NAFEMS Natural Frequency Benchmarks Contents In-Plane Vibrations of a Pin-Ended Cross Frame Determine the natural frequencies of a simply supported cross frame with four beams. Consider modes in the XY plane only. The frame is 10 m x 10 m and each beam has a square section of side 0.125 m. All dimensions are in m. In-Plane Vibrations of a Free Square Frame Determine the natural frequencies of a free square frame with four beams. Consider modes in the XY plane only. The frame is 10 m x 10 m and each beam has a square section of side 0.25m. In-Plane and Out-of-Plane Vibrations of a Circular Ring Determine the natural frequencies of an unsupported circular ring. Consider in-plane and out-of-plane modes. The ring has a diameter of 1 m and a circular cross-section of diameter 0.1 m. All dimensions are in m. Symmetric Modes of a Thin Square Cantilevered Plate Determine the symmetric modes of a square cantilevered plate. The plate is 10.0 m x 10.0 m and its thickness is 0.05 m. Only half of the plate is modeled due to symmetry. All dimensions are in m. Anti-Symmetric Modes of a Thin Square Cantilevered Plate Determine the anti-symmetric modes of a square cantilevered plate. The plate is 10.0 m x 10.0 m and its thickness is 0.05 m. Only half of the plate is modeled due to symmetry. All dimensions are in m. Vibrations of a Simply Supported Thick Square Plate Determine the frequencies of a simply supported thick square plate. The plate is 10.0 m x 10.0 m and its thickness is 1.0 m. All dimensions are in m. Vibrations of a Simply Supported Thin Square Plate Determine the frequencies of a simply supported thin square plate. The plate is 10.0 m x 10.0 m and its thickness is 0.05 m. All dimensions are in m. Vibrations of a Simply Supported Thin Annular Plate Determine the modes of vibration of a ring-shaped thin plate. The plate is simply supported around its circumference. The plate's inner radius is 1.8 m, its outer radius is 6.0 m, and its thickness is 0.06 m. All dimensions are in m. Vibrations of a Simply Supported Thick Annular Plate Determine the modes of vibration of a ring-shaped thick plate. The plate is simply supported around its circumference. The plate's inner radius is 1.8 m, its outer radius is 6.0 m, and its thickness is 0.6 m. All dimensions are in m. In-Plane Vibrations of a Free Annular Membrane Determine the in-plane modes of vibration of a ring-shaped membrane. The membrane has a thickness of 0.06 m and is simply-supported around its circumference. The membrane's inner radius is 1.8 m and its outer radius is 6.0 m. All dimensions are in m. In-Plane Vibrations of a Cantilevered Square Membrane Determine the in-plane modes of vibration of a cantilevered square membrane. The membrane is 10 m x 10 m and its thickness is 0.01 m. All dimensions are in m. Modes of Vibration of a Square Cantilevered Beam Determine the modes of vibration of a cantilevered square beam. The beam has a length of 10 m and a cross-section of 0.125 m x 0.125 m. All dimensions are in m. Modes of Vibration of a Cantilevered Solid Beam Determine the modes of vibration of a cantilevered beam modeled as a solid. The beam has a length of 10 m and a square cross-section of 2.0 m x 2.0 m. All dimensions are in m. Parent topicNAFEMS Benchmark Problems