Nonlinear dynamic analysis of Sigmoid functionally graded circular cylindrical shells on elastic foundations using the third order shear deformation theory in thermal environments

This work is the first exploration of the static bending and dynamic response analyses of piezoelectric bidirectional functionally graded plates by combining the third-order shear deformation theory of Reddy and the finite element approach, which can numerically model mechanical relations of the structure. The present approach and mechanical model are confirmed through the verification examples. The geometrical and material study is conducted to evaluate the effects of the feedback coefficients, volume fraction parameter, and constraint conditions on the static and dynamic behaviors of piezoelectric bidirectional functionally graded structures, and this work presents a wide variety of static and dynamic behaviors of the plate with many interesting results. There are many meanings that have not been mentioned by any work, especially the working performance of the structure is better than that when the feedback parameter of the piezoelectric component is added, that is, the piezoelectric layer increases the working efficiency. Numerical investigations are the important basis for calculating and designing related materials and structures in technical practice.

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Nonlinear Dynamic Analysis of Functionally Graded Graphene Reinforced Composite Truncated Conical Shells

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419501487 ◽

2019 ◽

Vol 29 (11) ◽

pp. 1950148 ◽

Cited By ~ 2

Author(s):

Aiwen Wang ◽

Youqing Pang ◽

Wei Zhang ◽

Pengcheng Jiang

Keyword(s):

Dynamic Analysis ◽

Nonlinear Dynamic ◽

Ritz Method ◽

Nonlinear Dynamic Analysis ◽

Shear Deformation Theory ◽

Distribution Patterns ◽

Equation Model ◽

Functionally Graded ◽

Conical Shells ◽

Reinforced Composite

Functionally graded (FG) graphene reinforced composite (GRC) is a new class of advanced composite materials. In GRC, several layers of graphene platelets (GPLs) are randomly or uniformly dispersed in matrix. These GPLs have uniform arrangement, or are arranged with gradient, in the direction of thickness in accordance with three different graphene distribution rules. In this study, the nonlinear dynamic analysis of FG GRC truncated conical shells, subjected to a combined action of transverse excitation and axial force, is performed using the first shear deformation theory (FSDT). Estimation of equivalent Young’s modulus of the composites is calculated using a modified Halpin–Tsai model. In addition, a partial differential equation model is developed based on the Hamilton principle and nonlinear strain-displacement relationship. The Galerkin method and the fourth-order Runge–Kutta method are used to solve the equation. The dimensionless linear natural frequency of an FG GRC truncated conical shell is calculated by the Rayleigh–Ritz method and compared with available results in the literature to verify the accuracy of the present model. Simultaneously, significant effects of the different parameters, such as the total layer numbers, semi-vertex angles, GPLs weight fractions, distribution patterns and the length-to-thickness ratios, on the nonlinear dynamics including bifurcation and chaos of FG GRC truncated conical shells are investigated.

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Nonlinear dynamic analysis of piezoelectric functionally graded porous truncated conical panel in thermal environments

Thin-Walled Structures ◽

10.1016/j.tws.2020.106837 ◽

2020 ◽

Vol 154 ◽

pp. 106837 ◽

Cited By ~ 2

Author(s):

Do Quang Chan ◽

Nguyen Van Thanh ◽

Nguyen Dinh Khoa ◽

Nguyen Dinh Duc

Keyword(s):

Dynamic Analysis ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Analysis ◽

Functionally Graded ◽

Thermal Environments

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

Noise & Vibration Worldwide ◽

10.1177/0957456519883265 ◽

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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