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Problem 1. (2.5%) A uniform cantilever beam of total mass m has a concentrated mass M at its free end. Assume that the deflection of the beam can be described as follow: $$y(x,t) = Y(\frac{x}{L})^2[(\frac{x}{L})^2 - 4(\frac{x}{L}) + 6]sin\omega t$$ where A is a constant involving the material properties of the post. Determine: 1. (2.0%) The kinetic energy of the system. 2. (0.5%) The effective mass of the system. y m M M x=0 x=L Bonus Questions: 1. (1%) Does the given shape function satisfy geometric boundary conditions? 2. (1%) Does the given shape function satisfy natural boundary conditions?

Name: problem 1 25 a uniform cantilever beam of total mass m has a concentrated mass m at its free end assume that the deflection of the beam can be described as follow yxt yfracxl2fracxl2 4fracxl 62227
Uploaded: 2023-09-04T12:42:13-08:00
Duration: 2 min 16 s
Channel: Adi S
Description: problem 1 25 a uniform cantilever beam of total mass m has a concentrated mass m at its free end assume that the deflection of the beam can be described as follow yxt yfracxl2fracxl2 4fracxl 62227

          Problem 1. (2.5%) A uniform cantilever beam of total mass m has a concentrated mass M at its free
end. Assume that the deflection of the beam can be described as follow:
$$y(x,t) = Y(\frac{x}{L})^2[(\frac{x}{L})^2 - 4(\frac{x}{L}) + 6]sin\omega t$$
where A is a constant involving the material properties of the post. Determine:
1. (2.0%) The kinetic energy of the system.
2. (0.5%) The effective mass of the system.
y
m
M
M
x=0
x=L
Bonus Questions:
1. (1%) Does the given shape function satisfy geometric boundary conditions?
2. (1%) Does the given shape function satisfy natural boundary conditions?

$problem 1 25 a uniform cantilever beam of total mass m has a concentrated mass m at its free end assume that the deflection of the beam can be described as follow yxt yfracxl2fracxl2 4fracxl 62227$

Added by Mark R.

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