The schematic diagram of a marine engine connected to a propeller through circular hollow composite shaft...

Transcribed Image Text:

The schematic diagram of a marine engine connected to a propeller through circular hollow composite shaft is shown in figure. The motor can be considered to be stationary (fixed). In A - A section, the material details are given which shows that the propeller shaft is made of steel and aluminum and they move together. Shear modulus of the steel and aluminum materials, respectively are Gsteef-80 GPa and Ga-25 GPa. Mass density (mass per unit volume) of steel and aluminum materials: Pated= 7850 kg /m'; pa- 2700 kg /m ; mass moment of inertia of the propeller; Jp-50kgm?. 1, Torsional moment of inertia (torsional constant) and J Polar moment of inertia for hollow cylinder is given as I, = J = n(Dout*- Din*)/32) propeller Stel Aluminum Section AA Solve the problem following the steps below: (a) (5P) Create the finite element model of the structure by using a single torsion element. (b) (20P) Obtain the global stiffness matrix and global mass matrix. Write the boundary conditions. (e) (15P) By using a torsion element, obtain the natural frequency. The schematic diagram of a marine engine connected to a propeller through circular hollow composite shaft is shown in figure. The motor can be considered to be stationary (fixed). In A - A section, the material details are given which shows that the propeller shaft is made of steel and aluminum and they move together. Shear modulus of the steel and aluminum materials, respectively are Gsteef-80 GPa and Ga-25 GPa. Mass density (mass per unit volume) of steel and aluminum materials: Pated= 7850 kg /m'; pa- 2700 kg /m ; mass moment of inertia of the propeller; Jp-50kgm?. 1, Torsional moment of inertia (torsional constant) and J Polar moment of inertia for hollow cylinder is given as I, = J = n(Dout*- Din*)/32) propeller Stel Aluminum Section AA Solve the problem following the steps below: (a) (5P) Create the finite element model of the structure by using a single torsion element. (b) (20P) Obtain the global stiffness matrix and global mass matrix. Write the boundary conditions. (e) (15P) By using a torsion element, obtain the natural frequency.