UCLA Extension

Structural Dynamics: Theory and Applications

The skillful application of the methods and analysis tools of structural dynamics is of paramount importance in the design of land, sea, air, and space vehicles. This is primarily due to the reality of variable loading on these types of systems. Therefore, a good working knowledge of structural dynamics is essential to the development of complex mechanical hardware.

This course provides participants with a good theoretical, as well as practical, knowledge of the methodologies for performing dynamic analysis on a wide range of structural and mechanical systems. Topics include energy methods, including the methods of Lagrange and Rayleigh; Newtonian dynamics; first- and second-order systems; introduction to random vibration; multiple-degree-of-freedom systems; the finite element method; and dynamics in the mechanical design process. Numerous examples discuss closed-form solutions and computer-based finite element analysis.

Course Benefits

  • Design engineers who would like to become more familiar with the techniques and modern practices of structural dynamics to help them be more efficient and productive in their work
  • Mechanical engineers who need to become more proficient in the area of structural dynamics due to a particular job assignment or new career opportunity that requires expertise in the dynamic analysis of structures
  • Department managers whose staff are involved in loads and dynamics work

Upon completing this course, participants should be able to:

  • Identify and correct problematic designs based on dynamic analysis results
  • Calculate margins of safety due to dynamic loading conditions
  • Understand the theory behind the analysis processes
  • Perform hand calculations to quickly solve structural dynamics problems without the aid of expensive computer software
  • Speak knowledgeably to customers and management about topics in the area of structural dynamics

Course Materials

Participants receive lecture notes on the first day of the course. These notes are for participants only and are not for sale or unauthorized distribution.

Coordinator and Lecturer

Dennis C. Philpot, MS, PE, Senior Staff Engineer & Section Head, Structural and Thermal Analysis, Defense Electronic Systems (DES) Division, Woodland Hills, California.

Mr. Philpot is responsible for the structural integrity of Alliant Techsystems (ATK) products and oversees the structural analyses performed at ATK Defense Electronic Systems and subcontractors that support ATK programs. He also serves as the test director for environmental testing that is conducted for the purpose of hardware development, acceptance, and qualification. Having performed structural analysis for more than 3 decades, Mr. Philpot has written internal procedures and created software tools for the analysis of various types of structural components. Over the past 10 years he has taught courses in engineering mechanics, stress analysis, and structural dynamics in various venues throughout the contiguous United States. Mr. Philpot is a Registered Professional Engineer in the state of California, U.S. Patent holder and has earned several NASA technology awards for demonstrating innovative ways of applying space technology to serve mankind. Mr. Philpot is a member of both the ASME and the AIAA.


Day 1


  • What do we mean by dynamics?
  • Deterministic and probabilistic analysis
  • Dynamics in mechanical design
  • The concept of dynamic response
  • Dynamics in the product development processes
  • The design synthesis process
  • Structural dynamics as a process
  • The importance of analysis early in the design cycle

Dynamic Loads and Boundary Conditions

  • Important terminology
  • Learn to think like a dynamicist
  • Dynamic loads: inertia-based and direct
  • Load categories
    — Harmonic
    — Random vibration
    — Acoustic
    — Shock
    — General
  • What we mean by “quasi-static loads”
  • Mode shapes and boundary conditions
  • The nature of dynamic response
  • Examples

Foundational Topics

  • Important terminology
  • Kinetic energy and momentum
  • Strain energy in structural elements
  • Virtual work
  • D’Alembert’s principle
  • Generalized coordinates
  • Lagrange’s equations of motion
  • The superposition principle
  • The unit impulse
  • The convolution integral
  • Examples

Day 2

Newtonian Dynamics: First- and Second-Order Systems

  • Important terminology
  • Newton’s laws of motion
  • Differential equations of motion of first-order systems
  • Response of first-order systems to harmonic loads
  • Differential equations of motion of second-order systems
  • Dynamic response of second-order systems
  • The octave rule
  • Force transmission of second-order systems
  • Second-order systems subject to inertial harmonic loading
  • Response to shock loading
  • Structural and viscous damping
  • Examples

Introduction to Random Vibration

  • Important terminology
  • Random processes in engineering design
  • Autocorrelation and stationarity
  • Frequency domain analysis
  • Stationarity and ergodicity
  • Probability density functions
  • Power spectral density functions
  • Response of SDOF systems to random vibration
  • Half-power points and bandwidth
  • Random vibration in mechanical design
  • Examples

Multiple-Degree-of-Freedom Systems

  • Important terminology
  • Mass, stiffness, and damping matrices
  • Computation of eigenvalues and eigenvectors
  • Static and inertial coupling of modes
  • Decoupling of modal vectors
  • Orthogonality of modes
  • MDOF systems with damping
  • Examples

Day 3

Dynamic Response of MDOF Systems

  • Important terminology
  • Direct integration of the equations of motion
  • Numerical methods
  • Modal superposition
  • Modal participation factors
  • Rigid body motion
  • Modal truncation vectors
  • Advantages of modal superposition
  • Response of MDOF systems to various load conditions
  • Examples

The Finite Element Method

  • Important terminology
  • Preprocessing essentials
  • Solution sequences
    — Eigenvalue solutions
    — Frequency response analysis
    — Random response analysis
    — Time history (shock) analysis
  • Identifying and correcting modeling errors
  • Postprocessing results
  • Special techniques
  • Examples

NASTRAN Examples in Structural Dynamics

  • Important terminology
  • Structural dynamics for failure prevention
    — Strength analysis
    — Fatigue analysis
    — Other criteria
  • Practical examples in structural dynamics
    — Primary structures
    — Secondary structures
    — Electronic equipment
  • Methods for correcting structural issues

For more information contact the Short Course Program Office:
shortcourses@uclaextension.edu | (310) 825-3344 | fax (310) 206-2815