Definition of Cantilever Beams with Piezoelectric Layers and Applications

Cantilever beams with bonded piezoelectric layers are widely studied in structural dynamics, energy harvesting, and vibration control. The piezoelectric element converts mechanical strain into electrical energy, making these systems ideal for structural health monitoring, sensors, and low-power energy harvesters.

The addition of a tip mass alters the natural frequencies and amplifies dynamic responses, which can enhance energy conversion efficiency. Finite Element Analysis (FEA) provides a powerful framework for predicting transient and harmonic responses, enabling engineers to evaluate strain, voltage output, and harvested power under various loading scenarios.

Key factors analyzed during FE simulations include:

• Effect of geometry scaling on dynamic response.

• Impact of tip mass on natural frequency and vibration amplitude.

• Strain distribution in the piezoelectric layer.

• Voltage generation and energy harvesting performance under different excitation types.

Project Highlights

• Geometry:

  • Beam: 62.5 mm × 10 mm × 0.6 mm (thickness).

  • Tip mass: 10 mm × 15 mm × 9.4 mm, weight ≈ 0.0046 kg.

• Materials:

  • Aluminum for the cantilever beam.

  • Piezoelectric layer bonded to the beam surface.

• Boundary conditions:

  • Transient analysis: base excitation applied initially, then fixed at one end.

  • Harmonic analysis: one end fully fixed, with distributed harmonic excitation.

• Analysis setup:

  • Transient excitation: applied at the fixed end to simulate realistic vibrations.

  • Harmonic excitation: frequency sweep from 22 Hz to 34 Hz.

• Scenarios studied:

  • Dynamic strain response of the piezoelectric layer.

  • Voltage generation across electrodes.

  • Power harvesting potential.

FE Analysis Tips and Tricks

• Use fine meshing near the piezoelectric–beam interface to accurately capture strain transfer.

• Apply coupled-field elements to directly link mechanical strain with electrical response.

• Verify frequency range with modal analysis before running harmonic excitation.

• Include tip mass modeling explicitly, as it significantly shifts resonance.

Material Selection

• Beam: Aluminum, chosen for its low density, ease of modeling, and well-documented mechanical properties.

• Piezoelectric patch: Standard PZT material, modeled with anisotropic properties to capture electromechanical coupling accurately. In addition to the elastic constants, the definition requires:

  • Anisotropic relative permittivity

  • Piezoelectric matrix (defined based on either stress or strain constants)

• Tip mass: Steel block (0.0046 kg) used to amplify strain and lower resonance frequency.

Geometry Editing

• Beam modeled as a rectangular cantilever with a bonded piezoelectric patch.

• Tip mass explicitly modeled and attached to the free end of the beam.

Mesh Generation

• 3D solid elements used for both beam and piezoelectric domains.

• Local refinement in piezoelectric and tip mass regions.

• Element count balanced for accuracy and computational efficiency.

  

Analysis Settings

• Transient analysis: base excitation applied to the fixed end, capturing strain and voltage response during free vibration.

• Harmonic analysis: frequency sweep between 22–34 Hz to investigate steady-state response at and around resonance.

• Piezoelectric coupling: mechanical strain directly converted into electrical potential across electrodes.

Connection Types

• Perfect bonding assumed between aluminum beam and piezoelectric patch.

• Rigid connection modeled between tip mass and beam free end.

Boundary Conditions

• One end of the beam fully fixed.

• Transient: excitation applied at base before fixing to simulate realistic loading.

• Harmonic: distributed harmonic excitation along the beam.

Load Conditions

• Transient: base excitation with time-dependent load.

• Harmonic: steady-state sinusoidal excitation, frequency sweep from 22–34 Hz.

Results Interpretation

• Transient analysis: showed realistic free vibration response, with strain transfer into the piezoelectric patch producing measurable voltage output.

• Harmonic analysis: captured resonance behavior, with maximum strain and voltage generation near the natural frequency.

• Tip mass effect: lowered the fundamental frequency and increased strain energy, improving voltage generation and power harvesting.

? This study demonstrates how geometry, tip mass, and excitation type influence the dynamic performance of cantilever beams with piezoelectric layers. The findings are directly applicable to energy harvesting devices, vibration sensors, and smart structures where efficient strain-to-voltage conversion is essential.