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

7/25/2019 HW1 MEC 518

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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