VM203

VM203
Dynamic Load Effect on Supported Thick Plate

Overview

Reference:

NAFEMS, Selected Benchmarks for Forced Vibration, Report prepared by W. S. Atking Engineering Sciences, April 1989, Test 21R.

Analysis Type(s):

Mode-frequency, Spectrum Analysis (ANTYPE = 8)

Element Type(s):

8-Node Finite Strain Shell Elements (SHELL281)

Input Listing:

vm203.dat

Test Case

A simply-supported thick square plate of length , thickness t, and mass per unit area m is subject to random uniform pressure power spectral density. Determine the peak one-sigma displacement at undamped natural frequency.

Figure 318: Thick Square Plate Problem Sketch

Material Properties

Geometric Properties

E = 200 x 10⁹ N/m²

μ = 0.3

m = 8000 kg/m³

= 10 m

t = 1.0 m

PSD = (10⁶ N/m²)² /Hz

Damping δ = 2%

Analysis Assumptions and Modeling Notes

A frequency range of 1.0 Hz to 80 Hz is used as an approximation of the white noise PSD forcing function frequency.

The model is solved using SHELL281 elements.

Results Comparison

	Target	Mechanical APDL	Ratio
SHELL281
Frequency f (Hz)	45.9	45.96 [1]	1.001
Peak Deflection PSD (mm²/Hz)	3402	3595 [2]	1.057

From modal analysis solution
Peak amplitude (x10⁶) from spectrum analysis results using POST26

The peak one-sigma standard deviation from spectrum analysis is 101.7 mm. No closed-form solution is available from the reference for this entity.

Figure 319: Spectral Response to Uniform PSD Force