Aims: This work is devoted to the development of a finite element algorithm for solving problem in forced vibrations of folded low shells. Methodology: The differential equations for harmonic analysis are obtained from the Lagrange variational principle. Description of the dynamic behavior is made by the structure discretization into a system of curvilinear iso-parametric finite elements used in modal analysis. The method is implemented by a calculation code on a square-plane folded shell model withnumber of crease edges in both directions k=l=3. Results: Displacement amplitudesare obtained by decomposition into vibration eigenforms. The maximum values of dynamic stresses are determined taking into account the shell's support conditions.The results of the harmonic analysis show thatimprovement in frequency characteristics and reduction of stresses in the folded shell depend on the constructive and internal damping of the structureand the increase in the number of fold edges k and l in both directions for examplebecause this contributes to decrease in the forced vibration amplitudes.

This work is devoted to forced vibration numerical analysis of reticulate bar systems. The dynamic finite element method was used for determination of frequencies, displacement amplitudes, rotation angles and the dynamic effort factors. By this method the components of the dynamic rigidity matrix and inertia matrix depend on applied external excitation frequency. Obtained results are compared with those calculated by the classical finite element method as well as by analytical method. It is shown that the dynamic finite element allows for exact solutions to the problems in forced vibration of structures. Accuracy of dynamic finite element solution is verified through obtaining analytical solutions on simple systems. In case of complex systems where analytical calculations are complicated the dynamic finite element can become a universal tool for dynamic analysis.

In this work a numerical model is developed for vibration analysis of low folded shells under dynamic actions. At first it is done to describe the used finite element discrete model based on Lagrange variational principles. To solve the eigen value problem of these structures a numerical algorithm is proposed using Householder's QR-iteration transformations. This method provides a tridiagonal matrix whose eigen values coincide with those of the initial matrix and significantly reduces the iteration number compared to the Lanczos method. Implementation of the method is carried out on seven folded shell mathematical models. Obtained results show that accuracy can be improved and computational time can be significantly reduced compared to the methods available in the technical literature for this class of problems.