lecture-iv fem applications in dynamics
DESCRIPTION
Lecture-IV FEM Applications in DynamicsTRANSCRIPT
![Page 1: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/1.jpg)
BITS Pilani Hyderabad Campus
CE G551 Dynamics of Structures Instructor: Mr. J S Kalyana Rama
Course Lecture-IV
Application of FEM to Structural Dynamics
![Page 2: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/2.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Contents
Dynamic analysis of Water Tanks
Dynamic analysis of Bridges
![Page 3: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/3.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Dynamic analysis of Water Tanks
Elephant-foot buckling of a tank wall (courtesy
of University of California at Berkeley)
Sloshing damage to upper shell of tank (courtesy of University of
California at Berkeley)
![Page 4: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/4.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Liquid-filled tank modelled by generalized single-degree-of-
freedom systems
Method of Dynamic Analysis
• The dynamic analysis of a liquid-filled
tank may be carried out using the
concept of generalized single-degree-of
freedom (SDOF) systems representing
the impulsive and convective modes of
vibration of the tank-liquid system.
• For practical applications, only the first
few modes of vibration need to be
considered in the analysis.
• For a given earthquake ground motion,
the response of various SDOF systems
may be calculated independently and
then combined to give the net base
shear and overturning moment.
![Page 5: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/5.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Solid model of experimental set-up
Water Sloshing in Rectangular Tanks – An Experimental Investigation &
Numerical Simulation: Mechanical Engineering, Petroleum Institute, P.O. Box
2533 Abu Dhabi, UAE
![Page 6: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/6.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Actual experimental set-up
![Page 7: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/7.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Schematic of the experimental setup
![Page 8: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/8.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Image Processing
![Page 9: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/9.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Comparison between experimental and numerical results for 50% fill level and 4.5 kg
![Page 10: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/10.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Comparison between experimental and numerical results for 50% fill level and 4.5 kg
![Page 11: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/11.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
A STUDY ON SLOSHING FREQUENCIES OF FLUID-TANK SYSTEM
Visvesvaraya National Institute of Technology, Nagpur, India
Where, fc = Sloshing frequency (Hz), h = height of water in tank (m), L = length of rectangular tank along direction of excitation
(m), D= diameter of circular tank (m), g = acceleration due to gravity (m/s2)
For the circular and rectangular tanks, the first sloshing frequency is given by Housner, 1963): as
![Page 12: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/12.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
Details of tanks of other shapes
Circular tank of 170
mm diameter and
230 mm
height (Model 1);
square tank of plan
size 270mm x
270mm and 300
mm height (Model
2); rectangular tank
of plan size 270
mm x 135 mm and
300 mm height
![Page 13: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/13.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
First sloshing mode of liquid in tanks of different shapes
![Page 14: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/14.jpg)
BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama
• Clough and Penzein
• A K Chopra
• Slides from Different foreign Universities
• Wikipedia.org
• Technical University of Denmark-Material for Dynamics
References
![Page 15: Lecture-IV FEM Applications in Dynamics](https://reader035.vdocuments.us/reader035/viewer/2022081723/5695d18d1a28ab9b0296ffed/html5/thumbnails/15.jpg)
BITS Pilani Hyderabad Campus
THANK YOU!