TY  - JOUR
AB  - Purpose Although high-order smooth reproducing kernel mesh-free approximation enables the analysis of structural vibrations in an efficient collocation formulation, there is still a lack of systematic theoretical accuracy assessment for such approach. The purpose of this paper is to present a detailed accuracy analysis for the reproducing kernel mesh-free collocation method regarding structural vibrations.Design/methodology/approach Both second-order problems such as one-dimensional (1D) rod and two-dimensional (2D) membrane and fourth-order problems such as Euler–Bernoulli beam and Kirchhoff plate are considered. Staring from a generic equation of motion deduced from the reproducing kernel mesh-free collocation method, a frequency error measure is rationally attained through properly introducing the consistency conditions of reproducing kernel mesh-free shape functions.Findings This paper reveals that for the second-order structural vibration problems, the frequency accuracy orders are p and (p − 1) for even and odd degree basis functions; for the fourth-order structural vibration problems, the frequency accuracy orders are (p − 2) and (p − 3) for even and odd degree basis functions, respectively, where p denotes the degree of the basis function used in mesh-free approximation.Originality/value A frequency accuracy estimation is achieved for the reproducing kernel mesh-free collocation analysis of structural vibrations, which can effectively underpin the practical applications of this method.
VL  - 36
IS  - 3
SN  - 0264-4401
DO  - 10.1108/EC-10-2018-0439
UR  - https://doi.org/10.1108/EC-10-2018-0439
AU  - Qi Dongliang
AU  - Wang Dongdong
AU  - Deng Like
AU  - Xu Xiaolan
AU  - Wu Cheng-Tang
PY  - 2019
Y1  - 2019/01/01
TI  - Reproducing kernel mesh-free collocation analysis of structural vibrations
T2  - Engineering Computations
PB  - Emerald Publishing Limited
SP  - 734
EP  - 764
Y2  - 2024/04/27
ER  -