Question

The beam, shown in the figure, is vibrating. We would like to estimate the first bending vibration natural frequency of the beam.\ y(x,t)\ 0\\??, ?? 1 x\\Tasks:\ Data:\ l = 0.8 [m] IE = 2 000 [Nm$^2$] Ap = 2.5 [kg/m]\\ a. Give the boundary conditions!\ b. Choose one of the following functions in order to estimate the first mode of the beam!\ $Y(x) = \sin(\frac{\pi}{l}x)$ $Y(x) = x^2(x-l)^2$ $Y(x) = \sin(\frac{2\pi}{l}x)$\ c. Estimate the first natural angular frequency of the beam using Rayleigh's principle!\ d. What type of estimation is given by Rayleigh's principle?

          The beam, shown in the figure, is vibrating. We would like to estimate the first bending vibration natural frequency of the beam.\
y(x,t)\
0\\??, ?? 1 x\\Tasks:\
Data:\
l = 0.8 [m]  IE = 2 000 [Nm$^2$]  Ap = 2.5 [kg/m]\\
a. Give the boundary conditions!\
b. Choose one of the following functions in order to estimate the first mode of the beam!\
$Y(x) = \sin(\frac{\pi}{l}x)$   $Y(x) = x^2(x-l)^2$   $Y(x) = \sin(\frac{2\pi}{l}x)$\
c. Estimate the first natural angular frequency of the beam using Rayleigh's principle!\
d. What type of estimation is given by Rayleigh's principle?

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The beam, shown in the figure, is vibrating. We would like to estimate the first bending vibration natural frequency of the beam.y(x,t)0
??, ?? 1 x
Tasks:Data:l = 0.8 [m] IE = 2 000 [Nm^2] Ap = 2.5 [kg/m]

a. Give the boundary conditions!b. Choose one of the following functions in order to estimate the first mode of the beam!Y(x) = sin((π)/(l)x) Y(x) = x^2(x-l)^2 Y(x) = sin((2π)/(l)x)c. Estimate the first natural angular frequency of the beam using Rayleigh's principle!d. What type of estimation is given by Rayleigh's principle?

Added by Brett M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Narayan Hari

01/28/2023

Step 1

The boundary conditions for a simply supported beam are typically that the deflection and slope are zero at both ends. Therefore, the boundary conditions for this beam can be stated as: At x = 0: y(0,t) = 0 and dy/dx(0,t) = 0 At x = l: y(l,t) = 0 and dy/dx(l,t) = Show more…

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The beam, shown in the figure, is vibrating. We would like to estimate the first bending vibration natural frequency of the beam. y(x,t) 0 M Data: l=0.8 [m] IE=2 000 [Nm2] Ap=2.5 [kg/m] `IE,Ap Tasks: a. Give the boundary conditions! b. Choose one of the following functions in order to estimate the first mode of the beam! 2T Y(x) =sin Y(x) =x2(x -1)2 Y(x)=sin 1 c. Estimate the first natural angular frequency of the beam using Rayleigh's principle! d. What type of estimation is given by Rayleigh's principle?

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