for simplified analysis of the vibration of a airplane in the vertical direction three degree of

First, we need to write down the system of differential equations that describe the motion of th

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For simplified analysis of the vibration of an airplane in the vertical direction, a three-degree-of-freedom model, as shown in the following Figure, can be used. The three masses indicate the masses of the two wings (m1 and m2) and the fuselage (m3). The stiffnesses (K1 and K2) correspond to the bending stiffness of the two wings, which can be modeled as cantilever beams. The equations of motion of the airplane using the three-degree-of-freedom model are given as: Solve this system of differential equations (using the method of differentiation operators) and find the natural frequencies and mode shapes (eigenvalues and eigenvectors) of the airplane. Give an interpretation of the results.

          For simplified analysis of the vibration of an airplane in the vertical direction, a three-degree-of-freedom model, as shown in the following Figure, can be used. The three masses indicate the masses of the two wings (m1 and m2) and the fuselage (m3). The stiffnesses (K1 and K2) correspond to the bending stiffness of the two wings, which can be modeled as cantilever beams.

The equations of motion of the airplane using the three-degree-of-freedom model are given as:

Solve this system of differential equations (using the method of differentiation operators) and find the natural frequencies and mode shapes (eigenvalues and eigenvectors) of the airplane. Give an interpretation of the results.

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