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Analytical Proof of Concept

Analytical Proof of Concept. Dhiman Basu , PhD Candidate A.M . Reinhorn, M.C . Constantinou Advisers. Concept. Introducing Negative Stiffness and Damping to Improve Overall Behavior of Structures. F e. (1-α)k. F m. F y. k. u e. u m. Infinitely Elastic System. Introducing

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Analytical Proof of Concept

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  1. Analytical Proof of Concept DhimanBasu, PhD Candidate A.M. Reinhorn, M.C. Constantinou Advisers

  2. Concept Introducing Negative Stiffness and Damping to Improve Overall Behavior of Structures

  3. Fe (1-α)k Fm Fy k ue um Infinitely Elastic System Introducing negative stiffness

  4. Effect of Negative Stiffness—Reduce Acceleration and Enhanced Displacement Elastic Response Fe Fm (1-α)k Fy k ua um ue Effect of Negative Stiffness

  5. Effect of Negative Stiffness and Damping -> Reduced Acceleration and Reduced Displacement Elastic Response Fe Fm (1-α)k Fy k ua um ue Effect of Negative Stiffness and Damping

  6. Proof of ConceptUsing On One-Story Model Building

  7. Model and Device Characteristics Device Characteristics • Stiffness: • Damping : 0-30% • Stiffness Activation Displacement: Uy • Damping activated throughout Model Characteristics • Stiffness (K): 3601kN/m • Mass: 745 ton • Inherent Damping: 1% • Frequency: 3.5Hz Model One Story Building

  8. Activation of Negative Stiffness Threshold Displacement Ua Chosen as a Fraction of Maximum Elastic Displacement….Ua=Ue/R

  9. Analytical Studies System Considered • Negative Stiffness is not activated: R=1 • Negative Stiffness is activated with : R=2, 4 and 8 Device Properties • Negative Stiffness Varied From 0 to 90% of Elastic Stiffness, i.e., as a Ratio ɣ = 0.9, 0.8, 0.7,….,0. • Damping Varied to Result Added Damping 0 to 30% Analysis Procedure • Nonlinear-Elastic Response History Analysis • Newmark’s Average-Accel • Time Step: 0.005sec Response Evaluation • Maximum Displacement • Maximum Pseudo Accel (Base- Force / Mass) • Absolute Maximum Accel

  10. Ground Acceleration History

  11. Comparative Performance

  12. Comparative Performance

  13. Limitations Structures Become Unstable at the Initiation of Yielding Negative Stiffness Needs to be Disengaged

  14. Fy (1-α)k Unstable State Fa k ua uy um Useful range for Building Useful range for Isolators Limitations

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