Example19 Resonant Frequency

General

Harmonic analysis is used in this Exercise while resonant analysis is used in Exercise 13.
Analysis with the initial stress taken into account is performed. See Analysis with the initial stress taken into account for the details.
The frequency characteristics of the displacement is solved.
Analysis 1: Apply the static load to the bar and pull it at both ends.
Analysis 2: Fix the bar at both ends. Vibrate it by applying the voltage. The displacement in the Analysis 1 is used to take into account the hardening effect of tensile force.

Analysis Space (Common to Analyses 1 and 2)

Item	Setting
Analysis Space	3D
Model unit	mm

Analysis Conditions (Analysis 1)

Item	Setting
Solver	Piezoelectric Analysis [Rayleigh]
Analysis Type	Static Analysis
Options	N/A

Graphical Objects (Analysis 1)

Two reversely polarized piezoelectric bars are stuck together. The ends are set with the “pressure” boundary condition. The top and bottom faces are set with the “voltage specified” boundary condition.

Body Attributes and Material properties Setting (Common to Analyses 1 and 2)

Body Number/Type	Body Attribute Name	Material Name
0/Solid	upper	000_P-4 *
1/Solid	lower	000_P-4 *

(*) Available from the Material DB

The polarizations are set as follows.

Body Attribute Name

Tab

Setting

upper

Direction

Specified by: Vector

Vector: X=Y=0.0, Z=1.0

lower

Direction

Specified by: Vector

Vector: X=Y=0.0, Z=-1.0

Boundary Conditions (Analysis 1)

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Setting
earth/Face	Electric	Electric wall	Voltage specified: Voltage 0[V]
hot/Face	Electric	Electric wall	Voltage specified: Voltage 10[V]
f_left/Face	Mechanical	Pressure	-1×10^9[Pa]
f_right/Face	Mechanical	Pressure	-1×10^9[Pa]

Results (Analysis 1)

The bar is pulled at both ends. The vector diagram of the displacement is shown below.

Analysis Conditions (Analysis 2)

Item	Setting
Solver	Piezoelectric Analysis [Rayleigh]
Analysis Type	Harmonic analysis
Options	Analysis with the initial stress taken into account Select Take into account. Select Use analysis result (Result import)

The harmonic analysis tab is set up as follows.

Tab	Setting Item	Setting
Harmonic Analysis	Sweep Values	Minimum: 35[KHz] Maximum: 50[KHz]
	Sweep Type	Select “Linear step by division number”. Division number: 50
	Sweep Setting	Discrete sweep

Result Import tab is set as follows.

Tab	Setting Item	Setting
Result Import	Specify Result	For analysis model, select [Analysis 1_Static load].

Graphical Objects (Analysis 2)

The analysis model is same as Analysis 1 (static analysis) except that both ends are fixed in Analysis 2.

Body Attributes and Material properties Setting (Analysis 2)

Same as Analysis 1.

Boundary Conditions (Analysis 2)

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Setting
FIX/Face	Mechanical	Displacement	Select all UX/UY/UZ components. X=Y=Z=0.0[mm]
earth/Face	Electric	Electric wall	Voltage specified: Voltage 0[V]
hot/Face	Electric	Electric wall	Voltage specified: Voltage 10[V]

Results (Analysis 2)

The frequency characteristics of displacement are solved by the analyses with and without the static load.

With static load/44.9KHz, Z displacement/Absolute

The contour above shows the displacement component Z absolute at the coordinates (5,1,0) near the resonant point in the analysis with static load.

The peak shifted to the higher frequency due to the tensile force. This is the same effect as the Exercise 13 where it shifted to 4481[Hz] from 4070[Hz].

See other Piezoelectric Analysis examples.