Vibration Characteristics Of Shells Research Articles

Free Vibration Characteristics of Thin Spherical Shells

Free vibration characteristics of thin spherical shells having freely boundary conditions are analyzed. In this study, the fundamental properties of natural vibration for the spherical shells are investigated. The power function is employed as the admissible function, displacement functions satisfying the geometric boundary conditions are expressed in the form of single series. The eigenvalue problem for free vibration of the shells derived by using the Lagrange’s equation of motion, is processed numerically to acquire the natural frequencies and mode shapes. The reliability and accuracy of the present results are verified by convergence tendencies of the present solutions and comparisons of the data between the current analysis, FEM (finite element method) and published literatures. In numerical results, the variations of natural vibration characteristics of the shells due to the circumferential wavenumber and various shell geometries are illustrated.

Analytical analysis of forced vibration of the hard-coating cylindrical shell with material nonlinearity and elastic constraint

In this paper, the nonlinear vibration characteristics of the hard-coating cylindrical shell with the base excitation and un-classical elastic constraint are investigated based on the Rayleigh-Ritz method. A continual variable stiffness elastic constraint is presented to introduce the actual uneven distribution of connection stiffness into the analytical vibration analysis. The nonlinear governing equations of motion are formulated by the Love’s first approximation theory and von Karman-type nonlinear strain-displacement relationship. The admissible displacement functions are constructed by the Gram-Schmidt orthogonal polynomials. To effectively consider the effects of the strain dependences of storage modulus and loss factor of hard coating on the vibration characteristics of the shell, a modified domain decomposition method is employed to determine the equivalent strain of hard coating under the action of base excitation. By extending the Newton-Raphson iterative scheme, a unified iterative solution method is developed for solving the nonlinear resonant frequencies and responses of the hard-coating cylindrical shell. The numerical and experimental examples of the cylindrical shell coated with NiCoCrAlY + YSZ are performed to validate the accuracy and reliability of the developed analytical model. The mechanism of soft nonlinearity displayed in the amplitude-frequency curves of the hard-coating cylindrical shell is discussed as well.

Structural dynamic modeling for rotating blades using three dimensional finite elements

A precise analysis model was developed in this paper to investigate the dynamic characteristics of rotating composite blades. An eighteen-node solid-shell finite element was used to model the blade structures. This study is focused on geometrically nonlinear problems, because the material is assumed linear elastic. Incremental total Lagrangian approach was adopted to allow estimations on arbitrarily large rotations and displacements. The equations of motion for the finite element model were derived by using Hamilton’s principle, and the resulting nonlinear equilibrium equations were solved by applying Newton-Raphson method combined with load control. A modified stress-strain relation was adopted to avoid the transverse shear locking problem, and fairly reliable results were obtained with no sign of locking phenomenon. The obtained numerical results were compared to several benchmark problems, and the results show a good correlation with the experimental data and other finite element analysis results. The vibration characteristics of shell- and beam-type blades were investigated. For shell-type blades, the dynamic characteristics may be significantly influenced by blade curvature, pre-twist, and geometric nonlinearity. For beam-type blades, one-dimensional beam and three-dimensional solid models offer comparable predictions for the straight and large aspect ratio blade. As blade aspect ratio decreases, considerable differences appear in the bending and torsion modes. The tip sweep angle tends to decrease the flap bending frequencies, but the torsion frequency increases with the tip sweep angle.