Reference: Dr. Glenn Rix Web Site

Overview

The course introduces students to concepts and tools that can be used to predict the response of soils and soil-structure systems to dynamic loads. Basic concepts of dynamics such as stiffness, damping, and inertial forces are discussed in the context of single degree of freedom (SDOF) and multiple degree of freedom (MDOF) systems. These concepts are used to analyze the response of shallow and deep foundations to dynamic loads. Dynamic properties (modulus and damping ratio) of soils are discussed to enable students to select appropriate values for use in analyses of soil-structure systems.

Man-made vibrations caused by construction activities, blasting, rail and vehicular traffic, and machinery can have an adverse impact on buildings and facilities, human occupants of buildings, and sensitive equipment housed within these facilities. Standard methods of selecting and mounting transducers, processing vibration data, and interpreting test results are reviewed. Specific measurement and analysis techniques and maximum allowable vibration criteria used for evaluating the influence of vibrations on humans, the potential for cosmetic damage to structures, and the impact on vibration-sensitive equipment are also summarized.

One dimensional wave propagation theory is presented followed by the application of the theory to laboratory resonant column tests, nondestructive tests of foundation systems, and dynamic analysis of pile driving. Elastic wave propagation in three-dimensional media is discussed including reflection and transmission of waves at interfaces between dissimilar layers and propagation of elastic waves in saturated media. In situ seismic test methods are used as examples of the application of these principles in practice.

This course also emphasizes the use of modern engineering calculation software including Matlab and Mathcad.

Vibration of Lumped Parameter Systems

	Single Degree of Freedom (SDOF) Systems Undamped and Damped Free Vibrations Undamped and Damped Forced Vibrations Forced Vibrations Due to Support Motions Random Loading Response Spectra
	Multiple Degree of Freedom (MDOF) Systems

Foundation Vibrations

	Shallow Foundations Uncoupled Motion Coupled Motion
	Deep Foundations Single Piles Group Interaction Effects

Dynamic Properties of Soils

	Simple Models of Hysteretic Behavior
	Factors Affecting Dynamic Stiffness and Damping of Soils
	Laboratory and In Situ Test Methods
	Empirical Estimates of Dynamic Soil Properties

Civil Engineering Vibrations

	Vibration Sources
	Signal Processing and Analysis
	Vibration Criteria Human Exposure Residential Structures Sensitive Equipment

Applications of the One-Dimensional Wave Equation

	One-Dimensional Wave Equation
	Resonant Column Tests
	Nondestructive Testing of Foundations
	Dynamic Analysis of Pile Driving

Applications of Three-Dimensional Wave Equation

• Three-Dimensional Wave Equation
• Elastic Waves in Layered Media
• In Situ Seismic Methods

Introduction

Vibration of Lumped Parameter Systems

• Complex Notation
• Free Vibrations
• Forced Vibrations
• Transfer (Frequency Response) Functions
• Response to Arbitrary Excitation
• Multiple Degree of Freedom Systems

Foundation Vibrations

• Soil-Structure Interaction
• Vibrations of Surface Foundations
• Vibrations of Foundations on a Layer Over Rock
• Vibrations of Pile-Supported Foundations
• Review of Foundation Vibrations

Civil Engineering Vibrations

One-Dimensional Wave Equation

• Derivation, D'Alembert Solution, Reflection and Transmission Coefficients, and Standing Waves
• Application - Nondestructive Integrity Testing

Mathcad

Vibration of Lumped Parameter Systems

• Undamped Free Vibrations
• Damped Free Vibrations
• Forced Vibrations
• Transfer Functions
  • Ground Displacement
  • Ground Acceleration
• Fourier Analysis
• Response of a SDOF to a Non-Harmonic Load
• Multiple Degree of Freedom Systems

Foundation Vibrations

• Surface Footings
  • Vertical Motion
  • Combined Motion
• Embedded Footings
  • Combined Motion
• Footings on a Layer Over Rock
• Footings on Piles

One Dimensional Wave Equation

• D' Alembert Solution
• Reflection and Transmission Coefficients
• Standing Waves
• Application - Resonant Column Test
• Application - Nondestructive Integrity Testing

Three Dimensional Wave Equation

• Seismic Waves in Particulate Media

Matlab/Simulink

Matlab M-Files and Scripts

• Undamped, Free Vibrations
• Damped, Free Vibrations
• Forced Vibrations
• Transfer (Frequency Response) Functions
• Fourier Analysis
• Response to an Arbitrary Forcing Function
• Multiple Degree of Freedom System (Modal Analysis)

Simulink Models

• Undamped, Free Vibrations
• Damped, Free Vibrations
• Forced Vibrations
• Transfer (Frequency Response) Functions

Additional Resources

The Stat/Math Center at Indiana University maintains a web page with information, tutorials, and links related to Matlab including several web sites related to vibration problems.

