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Dynamic Random Response Analysis Problems
This chapter contains dynamic random response analysis problems and results for Structure. A dynamic random analysis measures the systemâ€™s response to stationary, random loads of known power spectral density (PSD).
mvsr001: Deep Simply Supported Beam Random Force Vibration Response
mvsr002: Deep Simply Supported Thin Square Plate Random Forced Vibration Response
mvsr001 : Deep Simply Supported Beam Random Force Vibration Response
 Analysis Type: Dynamic Random Model Type: Beam Comparison: NAFEMS Benchmark Reference: Selected Benchmarks for Forced Vibration, Report No. E1261/R002 Issue 03.2/15 June 1990, pp. 20. Test 5R Description: Determine response of simple supported square section beam subjected to random forcing with uniform power spectral density (of force)
Specifications
 Element Type: Square Beam Units: MKS Dimensions: L: 10.0, a =2 Material Properties: Mass Density: 8000Young's Modulus: 2e11Poisson's Ratio: 0.3
 Constraints: Location: Degrees of Freedom: Placed on point APlaced on point B Fixed in TransX, TransY, TransZ, and Rotation RxFixed in TransY and TransZ
 Loads: Description Random Forcing with uniform power spectral density (of Uniformly distributed force)PSD = (10e6 N/m) ^2/Hz, damping = 2 % in all 16 modes used.
Comparison of Results Data
 NAFEMS Structure % Diff Peak Displacement PSD (mm^2/Hz) at mid-span 180.90 182.599 0.939 PSD Freq (Hz) 42.65 42.6002 0.116
mvsr002 : Deep Simply Supported Thin Square Plate Random Forced Vibration Response
 Analysis Type: Dynamic Random Model Type: 3D Comparison: NAFEMS Benchmark Reference: Selected Benchmarks for Forced Vibration, Report No. E1261/R002 Issue 03.2/15 June 1990, pp 25. Test 13R Description: Determine response of simple supported thin square plate subjected to random forcing with uniform power spectral density (of force)
Specifications
 Element Type: shell Units: MKS Dimensions: L: 10.0, thickness: 0.05 Material Properties: Mass Density: 8000Young's Modulus: 2e11 Poisson's Ratio: 0.3
 Constraints: Location: Degrees of Freedom: Placed on edges AD and BC :Placed on edges AB and DC : Fixed in TransY, TransZ , RotX and RotZFixed in TransX, TransZ , RotY and RotZ
 Loads Details Random force with uniform power spectral density (of uniform pressure over whole plate)PSD = (100 N/m ^2) ^2/Hz, damping = 2 % in all 16 modes used.
Comparison of Results Data
 NAFEMS Structure % Diff Peak Displacement PSD (mm^2/Hz) at centre 2063.20 2065.39 0.101 PSD Freq (Hz) 2.377 2.376 0.042