Vibrations Based Energy Harvesting (2)


Mechanical vibrations are a rich source of kinetic energy as far as quantity and availability. Vibrations are found in bridges, highways, engines, natural geological vibrations, sea waves, and human locomotion, all of these can serve as a source of vibrations and kinetic energy to be harvested.

By: Karim El-Rayes, Dr. Eihab Abdel-Rahman

Motion and Kinetic energy  

Energy harvesting

Environment around us is full of sources of kinetic energy such as the locomotion of living beings, acoustic and audible signals, moving systems and machines and vibrations in nature like earthquakes.

Mechanical vibrations are a rich source of kinetic energy as far as quantity and availability. Vibrations are found in bridges, highways, engines, natural geological vibrations, sea waves, and human locomotion, all of these can serve as a source of vibrations and kinetic energy to be harvested.

Understanding Mechanical Vibrations

Vibrations are periodic motions of an object, such that motion will repeat itself at time interval T. The vibration profile of an object is defined in terms of the amplitude Xo and frequency “ω” of the harmonic motion it performs:

where x(t) is the displacement of the object as a function of time t.



Figure 6 An example of Displacement – Time profile of a vibrating body

The time-history of a vibrating body may consist of a fundamental, deterministic tone, or multiple tones, or aperiodic chaotic motion, or stochastic motion. Spectrum analysis can be applied to the time-history of vibrations, such as FFT, to identify the frequency components in the history, the so called “Harmonics”.

Factors affecting the kinetic energy in vibrations

Three factors affect the kinetic energy in a mechanical oscillator (a vibrating object):

  • The mass m of the vibrating body: is proportional to input kinetic energy and therefore should be maximized.
  • Stiffness k of the oscillator: defines the center frequency of vibrations.
  • Mechanical damping c in the oscillator: defines the fraction of input energy lost.

A schematic of a mechanical oscillator is shown in figure 7.

Figure 7 A spring-mass-damper oscillator

Types of Mechanical Vibrations

Vibrations are classified according to:

  • Energy source: in to free and forced vibrations.
  • Energy leakage: into undamped and damped vibrations.

Each of these conditions has its equation of motion and parameters resulting in a different system response, for energy harvesting we are interested in free vibrations either damped or undamped which we are going to discuss.

1- Free – Undamped vibrations

Considering the mass and spring shown in figure 7 only, the forces acting on this system at equilibrium are the weight and spring force:

where xi is the static equilibrium position.

If the mass undergoes free vibrations due to any external disturbance, the mass m will start oscillating up and down away from the static position xi, according to the equation of motion:

where x is displacement with respect to the static equilibrium position xi.

The natural frequency ω of this oscillator where the energy level is maximum can be written as:

2- Free – Damped vibrations

Practically, damping will exist and due to damping oscillations will decay and die over time. Taking damping into consideration in the equation of motion, results in a n exponential decay in vibration. According to the damping level, we can identify three classes of system response:

  • Over – damped systems: where damping dominates the system response “killing” vibrations and allowing the system to settle down gradually to its equilibrium position.
  • Under – damped systems: where kinetic energy dominates the system response resulting in persistent oscillations as the motion in the system decay and die over long time.
  • Critically-damped systems: where damping and kinetic energy are “balanced” resulting in fast settling down of the system into its equilibrium position.

3- Forced-Damped Vibration

In forced vibrations an external force or excitation is applied to the system to force it to vibrate. In the absence of damping, continuous energy supply through forcing leads the system to blow-up if the forcing is high enough to reach the resonance of the oscillator and, therefore, is not of energy interest. On the other hand, in the presence of damping the oscillator’s equation of motion can be written as:


Summarizing all types of vibrations:

Building Vibrations based Energy Harvester

To harvest energy from vibrations in the environment, we need a suitable transduction mechanism as we discussed previously and an appropriate mechanical design that will hold and interact with the transducer to harvest energy.

Two main mechanical structures are commonly used by researchers to build vibrations based energy harvesters along with different transduction mechanisms discussed previously:

  • Mass – spring – damper mechanical structure.
  • Cantilever – beam mechanical structure.

Choosing the suitable mechanical structure depends mainly on the environment the harvester will operate in, since there are two main parameters in the operating environment affect the overall performance and amount of energy to be harvested: resonance (natural) frequency of the vibrations you are harvesting from energy and the bandwidth of frequency the harvester can operate within.

Mass – Spring – Damper structure

Mass-spring-damper structures are very popular in building vibrations based harvesters because of their simplicity. The model representing this class of harvesters has been extensively researched and validated. The simplest design in this class is a mass mounted to a vertically aligned spring attached to a source of vibrations as shown in figure 2.1. When external vibrations are applied to the base support of the spring, the mass will move up and down according to the equation of motion:


where x is the relative displacement with respect to the base of the mass from its static equilibrium position.

The center frequency fo of the harvester depends on the natural frequency of the oscillator:


In figure 8, the energy harvester designed by Amirtharajah et al. [1] is shown. It uses a mass-on-spring and electromagnetic transduction to harvest vibrations from human body motion to power medical sensors implanted or placed on the surface of the human body. They achieved a center frequency of fo = 94 Hz and an output power of 400 µW.

