21.1 Vibration-based energy harvesting in structures

Vibration-based energy harvesting in structures taps into ambient vibrations to generate power. This method uses piezoelectric materials to convert mechanical strain into electricity, offering a sustainable power source for sensors and small devices in buildings and infrastructure.

Designing effective harvesters involves understanding structural dynamics, optimizing geometry, and matching frequencies. Key considerations include power density, energy conversion efficiency, and developing techniques to harvest energy across a wide range of vibration frequencies.

Vibration Characteristics

Ambient Vibrations and Structural Resonance

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• Ambient vibrations occur naturally in structures due to environmental factors (wind, traffic, machinery)
• Structural resonance happens when external forces match natural frequencies of a structure
• Natural frequencies depend on mass, stiffness, and geometry of the structure
• Resonance amplifies vibration amplitude, increasing potential for energy harvesting
• Structures exhibit multiple resonant frequencies, each corresponding to a different mode of vibration

Vibration Modes and Structural Dynamics

• Vibration modes represent distinct patterns of motion in a structure
• Fundamental mode involves the entire structure moving in phase
• Higher modes display more complex patterns with nodes and antinodes
• Modal shapes describe the relative displacement of different parts of the structure
• Structural dynamics studies how structures respond to dynamic loads over time
• Damping affects vibration amplitude and duration in structures
• Mass-spring-damper systems model basic structural dynamic behavior
• Equation of motion for a single degree of freedom system: $m\ddot{x} + c\dot{x} + kx = F(t)$
  • m: mass, c: damping coefficient, k: stiffness, F(t): external force

Harvester Design

Cantilever Beam Harvesters

• Cantilever beam harvesters consist of a flexible beam fixed at one end
• Piezoelectric material attached to the beam converts strain energy to electrical energy
• Tip mass often added to lower resonant frequency and increase strain
• Beam dimensions and material properties affect resonant frequency and power output
• Single beam harvesters typically operate in a narrow frequency band
• Multi-beam arrays can harvest energy across a wider frequency range
• Cantilever beams can be designed for unimorph or bimorph configurations
  • Unimorph: single piezoelectric layer
  • Bimorph: two piezoelectric layers, can be connected in series or parallel

Tuned Mass Dampers and Frequency Matching

• Tuned mass dampers (TMDs) absorb vibration energy in structures
• TMDs can be modified to harvest energy while damping vibrations
• Frequency matching involves tuning harvester resonance to match ambient vibration frequencies
• Adaptive tuning mechanisms adjust harvester properties to maintain optimal performance
• Methods for frequency tuning include:
  • Adjustable tip mass
  • Variable beam stiffness
  • Magnetic force tuning
• Broadband energy harvesting techniques extend operational frequency range
  • Array of harvesters with different resonant frequencies
  • Nonlinear oscillators (bistable or tristable systems)

Modal Analysis for Harvester Design

• Modal analysis identifies vibration characteristics of structures
• Finite element analysis (FEA) used to simulate structural behavior
• Experimental modal analysis employs sensors to measure actual structural response
• Mode shapes and frequencies guide optimal placement of harvesters
• Modal participation factors indicate which modes contribute most to overall response
• Modal analysis helps in:
  • Selecting appropriate harvester designs
  • Determining optimal harvester locations
  • Predicting energy harvesting potential

Performance Metrics

Power Density and Energy Conversion Efficiency

• Power density measures harvested power per unit volume or mass of the device
• Typical power densities range from microwatts to milliwatts per cubic centimeter
• Energy conversion efficiency quantifies how much mechanical energy is converted to electrical energy
• Factors affecting power density and efficiency:
  • Piezoelectric material properties (coupling coefficient, dielectric constant)
  • Harvester geometry and design
  • Electrical circuit topology (resistive load, synchronized switching)
• Figure of merit for piezoelectric materials: $k^2Q$
  • k: electromechanical coupling coefficient
  • Q: quality factor
• Maximum theoretical efficiency for linear piezoelectric harvesters: $\eta_{max} = \frac{k^2}{4+2k^2}$

Measurement and Optimization Techniques

• Impedance matching optimizes power transfer to the load
• Synchronized switching techniques enhance energy extraction
  • SSHI (Synchronized Switch Harvesting on Inductor)
  • SECE (Synchronized Electrical Charge Extraction)
• Experimental characterization methods:
  • Shaker table tests for controlled excitation
  • Accelerometer measurements for ambient vibration analysis
• Power management circuits condition harvested energy for storage or use
  • Rectification converts AC to DC
  • DC-DC converters optimize voltage levels
• Performance comparison metrics:
  • Normalized power density (NPD) accounts for input acceleration
  • Effectiveness compares harvester performance to an ideal harvester