10 Spring With Mass
description
Transcript of 10 Spring With Mass
![Page 1: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/1.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 1/12
1
VERTICAL SPRING WITH MASSCONSIDER
Mass at end of mass-less spring
Spring with homogenous mass distribution
Spring with mass and point mass
At end of springAt arbitrary location
Spring with several point masses.
No damping
Transient response (breakage)
Harmonic loading
![Page 2: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/2.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 2/12
2
Point mass at end. Static deflection
![Page 3: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/3.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 3/12
3
mL << M
Natural freq.
Transient resp.
Time dep. load
![Page 4: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/4.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 4/12
4
Homogenous mass distribution (wire only)
• Equilibrium of element
• Separation of variables
• Eigenvalues (fixed at x=0, no forceat x=L)
![Page 5: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/5.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 5/12
5
Example. Transient response.(wire only)
Eigenmodes and modal participation
• L= 1000m
• E=2.1E11 N/m2
• R=0.03m
• Rho = 0.6*7800kg/m3
• U(L,0) = 0.44m (F(L,0)=264kN)
• Ut(L,0) = 0
![Page 6: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/6.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 6/12
6
Transient response cont’d(wire only)
Response at x=L
![Page 7: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/7.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 7/12
7
Transient response cont’d. (wire only)
Shock behaviour
![Page 8: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/8.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 8/12
8
Transient response cont’d (wire only)
![Page 9: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/9.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 9/12
9
Transient response. Point mass at x=L.
(M=2mL)
![Page 10: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/10.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 10/12
10
Transient response cont’d Point mass at x=L.
(M=2mL) Response at x=L
![Page 11: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/11.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 11/12
11
Transient response cont’d Point mass at x=L.
(M=2mL)
![Page 12: 10 Spring With Mass](https://reader036.fdocuments.us/reader036/viewer/2022062521/55cf85c3550346484b912574/html5/thumbnails/12.jpg)
7/21/2019 10 Spring With Mass
http://slidepdf.com/reader/full/10-spring-with-mass 12/12
12
M=0
M=0.1mL
M=2mL