Vibration Analysis Of Shell Structures Research Articles

A superconvergent alpha finite element method (SαFEM) for static and free vibration analysis of shell structures

A superconvergent alpha finite element method (SαFEM) based on triangular mesh is presented for static and free vibration analysis of shell structures. In the SαFEM model, a linear strain field is re-constructed from the standard FEM piecewise constant strain field by devising a unique procedure with a tunable parameter α. The discretized system equations are then established based on the re-constructed strain field and the Hellinger-Reissner variational principle. By changing the value of the parameter α, our SαFEM can provide a proper softer stiffness leading to a “nearly exact” solution in strain energy norm. To avoid the transverse shear locking (caused by the Hellinger-Reissner theory), the discrete shear gap technique for triangular element (DSG3) is employed. From several typical numerical examples, it is demonstrated that the proposed Sα-FEM-DSG3 (or Sα-DSG3) possesses supercovergence property and can provide very accurate solutions for shell structures.

A FINITE ELEMENT-BASED PERTURBATION METHOD FOR NONLINEAR FREE VIBRATION ANALYSIS OF COMPOSITE CYLINDRICAL SHELLS

In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation and is subsequently converted to a finite element notation. After the determination of the linear natural frequency and corresponding vibration mode, the perturbation approach yields the initial curvature of the amplitude–frequency relation with a modest additional computational cost. The implementation of the perturbation approach in a general purpose finite element code using a laminated curved shell element is described. The effectiveness of the approach is illustrated by application to single-mode and coupled-mode nonlinear vibration analyses of cylindrical shells. Results for isotropic and composite cylindrical shells are presented and compared with results obtained via alternative approaches.

A cylindrical strain-based shell element for vibration analysis of shell structures

A cylindrical shell element is developed for the calculation of natural frequencies of cylindrical panels as well as complete cylinders. The element is based on assumed strains rather than displacement and possesses the only five essential degrees of freedom. The displacement fields of the element satisfy the exact requirement of rigid-body modes. Convergence tests of the mesh discretisation are first carried out to establish the rate of convergence of the element. These have been applied to simply supported as well as clamped cylindrical panels. The tests show that good rate of convergence can be obtained when only a small number of elements are used. The element is then further applied to the analysis of complete cylinders and a comparison is made with available solutions.

Vibration analysis of shell structures based on a plate analogy

An approximated formula representing the vibration characteristics of a shell structure with finite curvature is proposed. The model is based on the dynamic analogy between a cylinder and a flat plate. In order to derive the formula, the dynamics of a shell with and without the curvature effect is introduced. Then, resonance frequencies, constant frequency loci, and number of modes in a flat plate and in a cylinder are also examined. After that, a simplified driving point mobility function of a shell with the plate mobility is derived. An experimental verification is conducted in order to examine the proposed formula. Cylinders having two different ring frequencies of 5.9 and 13.8 kHz are used as test structures. Comparisons are done for the resonance frequency and for the mobility function. The accuracy of the analysis falls within 6% error when resonance frequencies are compared with those of experimental data. The results show that the proposed mobility function predicts the vibration behavior for the frequency bandwidth below and above the ring frequency. The model is simple to use and could be easily extended to various boundary conditions for vibration and noise prediction purposes.