Engineers Edge

Deflection of Uniform Bar with Free Ends Mechanical  Vibration

Strength and Mechanics of Materials
Accelerometer Suppliers | Accelerometers About and Application

The following are equations which predict the deflection and mode patterns for beams. They are based on simple beam theory and are accurate for beams having a length to depth ratio of the order of ten or more.

The characteristics numbers for the first three modes of this beam are: 4.73, 7.853 and 10.996.

y = Deflection [in]
= The characteristic number for the nth mode and is the root of the equation
n = Mode number

Frequencies of higher modes for this beam are given below, in which w is the weight per unit length of the beam and g = 386 in/sec2.

Uniform Bar With Free Ends
Illustration Amplitude Profile Mode Natural Circular Frequency

2 Nodes

3 Nodes

4 Nodes

5 Nodes

Spider Optimizer

© Copyright 2000 - 2021, by Engineers Edge, LLC
All rights reserved
Disclaimer | Feedback
Advertising | Contact | Privacy Policy


Spider Optimizer

Register | Login

Engineering Book Store
Engineering Forum
Excel App. Downloads
Online Books & Manuals
Engineering News
Engineering Videos
Engineering Calculators
Engineering Toolbox
GD&T Training Geometric Dimensioning Tolerancing
DFM DFA Training
Training Online Engineering
Advertising Center

Copyright Notice

Publishing Program