Mann et. al. [2] design used a mass-on-spring harvester, figure [9], that uses a magnetic mass and magnets placed at both ends of a tube to serve as springs. Each of the end magnets has a pole identical to that of the magnetic mass facing it. They calculated the center frequency of the harvester as fo = 5.12 Hz and were able to demonstrate an output power up to 200 mW.

Mahmoud et. al. [3] design, in figure 10, for a horizontal motion electrostatic VEH is using an implicit mass-on-spring structure, the VEH uses two silicon dioxide coated electrodes, one is mounted on the fixed ceiling of the VEH and the other electrode is on the moving mass, the output voltage of 0.85v was achieved at a center frequency of 2 Hz.

Figure[8] Amirtharajah et al. mass on spring based energy harvester design



Figure[9] Mann et. al. design of mass-on-spring harvester

Figure[10] Mahmoud et. Al. Electrostatic based VEH


Beam – Support structure

Beam-support structures are the other common class of energy harvesters. Most of these harvesters use either cantilever or guided-end beams to support a seismic mass and/or a coil. The beams in this case behave as springs and add to the seismic mass. Cantilever beam-based, figure 11, energy harvesters are widely used. The stiffness of a cantilever beam spring is calculated using the formula


where E is Young’s modulus describing the strength of the material, I is the second moment of area of the beam cross-section, and L is the beam length.




Figure 11 Basic Beam – Support structure

 Sari et. al. [4] design used a coil mounted on top of a cantilever beam surface facing magnet poles, figure [12], once the cantilever beam is under excitation voltage starts to induce in the coil, achieving center frequency between 3.5 – 4.5  KHz  depending on beam length and maximum output power of 0.4µW Beeby et. al. [5] design used a coil mounted to the beam free end facing two magnet poles, figure [13], achieving center frequency between 52.1 – 53.2 KHz and maximum output power of 45.8 µW.


Figure [12] Sari et. al. electromagnetic harvester

Figure [13] Beeby et. al. micro cantilever harvester

Signal Conditioning

The ability of energy harvesters to supply power on demand and in DC form is essential to their successful commercial deployment. On the other hand, the input power from the environment to micro-energy harvesters is intermittent and low. Therefore, an important challenge in the design of micro-energy harvesters is to rectify and store output power in order to guarantee stable, continuous and sufficient supply of power. Further, electromagnetic energy harvesting encounter and additional challenge since its output voltage is on the order of a few to a few hundreds of mili-volts. As a result, three stages of electronic solutions are used to address these challenges:

  • Using a charge-pump DC – DC converter, voltage multiplier, or a transformer to boost the output voltage to meet the requirements of electronic power supply and increase the efficiency of rectification circuits.
  • Using full-wave or half-wave rectifier bridge circuits to rectify the output of the harvester and stabilize it to a constant level.
  • Using a rechargeable battery or a super capacitor to store DC power. The battery or super capacitor will then act as the supply to the target system while the harvester charges the storage element instead of powering the target system directly.

The basic block diagram of an energy harvesting system is shown in figure 14.

Figure [14] Basic design of an Energy harvesting system

Build your own VEH

Here are few steps to build simple homemade electromagnetic vibrations/motion energy harvester, you will need the following components:

–          Magnetic wire: an isolated copper wire similar to the one used in electric motors and solenoids.

–          Plastic tube (around 12-15 cm long).

–          A cylindrical magnet (or ball shape).

–          Two rubber end stoppers.

Second, wound the magnetic wire around the plastic tube, let the magnetic wire cover most of the plastic tube length, insert the magnet inside the tube and enclose tube ends with the rubber end stoppers as in figure 15, shake it now and measure the voltage across the magnetic wire, have fun J

Figure [15] DIY Electromagnetic Vibrations Energy Harvester


[1] R. Amirtharajah, A.P. Chandrakasan, “Self-powered signal processing using vibration-based power generation”, IEEE Journal of Solid-State Circuits, Volume 33, no.5, pp.687-695, 1998.

[2] B.P. Mann, B.A. Owens, “Investigations of a nonlinear energy harvester with a bistable potential well”, Journal of Sound and Vibration, Volume 329, Issue 9, pp. 1215-1226, 2010.

[3] M. A. E. Mahmoud, E. M. Abdel-Rahman, R. R. Mansour, and E. F. El-Saadany, “Springless Vibration Energy Harvesters”, ASME IDETC 2010, Montreal, Canada, August 2010, DETC2010-29046.

[4] Ibrahim Sari, Tuna Balkan, Haluk Kulah, “An electromagnetic micro power generator for wideband environmental vibrations”, Sensors and Actuators A: Physical, Volumes 145-146, pp. 405-413, 2008.

[5] S. P. Beeby,  R. N. Torah,  M. J. Tudor,  P. Glynne-Jones, T. O’Donnell,  C. R. Saha, and S. Roy, “A micro electromagnetic generator for vibration energy harvesting”, Journal of Micromechanics and Microengineering, Volume 17, no. 7, pp. 1257-1265, 2007.

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