ISJ Theoretical & Applied Science 04(156) 2026

Philadelphia, USA

Krakhmaleva, Yu.R., Keikimanova, M.T., Egemberdi, Sh.K., & Aitkazina, A.M.

Modal analysis and D'Alembert's principle.

Full Article: PDF

Scientific Object Identifier: http://s-o-i.org/1.1/TAS-04-156-14

DOI: https://dx.doi.org/10.15863/TAS.2026.04.156.14

Language: English

Citation: Krakhmaleva, Yu.R., Keikimanova, M.T., Egemberdi, Sh.K., & Aitkazina, A.M. (2026). Modal analysis and D'Alembert's principle. ISJ Theoretical & Applied Science, 04 (156), 92-98. Soi: https://s-o-i.org/1.1/TAS-04-156-14 Doi: https://dx.doi.org/10.15863/TAS.2026.04.156.14

Pages: 92-98

Published: 30.04.2026

Abstract: The objective of this study is to ascertain the characteristics of seismic actions that define their hazard level for various limit states of structures. In addition, a methodology for modelling design actions in multi-level structural design is to be developed. The present study employs methodologies from the fields of structural mechanics, structural dynamics, and mathematical statistics. The findings facilitate the evaluation of the seismic resilience of structures in scenarios where seismological data is scarce or non-existent, a crucial consideration for standard design methodologies. A comprehensive investigation and analysis of the kinematic, spectral and energy characteristics of seismic actions has been conducted. A methodology is proposed for determining the design action level, taking into account the seismic hazard of the area and the structure's service life. A new model for calculating accelerograms has been developed, taking into account the expected limit states of structures and the characteristics of actual earthquakes. A modal analysis of systems with many degrees of freedom was performed based on D'Alembert's principle.

Key words: Seismic response, response modeling, response intensity, deterministic method, probabilistic method, Arias intensity, absolute cumulative velocity, accelerogram, limit state, structural mechanics.