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Modeling Scenario

5-040-TunedMassDamper-Part-I-Modeling Scenario

Author(s): Brian Winkel1, Keith Landry2

1. SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations 2. Georgia Southern University, Statesboro GA USA

Keywords: structure spring-mass-dashpot spring mass earthquake vibration tuned mass tuner restoring force control dampe

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Abstract

Resource Image We offer an opportunity to build mathematical models to mitigate dangerous displacements in structures using structural improvements called Tuned Mass Dampers. We model the motion of the original structure as a spring-mass-dashpot system.

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Differential Equation Type
Qualitative Analysis
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Technology
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Pedagogical Approaches
Bloom's Cognitive Level

Description

We model the motion of the original structure as a spring-mass-dashpot system (one degree of freedom) with stiffness replacing the spring constant in the model. We add another, smaller spring-mass-dashpot system whose frequency is tuned to reduce the overall oscillation of the original structure and consider the effects of this two degree of freedom model. Here we do not include resistance or damping forces which are often portrayed as being proportional to velocity.

In the 1800s and early 1900s, most large civil engineering infrastructure (buildings, dams, bridges, etc.) was designed and built using rather conservative design processes which resulted in fairly stiff, rigid structures. Vibrations in structural components such as the floor beams caused by dynamic loads were rarely a concern. In the late 1900s, significant improvements in engineering design, engineering science, and construction methods resulted in lighter, more slender structures which proved far more susceptible to large deflections resulting from dynamic wind or seismic loads caused when the dominant frequency in the loading or driving function neared the natural frequency of the structure. This undesirable condition (for typical infrastructure facilities) is known as resonance or near-resonance.

Engineers knew that damping served to remove energy from physical systems, but noted that providing too much damping acted to increase the stiffness of a system. In an attempt to mitigate the potentially catastrophic effects of near-resonance in buildings, structural engineers took note of the ``passive'' tuned mass dampers (TMD) being used by mechanical engineers to reduce vibration amplitudes in machinery, ships, automobiles, and electrical transmission lines among other things. By tuning the natural frequency of the damper to match that of the structure to which it is attached, engineers found that the TMD acted to significantly reduce the large displacements associated with resonance. Simply put, the energy that would have normally led to large displacements in the building itself is now being used to drive a large mass in the damping device, but in a direction opposing the building motion. Building goes to the left; TMD goes to the right.

 

 

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Authors

Author(s): Brian Winkel1, Keith Landry2

1. SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations 2. Georgia Southern University, Statesboro GA USA

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