Bivariate regression model for the natural vibration period analysis of masonry minarets

This paper investigates the natural vibration periods for a set of 111 historical masonry minarets from Egypt, Turkey, Jordan, and Bosnia and Herzegovina. The database is compiled from literature publications and local archives, and includes minarets characterized by various geometries, design features, architectural styles, state of preservation, age. In particular, this paper develops a bivariate empirical model to estimate the natural vibration period of historical masonry minarets using geometric parameters such as height <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> </mml:math> and base width <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> (or diameter). Through extensive log-log regression analysis, it is shown that combining the height <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> </mml:math> with the base width <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> offers good estimates of the natural period. The developed bivariate (LL-BI(H,B)) model, in particular, shows low dispersion and strong statistical reliability. As such, it represents a practical and data-efficient tool for estimating the vibration period of masonry minaret, supporting large-scale seismic risk and heritage assessment where detailed structural data are limited.