vibrational method and the Laplace transformation, the solutions of stresses and displacements are solved analytically. The validation study indicates that the present solution is correct and more effective than the finite element solution because of the fine mesh both in the geometric shape and the time step. In addition, the influences of the geometry and material parameters on the time-dependent behavior of the sandwich plate are investigated in detail.

scholarly journals Vibrational analysis of nanoplate with surface irregularity via Kirchhoff plate theory

2021 ◽  
Vol 11 ◽  
pp. 184798042110011
Author(s):  
Mahmoud M Selim ◽  
Taher A Nofal
Keyword(s):  
Natural Frequency ◽  
Plate Theory ◽  
Vibrational Analysis ◽  
Equation Of Motion ◽  
Frequency Equation ◽  
Kirchhoff Plate ◽  
Surface Irregularity ◽  
Structural Element ◽  
Kirchhoff Plate Theory ◽  
Parabolic Form

In this work, an attempt is done to apply the Kirchhoff plate theory to find out the vibrational analyses of a nanoplate incorporating surface irregularity effects. The effects of surface irregularity on natural frequency of vibration of nanomaterials, especially for nanoplates, have not been investigated before, and most of the previous research have been carried for regular nanoplates. Therefore, it must be emphasized that the vibrations of irregular nanoplate are novel and applicable for the nanodevices, in which nanoplates act as the main structure of the nanocomposite. The surface irregularity is assumed in the parabolic form at the surface of the nanoplate. A novel equation of motion and frequency equation is derived. The obtained results provide a better representation of the vibration behavior of irregular nanoplates. It has been observed that the presence of surface irregularity affects considerably on the natural frequency of vibrational nanoplates. In addition, it has been seen that the natural frequency of nanoplate decreases with the increase of surface irregularity parameter. Finally, it can be concluded that the present results may serve as useful references for the application and design of nano-oscillators and nanodevices, in which nanoplates act as the most prevalent nanocomposites structural element.

Size-dependent thermally affected wave propagation analysis in nonlocal strain gradient functionally graded nanoplates via a quasi-3D plate theory

2016 ◽  
Vol 232 (1) ◽  
pp. 162-173 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Strain Gradient ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Gradient Elasticity ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Thermal Environments ◽  
Size Dependent ◽  
Dispersion Behavior ◽  
Nonlocal Strain Gradient

This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded nanoplate in thermal environments. The theory contains two scale parameters corresponding to nonlocal and strain gradient effects. A quasi-3D plate theory considering shear and normal deformations is employed to present the formulation. Mori–Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton’s principle is employed to obtain the governing equations of nanoplate accounting for thickness stretching effect. These equations are solved analytically to find wave frequencies and phase velocities of functionally graded nanoplate. It is indicated that wave dispersion behavior of functionally graded nanoplates is significantly affected by temperature rise, nonlocality, length scale parameter, and material composition.

Analysis of Electromechanical Performance of Energy Harvesting Skin Based on the Kirchhoff Plate Theory

2014 ◽  
Author(s):  
Heonjun Yoon ◽  
Byeng D. Youn ◽  
Heung S. Kim
Keyword(s):  
Energy Harvesting ◽  
Differential Equations ◽  
Analytical Model ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Electrical Circuit ◽  
Kirchhoff Plate ◽  
Mode Shapes ◽  
Kirchhoff Plate Theory

As a compact and durable design concept, energy harvesting skin (EH skin), which consists of piezoelectric patches directly attached onto the surface of a vibrating structure as one embodiment, has been recently proposed. This study aims at developing an electromechanically-coupled analytical model of the EH skin so as to understand its electromechanical behavior and get physical insights about important design considerations. Based on the Kirchhoff plate theory, the Hamilton’s principle is used to derive the differential equations of motion. The Rayleigh-Ritz method is implemented to calculate the natural frequency and the corresponding mode shapes of the EH skin. The electrical circuit equation is derived by substituting the piezoelectric constitutive relation into Gauss’s law. Finally, the steady-state output voltage is obtained by solving the differential equations of motion and electrical circuit equation simultaneously. The results of the analytical model are verified by comparing those of the finite element analysis (FEA) in a hierarchical manner.

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