Online Resources

Hewlett Packard has several application notes that are good tutorials for Fourier analysis and signal processing including:

• Fundamentals of Signal Analysis
• Fourier Theory and Practice Part I: Theory
• Fourier Theory and Practice Part II: Practice

The Vibration Institute is a not-for-profit organization dedicated to the exchange of practical vibration information on machines and structures.

The Geophysics Department at Technical University - Clausthal in Denmark has developed a t Java applet that demonstrates the operation of a seismometer (i.e. a SDOF)

References

Engineering Vibrations

• Clough, R.W. and Penzien, J., "Dynamics of Structures", McGraw-Hill Book Co., 1975,
• Ewins, D.J., "Modal Testing: Theory and Practice", John Wiley and Sons, Inc., 1984.
• Inman, D.J., "Engineering Vibration," Prentice-Hall, 1994.
• Pax, M., "Structural Dynamics, Theory and Computation", Van Nostrand Reinhold Company, 1980.
• Thomson, W.T., "Theory of Vibration with Applications", Prentice-Hall, Inc., 1972.
• Timoshenko, S.P., Young, D.H. and Weaver, W., "Vibration Problems in Engineering", John Wiley and Sons, 1974.

Signal Processing

• Bendat, J.S., and Piersol, A.G., "Engineering Applications of Correlation and Spectral Analysis," Wiley-Interscience, 1980.
• Bendat, J.S., and Piersol, A.G., "Random Data: Analysis and Measurement Procedures," 2nd Ed., Wiley-Interscience, 1986.
• Bendat, J.S., "Nonlinear System Analysis and Identification," Wiley-Interscience, 1990.
• Bracewell, R.N., "The Fourier Transform and Its Applications," McGraw-Hill, 1978.
• Harger, R.O., "An Introduction to Digital Signal Processing with Mathcad," PWS Publishing, 1999.
• Kay, S.M., "Modern Spectral Estimation: Theory and Application," Prentice-Hall, Inc. 1988.
• Ramirez, R.W., "The FFT: Fundamental and Concepts," Prentice-Hall, Inc. 1985.
• Santamarina, J.C., and Fratta, D., "Introduction to Discrete Signals and Inverse Problems in Civil Engineering," ASCE Press, 1998.

• Williams, C.S., "Designing Digital Filters," Prentice-Hall, Inc., 1986.

Soil Dynamics

• Barkan, D.D., "Dynamics of Bases and Foundations", McGraw-Hill, New York, 1962.
• Das, B.M., "Principles of Soil Dynamics", PWS-Kent Publishing Company, 1993.
• Prakash, S., "Soil Dynamics", McGraw-Hill Book Co., 1981.
• Richart, F.E., Hall, J.R., and Woods, R.D., "Vibrations of Soils and Foundations", Prentice-Hall, Inc., New York, 1970.
• Wu, T.H., "Soil Dynamics", Allyn and Bacon, 1971.

Civil Engineering Vibrations

• Dowding, C.H., "Blast Vibration Monitoring and Control," Prentice-Hall, Inc. 1985.
• Dowding, C.H., "Construction Vibrations," Prentice-Hall, Inc. 1996.
• Skipp, B.O., Editor, "Ground Dynamics and Man-Made Processes," Thomas Telford, Ltd., 1998.

Dynamic Soil-Structure Interaction

• Wolf, J.P., "Dynamic Soil-Structure Interaction", Prentice Hall, 1985.
• Wolf, J.P., "Foundation Vibration Analysis Using Simple Physical Models," Prentice Hall, 1994.

Wave Propagation

• Achenbach, J.D., "Wave Propagation in Elastic Solids," North-Holland Publishing Company, 1984.
• Aki, K., and Richards, P.G., "Quantitative Seismology: Theory and Methods," W.H. Freeman and Company, 1980.
• Ewing, M., Jardetzky, W., and Press. F., "Elastic Waves in Layered Media," McGraw-Hill, 1957.
• Graff, K.F., "Wave Motion in Elastic Solids," Dover Publications, 1991.
• Kausel, E., and Manolis, G., Eds., "Wave Motion in Earthquake Engineering," WIT Press, 1999.
• Sato, H., and Fehler, M.C., "Seismic Wave Propagation and Scattering in the Heterogeneous Earth," Springer-Verlag, 1998.