Beam-based Nonlinear Spring

Technology #17455

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FIG. 1 is a side view of an embodiment of the invention disclosed herein. The embodiment in FIG. 1 has a depth into the page. In this embodiment, a beam 3 a is clamped between top surface la and bottom surface 1 b. In this embodiment, the beam 3 a is a cantilever. In other embodiments, the right end of beam 3 a may have another boundary condition or be attached to another object. In this embodiment, curves 2 a and 2 b are flat at their leftmost ends so that they clamp beam 3 a. To the right of the flat segment, Curves 2 a and 2 b have decreasing radius of curvature along their lengths in the right direction.FIG. 6 shows the embodiment as components in a two-degree-of-freedom oscillator application. 4 a is one mass of the oscillator. Surfaces 1 c and 1 d, which are rigidly attached to one another, are the second mass of the oscillator. Springs 13 c connects surface 1 c to the outer casing 11 b, and spring 13 d connects surface 1 d to outer casing 11 b. Spring 13 e connects end mass 4 a to outer casing 11 b.
Professor Alexander Slocum
Department of Mechanical Engineering, MIT
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Jocelyn Kluger
Department of Mechanical Engineering, MIT
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Professor Themistoklis Sapsis
Department of Mechanical Engineering, MIT
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Managed By
Christopher Noble
MIT Technology Licensing Officer - Clean and Renewable Energy
Patent Protection

Beam-Based Nonlinear Spring

US Patent 9,382,960

Beam-Based Nonlinear Spring

PCT Patent Application WO 2015-183352

Beam-Based Nonlinear Spring

US Patent 9,599,180


Beam-based nonlinear springs can be used in energy harvesting from ambient vibrations, shock absorption for external loads, and passive control or suppression of mechanical instabilities involving targeted energy transfer from one component of a structure to another.

Problem Addressed

Mechanical energy harvesting is inefficient because of the uncertain character of the excitation (e.g. someone walking does not create uniform ambient vibrations). This is overcome by using a nonlinear 2 degrees-of-freedom system, which creates strongly nonlinear energy transfers between the modes of the system.


Traditional single degree of freedom (1DOF) linear vibration harvesters are efficient only when close to their resonant design point: that is, when the excitation frequency matches the harvester’s natural frequency. In contrast, this design has two degrees of freedom (2DOF) and a nonlinear spring. The system consists of cantilever beams and contact surfaces with carefully chosen distribution of curvature, which has minimal frictional losses and moving parts. This system behaves nonlinearly (i.e. does not a have a preferential linear frequency) because longer lengths of the cantilever contact the surface as more force is applied. This behavior results in a theoretically infinite spring force for a critical finite displacement which protects the spring from extreme loading conditions. For the purposes of energy harvesting, the proposed design was tested for walking, walking quickly, and running and nearly doubled the average harvested power compared to 1DOF systems or 2DOF linear systems.


  • High power conversion efficiency over different excitation signals
  • Ability to harvest vibrational energy