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. 2025 Nov 26;25(23):7222.
doi: 10.3390/s25237222.

A Bio-Inspired Vibration Energy Harvesting System with Internal Resonance and Slapping Mechanism for Enhanced Low-Frequency Power Generation

Yi-Ren Wang  1 , Shian-Hsuan Chen  1 , Su-Sheng Ma  1
Affiliations

A Bio-Inspired Vibration Energy Harvesting System with Internal Resonance and Slapping Mechanism for Enhanced Low-Frequency Power Generation

Yi-Ren Wang et al. Sensors (Basel). .

Abstract

This study presents the development and validation of a bio-inspired vibration energy harvesting system, termed the Bio-Inspired Epiphytic-Plant Slapping Vibration Energy Harvesting System (BIS-VEHS). Inspired by the swaying and slapping behavior of epiphytic plants, the system integrates a circular plate, an elastic beam, a surface-bonded piezoelectric patch (PZT), and a lever-type slapping mechanism to enhance energy conversion. A nonlinear beam model is established and analyzed using the method of multiple scales, through which a 1:3 internal resonance between the first and third bending modes is identified as a key mechanism for promoting energy transfer from higher to lower modes. Time responses are obtained via numerical simulation using the Runge-Kutta method, and the model is validated experimentally. The results confirm that both internal resonance and the slapping mechanism significantly increase the harvested voltage compared with non-resonant and non-slapping configurations. Comparative tests under different excitation modes and plate configurations show good agreement between theory and experiment, with most discrepancies within 10%. These findings demonstrate that the BIS-VEHS is a promising candidate for sustainable low-frequency vibration energy harvesting, particularly for autonomous low-power sensor applications.

Keywords: bio-inspired energy harvesting; internal resonance; piezoelectric vibration energy harvester; slapping mechanism.

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Conflict of interest statement

The authors declare no conflicts of interest.

