Single-Degree-of-Freedom Spring-Mass System: Linear Theoretical Framework, Nonlinear Extensions, and Paradigm Evolution
DOI: https://doi.org/10.62517/jes.202602111
Author(s)
Shengjie Lin
Affiliation(s)
Rosedale Global High School, Fuzhou, Fujian, China
Abstract
The single-degree-of-freedom (SDOF) spring-mass system is one of the most basic idealized models in structural dynamics. This paper shows how the SDOF theoretical framework has evolved from the classical analytical theory based on Newtonian mechanics and linear assumptions to the numerical-computation paradigm for capturing physical reality via nonlinear constitutive relations, and finally to an emerging integrated-systems framework that couples real-time sensing with active control theory. Using a decomposition framework organized around the system’s fundamental physical attributes (damping, stiffness, and inertia), the paper systematically explains how nonlinear damping, dynamic-fracture mechanisms, and the introduction of the inerter fundamentally change dynamic behavior and lead to changes in modeling paradigms. The analysis indicates that the research paradigm has moved from seeking closed-form analytical solutions to finding a balance between computational tractability and physical fidelity, and is now moving toward the construction of intelligent systems marked by a modeldatacontrol closed loop. The paper ends by systematically identifying the core challenges and conceptual gaps left within the current theoretical landscape.
Keywords
Single-Degree-of-Freedom System; Linear Vibration; Nonlinear Dynamics; Damping Model; Inerter; Research Paradigm; Review
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