Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions

The main purpose of this paper is to provide a new semi analytical method to analyze the free vibration of functionally graded porous (FGP) cylindrical shell with arbitrary boundary restraints. According to the distributions of porous along thickness direction of the structure, two typical types of symmetric and non-symmetric porosity distributions are performed in this paper. The formulations are established on the basis of energy method and first-order shear deformation theory (FSDT). The displacement functions are expressed by unified Jacobi polynomials and Fourier series. The arbitrary boundary restraints are realized by penalty method. The final solutions of FGP cylindrical shell structure are obtained by Rayleigh–Ritz method. To sufficient illustrate the effectiveness of proposed method, some numerical examples about spring stiffness, Jacobi parameters etc. are carried out. In addition, to verify the accuracy of this method, the results are compared with those obtained by FEM, experiment and published literature. The results show that the proposed method has ability to solve the free vibration behaviors of FGP cylindrical shell.

Vibration analysis of functionally graded porous cylindrical shell with arbitrary boundary restraints by using a semi analytical method

Vibration analysis of the coupled doubly-curved revolution shell structures by using Jacobi-Ritz method

Combining Goldenveizer-Novozhilov shell theory, thin plate theory and electro-elastic surface theory, the size-dependent vibration of nano-sized piezoelectric double-shell structures under simply supported boundary condition is presented, and the surface energy effect on the natural frequencies is discussed. The displacement components of the cylindrical nano-shells and annular nano-plates are expanded as the superposition of standard Fourier series based on Hamilton's principle. The total stresses with consideration of surface energy effect are derived, and the total energy function is obtained by using Rayleigh-Ritz energy method. The free vibration equation is solved, and the natural frequency is analyzed. In numerical examples, it is found that the surface elastic constant, piezoelectric constant and surface residual stress show different effects on the natural frequencies. The effect of surface piezoelectric constant is the maximum. The effect of dimensions of the double-shell under different surface material properties is also examined.

Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures

In this paper, a semi analytical method is used to investigate the free vibration of doubly-curved shells of revolution with arbitrary boundary conditions. The doubly-curved shells of revolution are divided into their segments in the meridional direction, and the theoretical model for vibration analysis is formulated by applying Flugge’s thin shell theory. Regardless of the boundary conditions, the displacement functions of shell segments are composed by the Jacobi polynomials along the revolution axis direction and the standard Fourier series along the circumferential direction. The boundary conditions at the ends of the doubly-curved shells of revolution and the continuous conditions at two adjacent segments were enforced by the penalty method. Then, the natural frequencies of the doubly-curved shells are obtained by using the Rayleigh–Ritz method. For arbitrary boundary conditions, this method does not require any changes to the mathematical model or the displacement functions, and it is very effective in the analysis of free vibration for doubly-curved shells of revolution. The credibility and exactness of proposed method are compared with the results of finite element method (FEM), and some numerical results are reported for free vibration of the doubly-curved shells of revolution under classical and elastic boundary conditions. Results of this paper can provide reference data for future studies in related field.

A semi analytical method for the free vibration of doubly-curved shells of revolution

Thermo-elastic vibration of FGM beams with general boundary conditions is studied using a higher-order shear deformation beam theory (HSDBT) The HSDBT is proposed by introducing a new transverse shear stress function through the beam thickness The material properties of the FGM beam are assumed to be temperature-dependent, and change gradually in the thickness direction Three cases of temperature distribution in the form of uniformity, linearity, and nonlinearity, are considered through the beam thickness The energy stored in the boundary restraints is transformed into a quantifiable form by introducing a set of artificial springs at each boundary Rayleigh-Ritz method combined with improved Fourier series is utilized to obtain the vibration characteristics of the heated FGM beam The convergence and accuracy of the present method are discussed by comparing with the reference data The effects of the temperature changes, material parameters, and boundary conditions on the thermo-elastic vibration characteristics of the FGM beam are studied Furthermore, the natural frequency results of the FGM beam subjected to linear and nonlinear temperature distributions are compared

Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory

Vibration analysis of circular cylindrical double-shell structures under general coupling and end boundary conditions

In this study, the dynamic stiffness method (DSM) is applied to study the free and forced vibration behaviors of thin, three-dimensionally coupled plate structures. Both the flexural and in-plane vibrations are taken into consideration. In the formulation, the coupled plate structures are divided into several sub-plates, then the dynamic stiffness matrices of the sub-plates are derived separately by combining the superposition method with the projection method. According to the geometrical coupled condition between the sub-plates, the dynamic stiffness matrix of the whole coupled structure is assembled. To validate the present method, three numerical examples of coupled plate structures subjected to external excitations are performed and analyzed. The accuracy and reliability of the present method are demonstrated by comparing the present results with those obtained by the FEM. Then, the effects of the directions of external harmonic excitations and the coupled angle between the coupled plates on the dynamic responses are investigated. Furthermore, a computational efficiency study is given to illustrate the convergence and accuracy of the DSM.

Chunyu Zhang

Papers

Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory

Vibration analysis of circular cylindrical double-shell structures under general coupling and end boundary conditions

Harmonic response analysis of coupled plate structures using the dynamic stiffness method

Band gap property analysis of periodic plate structures under general boundary conditions using spectral-dynamic stiffness method

Quasi-3D dynamic analysis of rotating FGM beams using a modified Fourier spectral approach