Figure below shows a 2D cantilevered beam, length (L) 0.1 m, attached to an axial spring...

Transcribed Image Text:

Figure below shows a 2D cantilevered beam, length (L) 0.1 m, attached to an axial spring with spring stiffness (k) of 500,000 N/m. The square cross section of the cantilever beam measures 0.01 m x 0.01 m. It is manufactured from steel with density (p) 7850 kg/m and modulus (E) 200 GPa. I=1/12 bh, mass = PAL a) Using a consistent mass matrix and using one beam element to model the cantilever beam, write down the equations of motion for the two degrees of freedom system. b) Determine the first two natural frequencies of vibration of the beam. c) Determine the two corresponding mode shapes K 0.1 m (14 marks) (10 marks) (8 marks) Figure below shows a 2D cantilevered beam, length (L) 0.1 m, attached to an axial spring with spring stiffness (k) of 500,000 N/m. The square cross section of the cantilever beam measures 0.01 m x 0.01 m. It is manufactured from steel with density (p) 7850 kg/m and modulus (E) 200 GPa. I=1/12 bh, mass = PAL a) Using a consistent mass matrix and using one beam element to model the cantilever beam, write down the equations of motion for the two degrees of freedom system. b) Determine the first two natural frequencies of vibration of the beam. c) Determine the two corresponding mode shapes K 0.1 m (14 marks) (10 marks) (8 marks)

Answer rating: 100% (QA)

To solve this problem well use the finite element method to model the cantilever beam as a twodegreeoffreedom system Lets go step by step a Equations ... View the full answer