Figures

Figure 1
Figure 1
An epiphytic plant observed on campus, showing a circular leaf slender stalk.
Figure 2
Figure 2
Bio-inspired BIS-VEHS structure attached to a corresponding to the plant’s morphology. Tags: (1) Circular plate (leaf-like part), (2) Elastic beam (stem), (3) Piezoelectric patch (PZT) at the root, and (4) Rigid slapping lever mechanism.
Figure 3
Figure 3
Coordinate definition of the fixed–free beam system: (a) side view and (b) front view, where l  denotes the beam length and the arrows indicate the coordinate axes.
Figure 4
Figure 4
The first three mode shapes of the fixed–free beam.
Figure 5
Figure 5
Fixed-point plots of the BIS-VEHS system under first-mode excitation: (a) diameter ratio = 0.4, (b) diameter ratio = 0.8, and (c) diameter ratio = 1.2. As the diameter ratio increases, the fixed-point spacing and amplitude level broaden, indicating stronger modal coupling and enhanced energy transfer potential under internal resonance conditions.
Figure 6
Figure 6
Fixed-point plots of the BIS-VEHS system under third-mode excitation: (a) diameter ratio = 0.4, (b) diameter ratio = 0.8, and (c) diameter ratio = 1.2. It can be seen that when the third mode is excited, the amplitude of the first mode becomes significantly larger, indicating the occurrence of internal resonance.
Figure 7
Figure 7
Dimensionless fixed-point and time response plots under first-mode excitation for a circular plate with a diameter ratio of 0.4: (a) E1m1, (b) E1m3.
Figure 8
Figure 8
Dimensionless fixed-point and time response plots under third mode excitation, the diameter ratio of the circular plate is 0.4: (a) E3m1, (b) E3m3.
Figure 9
Figure 9
Dimensionless fixed-points and time response plots under first mode excitation, the diameter ratio of the circular plate is 0.8: (a) E1m1, (b) E1m3.
Figure 10
Figure 10
Dimensionless fixed-points and time response plots under third mode excitation, the diameter ratio of the circular plate is 0.8: (a) E3m1, (b) E3m3.
Figure 11
Figure 11
Dimensionless fixed-points and time response plots under first mode excitation, the diameter ratio of the circular plate is 1.2: (a) E1m1, (b) E1m3.
Figure 12
Figure 12
Dimensionless fixed-points and time response plots under third mode excitation, the diameter ratio of the circular plate is 1.2: (a) E3m1, (b) E3m3.
Figure 13
Figure 13
Dimensionless fixed-point and time response plots under first to third mode excitation for a circular plate with a diameter ratio of 0.4: (a) E1m1, (b) E2m2, (c) E3m3.
Figure 14
Figure 14
Dimensionless fixed-point and time response plots under first to third mode excitation for a circular plate with a diameter ratio of 0.8: (a) E1m1, (b) E2m2, (c) E3m3.
Figure 15
Figure 15
Dimensionless fixed-point and time response plots under first to third mode excitation for a circular plate with a diameter ratio of 1.2: (a) E1m1, (b) E2m2, (c) E3m3.
Figure 16
Figure 16
BIS-VEHS structural diagram, where F represents the slapping force (acting on the root of the main structure), and Fb represents the wind force acting on both the circular plate and the rectangular plate.
Figure 17
Figure 17
Time response of the first mode under first-mode excitation for a circular plate with a diameter ratio of 0.4 (a) Without slapping force, (b) with slapping force, (c) zoom out of Figure (a), (d) zoom out of Figure (b).
Figure 17
Figure 17
Time response of the first mode under first-mode excitation for a circular plate with a diameter ratio of 0.4 (a) Without slapping force, (b) with slapping force, (c) zoom out of Figure (a), (d) zoom out of Figure (b).
Figure 18
Figure 18
Time response of the third mode under third-mode excitation for a circular plate with a diameter ratio of 0.4. (a) Without slapping force, (b) with slapping force, (c) zoom out of Figure (a), (d) zoom out of Figure (b).
Figure 19
Figure 19
Time response of the first mode under first-mode excitation for a circular plate with a diameter ratio of 0.8. (a) Without slapping force, (b) with slapping force, (c) zoom out of Figure (a), (d) zoom out of Figure (b).
Figure 20
Figure 20
Time response of the third mode under third-mode excitation for a circular plate with a diameter ratio of 0.8. (a) Without slapping force, (b) with slapping force, (c) zoom out of Figure (a), (d) zoom out of Figure (b).
Figure 20
Figure 20
Time response of the third mode under third-mode excitation for a circular plate with a diameter ratio of 0.8. (a) Without slapping force, (b) with slapping force, (c) zoom out of Figure (a), (d) zoom out of Figure (b).
Figure 21
Figure 21
Time response of the first mode under first-mode excitation for a circular plate with a diameter ratio of 1.2. (a) Without slapping force, (b) with slapping force, (c) zoom out of Figure (a), (d) zoom out of Figure (b).
Figure 22
Figure 22
Time response of the third mode under third-mode excitation for a circular plate with a diameter ratio of 1.2. (a) Without slapping force, (b) with slapping force, (c) zoom out of Figure (a), (d) zoom out of Figure (b).
Figure 23
Figure 23
Conceptual schematic of the BIS-VEHS experimental setup: (a) overall system configuration; (b) rail-mounted linkage device (Device A), which enables synchronized excitation of both the circular plate and the bottom-slapping mechanism by the actuator.
Figure 24
Figure 24
Frequency diagram of a specific circular plate and elastic steel combination, (a) internal resonance, (b) non-resonant case with circular plate diameter = 5 cm, (c) non-resonant case with circular plate diameter =10 cm.
Figure 25
Figure 25
Experimental setup and system schematic diagram.
Figure 26
Figure 26
Experimental setup photo.
Figure 27
Figure 27
Experimental frequency–response curve of the BIS-VEHS internal resonance system under first-mode excitation, showing displacement amplitude (mm) versus excitation frequency (Hz). (a) Experimental displacement, (b) theoretical dimensional displacement.
Figure 28
Figure 28
Experimental frequency–response curve of the BIS-VEHS internal resonance system under third-mode excitation, showing displacement amplitude (mm) versus excitation frequency (Hz). (a) Experimental displacement, (b) theoretical dimensional displacement.
Figure 29
Figure 29
Non-resonant system with 5 cm diameter plate under first-mode excitation, (a) experimental displacement, (b) theoretical dimensional displacement.
Figure 30
Figure 30
Non-resonant system with 5 cm diameter plate under second-mode excitation, (a) experimental displacement, (b) theoretical dimensional displacement.
Figure 31
Figure 31
Non-resonant system with 5 cm diameter plate under third-mode excitation, (a) experimental displacement, (b) theoretical dimensional displacement.
Figure 32
Figure 32
Non-resonant system with 10 cm diameter plate under first-mode excitation, (a) experimental displacement, (b) theoretical dimensional displacement.
Figure 33
Figure 33
Non-resonant system with 10 cm diameter plate under second-mode excitation, (a) experimental displacement, (b) theoretical dimensional displacement.
Figure 34
Figure 34
Non-resonant system with 10 cm diameter plate under third-mode excitation, (a) experimental displacement, (b) theoretical dimensional displacement.
Figure 35
Figure 35
Output voltage of the internal resonance system under first-mode excitation, (a) without slapping, (b) with slapping.
Figure 36
Figure 36
Output voltage of the internal resonance system under third-mode excitation, (a) without slapping, (b) with slapping.
Figure 37
Figure 37
Output voltage of the 5 cm diameter plate without internal resonance under excitation of the first mode, (a) without slapping, (b) with slapping.
Figure 38
Figure 38
Output voltage of the 5 cm diameter plate without internal resonance under excitation of the second mode, (a) without slapping, (b) with slapping.
Figure 39
Figure 39
Output voltage of the 5 cm diameter plate without internal resonance under excitation of the third mode, (a) without slapping, (b) with slapping.
Figure 40
Figure 40
Output voltage of the 10 cm diameter plate without internal resonance under excitation of the first mode, (a) without slapping, (b) with slapping.
Figure 41
Figure 41
Output voltage of the 10 cm diameter plate without internal resonance under excitation of the second mode, (a) without slapping, (b) with slapping.
Figure 42
Figure 42
Output voltage of the 10 cm diameter plate without internal resonance under excitation of the third mode, (a) without slapping, (b) with slapping.
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