Application of dynamic analysis in systems with MDOF and distributed parameters using MathCad software

Abstract

Dynamic analysis plays a fundamental role in evaluating the response of structural systems
subjected to time-dependent actions such as seismic, wind, or impact loads. This study focuses on the
dynamic characterization of structures through the use of the distribution parameter MDF, which is
employed to describe the contribution and spatial distribution of dynamic effects within the system. The
MDF parameter is formulated based on modal properties and governing dynamic equilibrium equations,
allowing the interaction between mass, and stiffness, to be consistently represented. A systematic analytical
framework is presented to evaluate the sensitivity of the dynamic response to variations in MDF,
highlighting its influence on displacement, acceleration, and internal force demands. The proposed
approach enables an efficient interpretation of modal participation and load distribution under dynamic
excitation, offering improved accuracy compared to conventional simplified methods. The results
demonstrate that MDF is a key parameter for capturing the dynamic behavior of complex structural systems
and can be effectively used to support performance-based design and assessment.