2103433 introduction to mechanical vibration -...
TRANSCRIPT
![Page 1: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/1.jpg)
2103433
Introduction to Mechanical Vibration
Nopdanai Ajavakom (NAV)
12103433 Intro to Mech Vibration, NAV
![Page 2: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/2.jpg)
Chapter 2: Free Vibration of SDOF Systems
• Introduction
• Undamped Free Vibration
• Damped Free Vibration
– Underdamped
– Overdamped
– Critically Damped
• Measurement
• Design Consideration
22103433 Intro to Mech Vibration, NAV
![Page 3: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/3.jpg)
2.1 Introduction• A system is said to undergo free vibration when it
oscillates only under an initial disturbance with no external forces after the initial disturbance.
Examples
• The oscillations of the pendulum of a clock
• The vertical oscillatory motion felt by a bicyclist after hitting a road bump
• The motion of a child on a swing under an initial push
32103433 Intro to Mech Vibration, NAV
![Page 4: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/4.jpg)
2.1 Introduction• EOM of a single degree of freedom system
42103433 Intro to Mech Vibration, NAV
![Page 5: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/5.jpg)
2.1 Introduction• Review of Linear Second Order Differential Equation
52103433 Intro to Mech Vibration, NAV
![Page 6: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/6.jpg)
2.1 Introduction• Three Solutions
62103433 Intro to Mech Vibration, NAV
![Page 7: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/7.jpg)
• Three Solutions
72103433 Intro to Mech Vibration, NAV
2.1 Introduction
![Page 8: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/8.jpg)
82103433 Intro to Mech Vibration, NAV
2.2 Free Undamped Vibration
![Page 9: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/9.jpg)
92103433 Intro to Mech Vibration, NAV
2.2 Free Undamped Vibration
![Page 10: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/10.jpg)
102103433 Intro to Mech Vibration, NAV
2.2 Free Undamped Vibration
![Page 11: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/11.jpg)
112103433 Intro to Mech Vibration, NAV
2.2 Free Undamped Vibration• Relationship between displacement, velocity, and
acceleration
![Page 12: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/12.jpg)
122103433 Intro to Mech Vibration, NAV
2.3 Free Damped Vibration
![Page 13: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/13.jpg)
132103433 Intro to Mech Vibration, NAV
2.3 Free Damped Vibration
![Page 14: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/14.jpg)
142103433 Intro to Mech Vibration, NAV
2.3 Free Damped Vibration
![Page 15: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/15.jpg)
152103433 Intro to Mech Vibration, NAV
2.3.1 Underdamped Vibration
![Page 16: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/16.jpg)
162103433 Intro to Mech Vibration, NAV
2.3.2 Overdamped Vibration
![Page 17: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/17.jpg)
172103433 Intro to Mech Vibration, NAV
2.3.3 Critically Damped Vibration
![Page 18: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/18.jpg)
182103433 Intro to Mech Vibration, NAV
2.3 Free Damped Vibration• Exercises
1. A Spring-mass-damper system has mass of 100 kg, stiffness of 3000 N/m and damping coefficient of 300 kg/s. Calculate the (undamped) natural frequency, the damping ratio and the damped natural frequency. Does the solution oscillate? This system is given a zero initial velocity and an initial displacement of 0.1 m. Calculate the vibration response. [inman1.40, 1.42]
![Page 19: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/19.jpg)
192103433 Intro to Mech Vibration, NAV
2.3 Free Damped Vibration2. A Spring-mass-damper system has mass of 150 kg,
stiffness of 1500 N/m and damping coefficient of 200 kg/s. Calculate the undamped natural frequency, the damping ratio and the damped natural frequency. Is the system overdamped, underdamped or critically damped? Does the solution oscillate? This system is given an initial velocity of 10 mm/s and an initial displacement of -5 mm. Calculate the vibration response. [inman1.41, 1.43]
![Page 20: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/20.jpg)
202103433 Intro to Mech Vibration, NAV
2.3 MeasurementLogarithmic Decrement
![Page 21: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/21.jpg)
212103433 Intro to Mech Vibration, NAV
2.3 MeasurementLogarithmic Decrement
![Page 22: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/22.jpg)
222103433 Intro to Mech Vibration, NAV
2.3 MeasurementExample:
![Page 23: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/23.jpg)
232103433 Intro to Mech Vibration, NAV
2.3 MeasurementExample:
![Page 24: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/24.jpg)
242103433 Intro to Mech Vibration, NAV
2.4 Design Consideration
• Design in vibration: adjusting the physical parameters of a device to cause its vibration response to meet a specified shape or performance criterion.
Example
– Design a m-c-k system to have the desired response.
• underdamped, overdamped, critically damped
– Design a system that has a given natural frequency.
• Select connection of springs (series or parallel)
• Use elastic elements as springs
• Consider acceptable static deflection
![Page 25: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/25.jpg)
252103433 Intro to Mech Vibration, NAV
2.4 Design Consideration• Example:
![Page 26: 2103433 Introduction to Mechanical Vibration - Chulapioneer.netserv.chula.ac.th/~anopdana/433/ch2.pdf2103433 Intro to Mech Vibration, NAV 18 2.3 Free Damped Vibration •Exercises](https://reader036.vdocument.in/reader036/viewer/2022081800/5b01f2ba7f8b9a952f8f21dd/html5/thumbnails/26.jpg)
262103433 Intro to Mech Vibration, NAV
2.4 Design Consideration• Example:
Consider modeling the vertical suspension system of a small sports car, as a single-DOF system. The mass of the automobile is 1361 kg. The static deflection of the spring is 0.05 m. Calculate c and k of the suspension system of the car to be critically damped. If there are passengers and baggage of 290 kg in the car, how does this affect the damping ratio?