SENSITIVITY ANALYSIS OF BAR STRUCTURES IN LINEAR DYNAMICS

This monograph provides a comprehensive introduction to sensitivity analysis in dynamic problems, presenting classical mathematical methods for determining solution derivatives. It is an invaluable source of knowledge for engineers and scientists involved in structural mechanics.

• Detailed discussion of the basic concepts of sensitivity analysis.
• Presentation of classical mathematical methods for determining solution derivatives.
• Sensitivity analysis limited to bar systems.
• Two basic methods of sensitivity analysis: the direct differentiation method and the adjoint system method.
• Practical applications in the design of building structures.
• Supplementing knowledge in the field of analysis of bar systems.
• Help in understanding software for sensitivity analysis and gradient optimization.

Sensitivity analysis is a broad class of problems concerning the determination of changes in solutions with changes in selected construction parameters. The basis of this analysis is the differential calculus of functions of many variables and methods for solving mechanical problems. In dynamics, in contrast to statics, it is necessary to solve the equations of motion in time and to search for solution derivatives as functions defined in time.

The monograph focuses on the sensitivity analysis of bar systems, which are common in building design practice. Two basic methods are presented: the direct differentiation method and the adjoint system method. The limitation is to dynamic problems relevant to building problems. This work continues the author's previous publication on the sensitivity analysis of bar structures in linear statics.

Extending the topic of sensitivity analysis from static to dynamic problems involves introducing the time parameter into the equations of motion and taking into account a wider range of phenomena. The steady-state responses of the structure to harmonic excitations are analyzed, as well as the sensitivity issues of natural frequencies and their corresponding eigenvectors. These problems find practical applications in design offices specializing in unusual structures.

This monograph can be a valuable supplementary material for lectures on the finite element method in the field of bar structures in statics and dynamics at the second and doctoral levels. It will also be useful for designers who want to expand their knowledge in the field of analysis of bar systems. It can also help in understanding the functioning of software containing algorithms for sensitivity analysis and gradient optimization. Publication of AGH Publishing House, year of publication 2025, paperback, format 241x169 mm, 308 pages.