hw1 mec 518
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7/25/2019 HW1 MEC 518
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MEC 518 Energy Harvesting Instructor: Prof. Ya Wang
HW1 (Due on Feb 8, 4pm, Blackboard Submission Only)
An energy harvester is designed to convert external energy exerted by force F(t) into electricity using
piezoelectric stack actuator with a force amplification frame. Its schematic diagram, and
material/mechanical properties are shown in the following figures and Table. The stack actuator is 7mm
by 7mm by 32.4mm. The external force is F(t) = 210.6sin 3.918t+ 0.1854( )+ 0.2465sin 16.5t! 0.8601( ) .
Schematic Diagram Top view Side view.
Figure Schematic and Dimension of the Energy Harvester (unit: mm).
Table Material and mechanical properties of the energy harvester.
Property Unit Value
Density of Frame kg/m3 7850
Elastic Modulus of Frame GPa 200
Poisson Ratio of Frame 0.29
Yield Tensile Strength of Frame MPa 260
Density of Piezoelectric Stack kg/m3 7700
Elastic Modulus of Piezoelectric Stack GPa 41.7
Capacitance of Piezoelectric Stack nF 2000
Number of layers of Piezoelectric Stack 300Layer thickness of Piezoelectric Stack mm 0.1
Piezoelectric constant (d33) m/V 475e-12
Dielectric permittivity constant (!33 ) F/m 1.67e-8
1.1Consider the energy harvester a 1 DOF spring-mass system shown in Figure 1.1, -- derive itsequation of motion using energy methods and piezoelectric constitutive equations; --
theoretically solve and numerically simulate the displacement of the piezoelectric stack and thepower output of the piezoelectric stack.
Figure 1.1 Equivalent dynamic representation 1DOF
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7/25/2019 HW1 MEC 518
2/2
MEC 518 Energy Harvesting Instructor: Prof. Ya Wang
1.2 If the energy harvester is modeled as a 2DOF spring-mass system shown in Figure 1.2, --derive its equation of motion using energy methods and piezoelectric constitutive equations; --
theoretically solve and numerically simulate the displacement of the piezoelectric stack and thepower output of the piezoelectric stack; discuss both models.
Figure 1.2 Equivalent dynamic representation 2DOF
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