Home / Examples / Piezoelectric Analysis [Rayleigh] / Example 27: Transient Analysis of Pressure Drive

Example 27: Transient Analysis of Pressure Drive

General

Transient analysis is explained in this example.
Results will vary depending on Femtet version and the PC environment.
Unless specified in the list below, the default conditions will be applied.
Transient analysis is available in an optional package. However, transient analysis using resonant mode is not optional.

Analysis Space

Item	Settings
Analysis Space	2D
Model Unit	mm

Analysis Conditions

Item	Settings
Solver	Piezoelectric Analysis [Rayleigh]
Analysis Type	Transient Analysis
Transient Analysis Using Resonant Mode (Model 1)	Deselected
Transient Analysis Using Resonant Mode (Model 2)	Selected

The settings on the transient analysis tab are required.

For model 2, the settings on the resonant analysis tab are required.

The resonant analysis tab is set up as follows.

Tab	Setting Item	Settings
Resonant Analysis (only for model 2)	Number of Modes	3
Resonant Analysis (only for model 2)	Approximated Frequency	0 [Hz]
Transient Analysis	Timestep	Select [Manual] 5x10-6 [Sec] (*)
	Output Interval	1
	Calculation Steps	100
Mesh	Meshing Setup/Element Type	Select [Rectangle] (**)

(*) For the timestep, the period of the lowest resonant frequency (8 kHz) is used as the reference. In this case, it is 1.25e-4 [s]. The standard timestep is set as [period/10], but to be on the safe side, it is set as [period/25] to give more steps. (**)The triangle is the standard element for the 2D analysis. In this example, rectangle is selected to demonstrate that the rectangular mesh also can be used.

Model

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Face	METAL	001_Al *
1/Face	PIEZO	000_P-4 *

* Available from the material DB

Boundary Condition

The time dependency of the applied pressure is defined by weight function.

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
P/Edge	Mechanical	Pressure	2 [Pa] Select [Time Dependency] Enter [Weight Function] as shown in the diagram below.
P/Edge	Electric	Electric Wall	Magnetic Wall
V0/Edge	Mechanical	Free
V0/Edge	Electric	Electric Wall	Specify electric potential: Electric Potential 0 [V]
FLOAT/Edge	Mechanical	Free
FLOAT/Edge	Electric	Electric Wall	Floating Electrode
FIX/Edge	Mechanical	Displacement	UX=0.0, UY=0, UZ=0
FIX/Edge	Electric	Magnetic Wall

Below are the [Weight Function] table of the pressure-specified boundary condition and graphs. Since the input pressure is 2 [Pa] and the maximum weight is 1, the maximum value of the applied pressure is also 2 [Pa].

Results (Model 2: Resonant Analysis)

The displacement diagram is shown below with the mesh diagram.

Results (Model 2: Transient Analysis)

Shown below is the X normal stress of the result of the last analysis time.

Shown below is the electric potential distribution of the result of the last analysis time.

Results (Comparison of Models 1 and 2)

The electric potential change of the floating electrode over time is shown in the graph below.

The horizontal axis is the modes. The coordinates on the floating electrode are specified. The coordinates can be obtained with the mouse.

The overlapping plots of results of models 1 and 2 are shown below. They match very well.

See here for creating graph.
For the [Type] on the [Field Graph Setting] tab , select [Horizontal Axis: Mode (frequency, time, step, etc)]
For overlapping plots, see [drag-and-drop on the graph window].