The differential equation for small-amplitude vibrations y(x, t) of a simple beam is given by = 0 d'y Ət ² PA where +EI O¹y əx4 p= beam material density A cross-sectional area /= area moment of inertia

The differential equation for small-amplitude vibrations y(x, t) of a simple beam is given by = 0 d'y Ət ² PA where +EI O¹y əx4 p= beam material density A cross-sectional area /= area moment of inertia

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

!
Required information
The differential equation
for small-amplitude
vibrations y(x, t) of a
simple beam is given by
PA + EI¹y = 0
əx4
where
p=beam material
density
A = cross-sectional area
/= area moment of inertia
E = Young's modulus
dy
Ət²
Use only the quantities p, E, and A to
nondimensionalize y, x, and t, and
rewrite the differential equation in
dimensionless form.

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