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SS-V: 2030 Free Thin Square Plate
Test No. VM04 Determine the first fourteen modal frequencies for a free thin square plate.

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- Introduction
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- Static Analysis
- Modal Analysis
  - SS-V: 2000 Free Vibration of a Wedge
    Test No. VM01 Determine the first fundamental frequency and vibration mode of a wedge constrained at the wide end.
  - SS-V: 2010 In-plane Vibration of a Cantilever Plate
    Test No. VM01 Find the fundamental frequency for in-plane vibration of a cantilevered plate.
  - SS-V: 2020 Cylindrical Shell
    Test No. VM03 Find the fundamental frequency of a cantilever cylindrical shell.
  - SS-V: 2030 Free Thin Square Plate
    Test No. VM04 Determine the first fourteen modal frequencies for a free thin square plate.
  - SS-V: 2040 Thick Skewed Plate
    Test No. VM05 Find the fundamental frequency of a thick clamped skewed plate.
  - SS-V: 2050 Thick Square Plate
    Test No. VM06 Determine the first twelve modes and frequencies for a simply supported thick square plate.
  - SS-V: 2060 In-plane Vibration of Pin-ended Cross
    Test No. VM07 Find the first eight modal frequencies for in-plane vibration of a cross with pin joints at the ends.
  - SS-V: 2070 Cantilever Beam
    Test No. VM08 Perform normal mode dynamic analysis of a cantilevered beam.
  - SS-V: 2080 Circular Ring - In-plane and Out-of-plane Vibration
    Test No. VM09 Perform normal mode dynamic analysis of an unconstrained circular ring.
  - SS-V: 2090 Triangular Wing - Fixed Vibration
    Test No. VM10 Perform a normal mode dynamic analysis of a fixed right triangular plate.
  - SS-V: 2100 Cantilevered Tapered Beam
    Test No. VM11 Shear behavior of a cantilevered tapered beam.
  - SS-V: 2110 Cantilever with Off-Center Remote Mass
    Test No. VM12 Find the frequencies of a cantilever with off center remote masses at the free end.
  - SS-V: 2120 Two-body Symmetric Damped Oscillators System
    Test No. VM13Determine the frequency and damping rate of a 1D damped oscillator.
  - SS-V: 2130 1D Damped Oscillator: Translation or Rotation
    Test No. VM14Determine the frequency and damping rate of a 1D damped oscillator.
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SS-V: 2030 Free Thin Square Plate

Test No. VM04 Determine the first fourteen modal frequencies for a free thin square plate.

Definition

Figure 1.

The units are SI.

The material properties are:

Properties: Value
Modulus of Elasticity: 2e+11 Pa
Poisson's Ratio: 0.3
Mass density: 8.3e³ kg/m³

Results*

The following table summarizes the modes.


	Theory	SimSolid	% Difference
Flexible mode 1 [Hz]	1.622	1.618	-0.25%
Flexible mode 2 [Hz]	2.360	2.358	-0.08%
Flexible mode 3 [Hz]	2.922	2.920	-0.08%
Flexible mode 4 [Hz]	4.190	4.177	-0.31%
Flexible mode 5 [Hz]	4.190	4.177	-0.31%
Flexible mode 6 [Hz]	7.356	7.347	-0.12%
Flexible mode 7 [Hz]	7.356	7.347	-0.12%
Flexible mode 8 [Hz]	7.668	7.628	-0.52%
Flexible mode 9 [Hz]	NA	8.308
Flexible mode 10 [Hz]	NA	9.259
Flexible mode 11 [Hz]	NA	12.607
Flexible mode 12 [Hz]	NA	12.609
Flexible mode 13 [Hz]	NA	14.075
Flexible mode 14 [Hz]	NA	14.715

*Modes 4-5 and 6-7 are not available in NAFEMS solution.

¹ The Standard NAFEMS Benchmarks TNSB, Rev. 3, 5 October, 1990.

² Iguchi S. Biegeschwingungen and Klangfiguren der Vierseitg freien rechteckigen Platte. Ing. - Archiv, Bd 21, p. 5-6, 1953.