fundamentos de estruturas dinamicas
217 pág.

fundamentos de estruturas dinamicas


DisciplinaAerodinâmica de Veículos Aeroespaciais37 materiais95 seguidores
Pré-visualização48 páginas
Course \u201cFundamentals of Structural Dynamics\u201d
An-Najah National University
April 19 - April 23, 2013
Lecturer: Dr. Alessandro Dazio, UME School
A. Dazio, April 19, 2013 Page 1/2
Fundamentals of Structural Dynamics
1 Course description
Aim of the course is that students develop a \u201cfeeling for dynamic problems\u201d and acquire the theoretical
background and the tools to understand and to solve important problems relevant to the linear and, in
part, to the nonlinear dynamic behaviour of structures, especially under seismic excitation.
The course will start with the analysis of single-degree-of-freedom (SDoF) systems by discussing: (i)
Modelling, (ii) equations of motion, (iii) free vibrations with and without damping, (iv) harmonic, pe-
riodic and short excitations, (v) Fourier series, (vi) impacts, (vii) linear and nonlinear time history anal-
ysis, and (viii) elastic and inelastic response spectra.
Afterwards, multi-degree-of-freedom (MDoF) systems will be considered and the following topics will
be discussed: (i) Equation of motion, (ii) free vibrations, (iii) modal analysis, (iv) damping, (v) Rayleigh\u2019s
quotient, and (vi) seismic behaviour through response spectrum method and time history analysis.
To supplement the suggested reading, handouts with class notes and calculation spreadsheets with se-
lected analysis cases to self-training purposes will be distributed.
Lecturer: Dr. Alessandro Dazio, UME School
2 Suggested reading 
[Cho11] Chopra A., \u201cDynamics of Structures\u201d, Prentice Hall, Fourth Edition, 2011.
[CP03] Clough R., Penzien J., \u201cDynamics of Structures\u201d, Second Edition (revised), Computer and
Structures Inc., 2003.
[Hum12] Humar J.L., \u201cDynamics of Structures\u201d. Third Edition. CRC Press, 2012.
3 Software
In the framework of the course the following software will be used by the lecturer to solve selected ex-
amples:
[Map10] Maplesoft: \u201cMaple 14\u201d. User Manual. 2010
[Mic07] Microsoft: \u201cExcel 2007\u201d. User Manual. 2007
[VN12] Visual Numerics: \u201cPV Wave\u201d. User Manual. 2012
As an alternative to [VN12] and [Map10] it is recommended that students make use of the following
software, or a previous version thereof, to deal with coursework:
[Mat12] MathWorks: \u201cMATLAB 2012\u201d. User Manual. 2012
Course \u201cFundamentals of Structural Dynamics\u201d April 19 - April 23, 2013
Page 2/2
4 Schedule of classes 
Date Time Topic
Day 1
Fri. April 19
2013
09:00 - 10:30 1. Introduction
2. SDoF systems: Equation of motion and modelling
11:00 - 12:30 3. Free vibrations
14:30 - 16:00 Assignment 1
16:30 - 18:00 Assignment 1
Day 2
Sat. April 20
2013
9:00 - 10:30 4. Harmonic excitation
11:00 - 12:30 5. Transfer functions
14:30 - 16:00 6. Forced vibrations (Part 1)
16:30 - 18:00 6. Forced vibrations (Part 2)
Day 3
Sun. April 21
2013
09:00 - 10:30 7. Seismic excitation (Part 1)
11:00 - 12:30 7. Seismic excitation (Part 2)
14:30 - 16:00 Assignment 2
16:30 - 18:00 Assignment 2
Day 4
Mon. April 22
2013
9:00 - 10:30 8. MDoF systems: Equation of motion
11:00 - 12:30 9. Free vibrations
14:30 - 16:00 10. Damping
11. Forced vibrations
16:30 - 18:00 11. Forced vibrations
Day 5
Tue. April 23
2013
09:00 - 10:30 12. Seismic excitation (Part 1)
11:00 - 12:30 12. Seismic excitation (Part 2)
14:30 - 16:00 Assignment 3
16:30 - 18:00 Assignment 3
Course \u201cFundamentals of Structural Dynamics\u201d An-Najah 2013
Table of Contents Page i 
Table of Contents
Table of Contents...................................................................... i
1 Introduction
1.1 Goals of the course.............................................................................. 1-1
1.2 Limitations of the course..................................................................... 1-1
1.3 Topics of the course ............................................................................ 1-2
1.4 References ............................................................................................ 1-3
2 Single Degree of Freedom Systems
2.1 Formulation of the equation of motion............................................... 2-1
2.1.1 Direct formulation......................................................................................... 2-1
2.1.2 Principle of virtual work............................................................................... 2-3
2.1.3 Energy Formulation...................................................................................... 2-3
2.2 Example \u201cInverted Pendulum\u201d............................................................ 2-4
2.3 Modelling............................................................................................. 2-10
2.3.1 Structures with concentrated mass.......................................................... 2-10
2.3.2 Structures with distributed mass ............................................................. 2-11
2.3.3 Damping ...................................................................................................... 2-20
3 Free Vibrations
3.1 Undamped free vibrations ................................................................... 3-1
3.1.1 Formulation 1: Amplitude and phase angle............................................... 3-1
3.1.2 Formulation 2: Trigonometric functions .................................................... 3-3
3.1.3 Formulation 3: Exponential Functions ....................................................... 3-4
Course \u201cFundamentals of Structural Dynamics\u201d An-Najah 2013
Table of Contents Page ii 
3.2 Damped free vibrations ....................................................................... 3-6
3.2.1 Formulation 3: Exponential Functions ....................................................... 3-6
3.2.2 Formulation 1: Amplitude and phase angle............................................. 3-10
3.3 The logarithmic decrement .............................................................. 3-12
3.4 Friction damping ............................................................................... 3-15
4 Response to Harmonic Excitation 
4.1 Undamped harmonic vibrations ......................................................... 4-3
4.1.1 Interpretation as a beat ................................................................................ 4-5
4.1.2 Resonant excitation (\u3c9 = \u3c9n) ....................................................................... 4-8
4.2 Damped harmonic vibration.............................................................. 4-10
4.2.1 Resonant excitation (\u3c9 = \u3c9n) ..................................................................... 4-13
5 Transfer Functions
5.1 Force excitation.................................................................................... 5-1
5.1.1 Comments on the amplification factor V.................................................... 5-4
5.1.2 Steady-state displacement quantities ........................................................ 5-8
5.1.3 Derivating properties of SDoF systems from harmonic vibrations....... 5-10
5.2 Force transmission (vibration isolation) ......................................... 5-12
5.3 Base excitation (vibration isolation)................................................. 5-15
5.3.1 Displacement excitation ........................................................................... 5-15
5.3.2 Acceleration excitation ............................................................................. 5-17
5.3.3 Example transmissibility by base excitation .......................................... 5-20
5.4 Summary Transfer Functions ........................................................... 5-26
6 Forced Vibrations
6.1 Periodic excitation .............................................................................. 6-1
6.1.1 Steady state response due to periodic excitation..................................... 6-4
Course \u201cFundamentals of Structural Dynamics\u201d An-Najah