Abstract
This study presents the multi-stepped functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate model for the first time, and its free and forced vibration is analyzed by employing the domain decomposition method. The segmentation technique is employed to discretize the structure along the length direction. The artificial spring technique is applied to the structural boundary and piecewise interface for satisfying the boundary conditions and the combined conditions between subplates. Based on this, the boundary conditions of subdomains could be considered as a free boundary constraint, reducing the difficulty in constructing the allowable displacement function. Since all the structures of subdomains are identical, the allowable displacement functions of them can be uniformly constructed using the two-dimensional ultraspherical polynomial expansion. The potential energy function of the plate is derived from the first-order shear deformation theory (FSDT). The allowable displacement function is substituted into the potential energy function, and then the natural frequencies and mode shapes of the multi-stepped FG-CNTRC plate are decided by using the Rayleigh–Ritz method. The accuracy and reliability of the proposed method are confirmed by the results of the previous literature and finite element method (FEM). On this basis, the influences of the geometric and material parameters on free and forced vibration of the multi-stepped FG-CNTRC plate are also studied.
Highlights
As the advanced manufacturing technology is rapidly developed, the FG-CNTRC has appeared as a prospective kind of composites in the past few years. e FG-CNTRC is composed of carbon nanotubes (CNTs) and functionally graded materials (FGMs) and considered as the advanced material with extraordinary mechanical, optical, thermal, and electrical features
Shock and Vibration and non-linear analysis. e wide range of investigations on the free vibration analysis has firstly paid attention to the analysis of the vibrational behavior of functionally graded materials [8,9,10,11,12,13,14,15]. en, the research was enlarged to the analysis of the FG-CNTRC. e following paragraphs illustrate several research studies related to the analysis of the free vibration of FG-CNTRC shell structures
In this paper, using the domain decomposition method, dynamic behavior of multi-stepped FG-CNTRC plate with random boundary conditions is analyzed based on the first-order shear deformation theory (FSDT)
Summary
As the advanced manufacturing technology is rapidly developed, the FG-CNTRC has appeared as a prospective kind of composites in the past few years. e FG-CNTRC is composed of carbon nanotubes (CNTs) and functionally graded materials (FGMs) and considered as the advanced material with extraordinary mechanical, optical, thermal, and electrical features. Using the FSDT theory to describe the kinematics of the considered structure, Mirzaei and Kiani [27] employed the Ritz method to obtain the vibrational solutions, and they summarized the research studies mentioned above which were studying the influence of carbon nanotube reinforcements on the improvement of the vibrational behavior of FG-CNTRC structures. Selim et al [34] analyzed the free vibration behavior of FG-CNTRC plates based on Reddy’s higher-order shear deformation theory (HSDT) and element-free kp-Ritz method in the thermal environment Parametric effects such as CNT distribution, boundary conditions, plate aspect ratio, plate thickness-to-width ratio, and CNT volume fraction on the dimensionless frequencies were examined. The global potential energy functional of the multistepped FG-CNTRC plate is constructed by employing the FSDT. e polynomials’ unknown coefficient is treated using the standard variational operation to study the dynamic characteristics of the FG-CNTRC plate. e convergence and accuracy of the proposed model are validated using numerical examples
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