scholarly journals Effects of Material Constructions on Supersonic Flutter Characteristics for Composite Rectangular Plates Reinforced with Carbon Nano-structures

2021 ◽  
Vol 28 (1) ◽  
pp. 107-115
Author(s):  
Aleksander Muc ◽  
Małgorzata Muc-Wierzgoń
Keyword(s):  
Carbon Nanotubes ◽  
Material Properties ◽  
Natural Frequencies ◽  
Rectangular Plates ◽  
Design Procedures ◽  
Nano Structures ◽  
Method Of Solution ◽  
Supersonic Flutter ◽  
Shear Effects ◽  
Transverse Shear Effects

Abstract In this paper effects of material constructions on natural frequencies and critical aerodynamic pressures are investigated. It is assumed that the rectangular plate is made of a polymeric matrix reinforced with graphene nanoplatelets or carbon nanotubes. A general closed analytical method of solution is presented. It is demonstrated that three parameters define entirely the location of the critical flutter pressure. The influence of material properties and transverse shear effects is characterized by a set of multipliers. They can be easily adopted in design procedures.

On a General Approach to Free Vibrations Response of Integrally-Stiffened and/or Stepped-Thickness Rectangular Plates or Panels

2008 ◽  
Author(s):  
Umur Yuceoglu ◽  
Jaber Javanshir ◽  
O¨zen Guvendik
Keyword(s):  
Natural Frequencies ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Width Ratio ◽  
Al Alloy ◽  
Rectangular Plates ◽  
Stiffened Plate ◽  
Governing System ◽  
Stress Resultant ◽  
Method Of Solution

This study is mainly concerned with a “General Approach” to the “Theoretical Analysis and the Solution of the Free Vibrations Response of Integrally-Stiffened and/or Stepped-Thickness Plates or Panels with Two or more Integral Plate Stiffeners”. In general, the “Stiffened System” (regardless of the number of “Plate Stiffeners”) is considered to be composed of dissimilar “Orthotropic Mindlin Plates” with unequal thicknesses. The dynamic governing equations of the individual plate elements of the “System” and the stress resultant-displacement expressions are combined and algebraically manipulated. These operations lead to a new “Governing System of the First Order Ordinary Differential Equations” in “state vector” forms. The new “Governing System of Equations” facilitates the direct application of the present method of solution, namely, the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. As shown in the present study, the “MTMM” is sufficiently general to handle the “Free Vibrations Response” of the “Stiffened System” (with, at least, one or up to three or four “Integral Plate Stiffeners”). The present analysis and the method of solution are applied to the typical “Stiffened Plate or Panel System with Two Integral Plate Stiffeners”. The mode shapes with their natural frequencies are presented for the “Isotropic Al-Alloy” and “Orthotropic Composite” cases and for several sets of support conditions. As an additional example, the case of the “Stiffened Plate or Panel System with Three Integral Plate Stiffeners” is also considered and is shown in terms of the mode shapes and their natural frequencies for one set of the boundary conditions. Also, some parametric studies of the natural frequencies versus the “Stiffener Thickness Ratio” and the “Stiffener Length (or Width) Ratio” are investigated and are graphically presented.

scholarly journals Vibration characteristics of functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports

2018 ◽  
Vol 5 (1) ◽  
pp. 10-34 ◽  
Author(s):  
Rui Zhong ◽  
Qingshan Wang ◽  
Jinyuan Tang ◽  
Cijun Shuai ◽  
Qian Liang
Keyword(s):  
Carbon Nanotubes ◽  
Natural Frequencies ◽  
Functionally Graded ◽  
Internal Line ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Pasternak Foundation ◽  
Arbitrary Boundary ◽  
Reinforced Composite ◽  
Internal Line Supports

Abstract This paper presents the first known vibration characteristics of moderately thick functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports on the basis of the firstorder shear deformation theory. Different distributions of single walled carbon nanotubes (SWCNTs) along the thickness are considered. Uniform and other three kinds of functionally graded distributions of carbon nanotubes along the thickness direction of plates are studied. The solutions carried out using an enhanced Ritz method mainly include the following three points: Firstly, create the Lagrange energy function by the energy principle; Secondly, as the main innovation point, the modified Fourier series are chosen as the basic functions of the admissible functions of the plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges; Lastly, solve the natural frequencies as well as the associated mode shapes by means of the Ritz-variational energy method. In this study, the influences of the volume fraction of CNTs, distribution type of CNTs, boundary restrain parameters, location of the internal line supports, foundation coefficients on the natural frequencies and mode shapes of the FG-CNT reinforced composite rectangular plates are presented.

Preparation and Properties of Heat-Dissipation Coating Filled with Carbon-Based Filler

2017 ◽  
Vol 898 ◽  
pp. 1532-1538
Author(s):  
Yue Gao ◽  
Qian Jin Mao ◽  
Hai Wang ◽  
Zi Ming Wang ◽  
Su Ping Cui
Keyword(s):  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Heat Dissipation ◽  
Filler Content ◽  
Simulated Data ◽  
Content Type ◽  
Element Simulation ◽  
Method Of Solution ◽  
High Emissivity ◽  
Pure Resin

Aiming at the heat dissipation of equipment, and based on ANSYS finite element simulation of thermal conductivity of coatings, the heat-dissipation coating filled with graphite and carbon nanotubes respectively, which integrates heat conduction (high thermal conductivity) and radiation (high emissivity), was successfully prepared by the method of solution mixing. Meanwhile, the effects of filler content, type and shape on thermal conductivity and emissivity of the coating were also investigated. The results indicate that the rising tendency between the simulated data by FEM and experimental value is consistent, which has a certain directive significance. In addition, graphite can improve the thermal conductivity and emissivity of the coating effectively; however, the emissivity decreases when the content exceeds 23.08%. The carbon nanotubes can improve the thermal conductivity and emissivity simultaneously, the thermal conductivity is 2.3 times that of pure resin, and the emissivity is up to 0.91 at the 2.0% mass fraction of carbon nanotubes.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

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