Vibration analysis of FGM cylindrical shell under thermal field or axial load

Dissertation for M.Sc master's degree

Mechanical Engineering - Applied Design

Abstract

With the emergence of composite materials, a huge progress was achieved in many engineering applications. Nevertheless, problems such as delamination, stress concentration, and discontinuous distribution of stress, the idea of ??creating a new type of composite materials in which properties change continuously and overcome the above-mentioned problems, led researchers to the construction and production of materials with graded properties. The characteristics and advantages of these materials are such that the research and demand for the use of these materials has increased greatly in recent years in various industries, including the air and space industries.

The destructive effects that the resonance phenomenon can have, show the importance of investigating and analyzing free vibrations, especially in geometries (e.g. cylindrical, etc.) and widely used materials (e.g. steels) and also Due to the little connection between industry and university in Iran, the advancement of science finds its way less to old and working industries, so it is important to investigate the cylindrical shell (similar to the furnaces in the Sarcheshme copper complex) with FGM materials. In this thesis, first, the kinematic relations and structural relations of a cylindrical shell for linear and non-linear modes are defined, then the equations of motion are obtained using these relations, and then a cylindrical shell made of FGM material is modeled in terms of geometry, taking into account some assumptions similar to converter furnaces [1] in the copper complex. After meshing the model and applying thermal loads, mechanical loads and supports, a numerical solution is obtained.

Frequency changes were investigated for different temperatures, masses and supports. The results show that with the increase in mass and temperature, the frequency decreases, with the increase and change in the support, the frequency increases, and finally, according to the results obtained for stress and frequency, it is suggested to use FGM material in the furnace body instead of using the old furnace structure.

Key words: free vibrations - cylindrical shell - materials with graded properties

1-1 Introduction

The irreplaceable role and various effects of vibration phenomena on engineering systems and structures, especially adverse effects such as failure, reduction of comfort and convenience, and disruption of the performance of precision instruments, indicate the necessity and importance of investigating, analyzing and controlling vibrations. In the field of mechanical vibrations, due to the irreparable and destructive consequences that the resonance phenomenon can have, it is not possible to accurately check and control vibrations without identifying natural frequencies and analyzing free vibrations. Among the geometries used in the industry, shells, due to their light weight due to their small thickness, are one of the most widely used structures in various industries, including the automotive industry. Air and space are marine and submarine industries. The body, diffuser and nose of spacecraft, airplane and missile, submarine body, tanks, transmission pipes and reactor are among the most obvious examples in this field. So that progress in various fields of science and technology is limited without progress in material science and obtaining materials with superior characteristics and efficiency. Therefore, mankind has always sought to discover materials with different and new capabilities or to produce synthetic materials to improve the properties of existing materials.

In recent years, with the expansion of high-power electric motors, turbines, reactors and high-speed vehicles, materials resistant to harsh environmental conditions, including very high temperatures and high temperature gradients, have received much attention. The need for a material with high thermal and mechanical resistance led to the introduction of materials with graded properties [1] in 1984 in Japan as a resistant and widely used material.The need for a material with high thermal and mechanical resistance led to the introduction of materials with graded properties [1] in 1984 in Japan, as a resistant and widely used material. The selection of materials with graded properties in 1992 as one of the 10 advanced technologies in Japan reminds the importance and position of this technology.

The importance of free vibration analysis, the wide application of cylindrical shells, the capabilities of materials with graded properties can greatly clarify the importance of investigating and carrying out this project.

1-2 History of work

Vibrations in cylindrical shells were first studied by Sophie Germain[2] in 1821 and then continued by Rayleigh[3]]1[ and Love[4]]2[ at the end of the 19th century. Lau first presented the linear shell theory based on the Kirchhoff plate hypothesis. Lowe's equations can be considered as the most general equations in the integration of the theory of shell structures where the thickness is small compared to other dimensions. The vibrations of the shells considering rotational inertia and shear deformation were presented by Sudel [5] in 1982. The vibrations of cylindrical shells made of a material with graded properties consisting of stainless steel and nickel were investigated by Levy et al. [3] and using Rayleigh-Ritz method. The purpose of this work is to study the natural frequencies, the effect of the volume fractions of the compounds and the effects of the configurations of the building materials on these frequencies. This analysis was done using the strain-displacement relations from Love's shell theory, and the eigenvalues ??of the governing equations were obtained using Rayleigh-Ritz method. This study has been done for two types of cylindrical shells with graded properties, and the configurations of the building materials in these cylindrical shells with graded properties are different. The characteristics of the first type of these shells change continuously from nickel on the inner surface to stainless steel on the outer surface. In the second type of these shells, the characteristics change continuously from stainless steel on the inner surface to nickel on the outer surface.

This study shows that the frequency characteristics of cylindrical shells with graded properties are similar to isotropic homogeneous cylindrical shells. Due to material grading, shells with graded properties exhibit interesting frequency characteristics when the volume fractions of the compounds are changed. This was done by changing the power of the volume ratio. The effect of the volume fractions of the compounds on the frequencies of the first and second type shells was different. For shells with graded properties of the first type, when the volume ratio power increases, the natural frequencies decrease, and for the second type of these shells, when this power decreases, its natural frequencies also decrease. The volume fractions of the compositions and configuration of the building materials affect the natural frequencies.

Malkzadeh and Heydarpour [4] analyzed the free vibrations of the rotating cylindrical shells that are exposed to the thermal environment based on the first order shear theory of the shells. This formulation includes centrifugal and cryolis forces caused by crustal rotation. In this research, it is assumed that the properties of the material depend on the temperature and are graded according to the thickness. The equations of motion are derived using Hamilton's principle. Effective and accurate differential integral method has been used to discretize thermoelastic balance equations and motion equations. Pradhan et al. [5] investigated the vibrations of a cylindrical shell with graded properties consisting of stainless steel and zirconia using the Rayleigh method. They used the strain-displacement relations related to Love's shell theory and used the Rayleigh method to derive the equations governing the problem.

Sheng and Wang [6] in 2009 based on the first-order shear theory, Hamilton's principle and Maxwell's equation, entanglement equations to determine the electric potential and electric displacements of the shell presented a cylinder with graded properties with a surface limited to a piezoelectric layer and subjected to moving loads. Frequency equations were obtained using displacement functions and an electric potential function. Modal analysis method and Newmark's integral method are used to calculate the displacements and electrical potential of the sensor of this shell which is exposed to moving loads.