Vibration shape functions

This paper presents a unified approach to vibration analysis of functionally graded beams with transverse open-edge cracks based on the so-called vibration shape obtained as a general solution of vibration equations in the frequency domain.

31p viwolverine 11-07-2023 4 2   Download

Molecular and electronic structures of a novel Al30O30 star-shaped alumina nanocage (SANC) were studied using the recently developed CAM-B3LYP density functional method. Comparison of the stretching vibrational modes of this compound with the corresponding modes related to an Al20O30 perfect cage and Al50O75 tubular alumina nanomaterials showed a shift to lower frequencies, while the bending modes moved to higher frequencies. The highest occupied molecular orbital (HOMO) of the SANC had 65% nonbonding character, whereas the lowest unoccupied molecular orbital (LUMO) was 72% antibonding.

11p langthannam 29-12-2021 9 1   Download

The dynamic response of functionally graded (FG) sandwich beams excited by a moving point load is studied by the finite element method. Based on the first-order shear deformation beam theory, a finite beam element is formulated by using the hierachical shape functions.

6p viatani2711 14-02-2020 23 0   Download

In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element’s strain-displacement matrix in bending.

14p caygaocaolon1 13-11-2019 19 1   Download

The classical 3D beam element has been modified and developed as a new finite element for vibration analysis of frame structures with flexible connections and cracked mem hers. The mass and stiffness matrices of the modified elements are established basing on a new form of shape functions, which are obtained in investigating a beam with flexible supports and crack modeled through equivalent springs.

18p chikychiky 01-11-2018 41 1   Download

This article presents some results on the determination of the vibration shape function of a multiple cracked elastic beam element, which is modeled as an assembly of intact sub-segments connected by massless rotational springs. Algorithms and computer programs to analyze changes of natural mode shapes of multiple cracked beams have been carried out.

13p thienthanquydu 19-10-2018 41 0   Download

This paper introduces an improved response surface-based fuzzy finite element analysis of structural dynamics. The free vibration of structure is established using superposition method, so that fuzzy displacement responses can be presented as functions of fuzzy mode shapes and fuzzy natural frequencies. Instead of direct determination of these fuzzy quantities by modal analysis which will involve the calculation of the whole finite element model, the paper proposes a felicitous approach to design the response surface as surrogate model for the problem.

11p thienthanquydu 19-10-2018 61 1   Download

This paper deals with the nonlinear dynamic problem of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure by analytical approach. The present novelty is that an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the nonlinear dynamic second-order differential three equations system is established and the frequency-amplitude relation of nonlinear vibration is obtained in explicit form.

0p thienthanquydu 19-10-2018 40 0   Download

Rayleigh’s quotient for Euler-Bernoulli multiple cracked beam with different boundary conditions has been derived from the governed equation of free vibration. An appropriate choosing of approximate shape function in terms of mode shape of uncracked beam and specific functions satisfying conditions at cracks and boundaries leads to an explicit expression of natural frequencies through crack parameters that can simplify not only the analysis of natural frequencies of cracked beam but also the crack detection problem.

12p thienthanquydu 17-10-2018 29 0   Download