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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.

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.

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.

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.

The purpose of this paper is to provide the historical background of genealogical records and analyze the value of Chinese genealogical research through the study of names and genealogical resources.

The paper examines the historical evolution and value of Chinese genealogical records, with the focus on researching the Islamic Chinese names used by the people living in Guilin. The highlight of this paper includes the analysis and evolution of the Islamic Chinese names commonly adopted by the local people in Guilin. It concludes with the recommendations on emphasizing and making the best use of genealogical records to enhance the research value of Chinese overseas studies.

The paper covers the history of Islam and describes how the religion was introduced into China, as well as Muslims' ethnicity and identity. It also places focus on the importance of building a research collection in Asian history and Chinese genealogy.

This research study has a strong subject focus on Chinese genealogy, Asian history, and Islamic Chinese surnames. It is a narrow field that few researchers have delved into.

The results of this study will assist students, researchers, and the general public in tracing the origin of their surnames and developing their interest in the social and historical value of Chinese local history and genealogies.

The study of Chinese surnames is, by itself, a particular field for researching the social and political implications of contemporary Chinese society during the time the family members lived.

Very little research has been done in the area of Chinese local history and genealogy. The paper would be of value to researchers such as historians, sociologists, ethnologists and archaeologists, as well as students and anyone interested in researching a surname origin, its history and evolution.