CE 57300 – Structural Dynamics

Credits and contact hours:

  • 3 credits
  • Lecture meets 3 times per week for 50 minutes per meeting for 15 weeks

Specific course information:

  • Catalog description: Analysis of structural members and systems subject to dynamic load such as wind and earthquake loads; basic theory for single-degree-of-freedom and multi- degree-of-freedom analytical models of civil engineering structures; free vibration, harmonic and transient excitation, foundation motion, resonance spectrum, Lagrange's equation, modal analysis, lumped parameter methods, computer methods.
  • Prerequisites: CE 47400 or Graduate standing
  • Course status: Elective course

Specific Goals for the course:

  • Student learning outcomes - Upon successful completion of this course the student shall be able to:
    • Determine the natural dynamic response of a linear structure to initial conditions.
    • Determine the forced dynamic response of a linear structure to various types of time-varying loads.
  •  Relationship of course to program outcomes
    • Outcome 1: An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.

Topics:

  • Single-degree-of-freedom systems
    • Equations of motion, natural frequency, D’Alembert’s principle, energy method, principle of virtual displacement.
    • Free vibration - Undamped systems: simple harmonic motion, equivalent stiffness, Rayleigh’s method. Damped free vibration: viscous damping, logarithmic decrement, Coulomb damping.
    • Harmonic excitation - Undamped system, beating, resonance. Damped system, steady-state response, experimental determination of damping, rotating unbalance, base excitation, vibration isolation, transmissibility, vibration transducers, equivalent viscous damping, hysteresis damping. General periodic excitation.
    • Arbitrary dynamic excitation - Response spectrum, ideal step force, rectangular pulse force, step force with a ramp, triangular pulse force, impulsive force, Duhamel integral, earthquake excitation.
  • Multi-degree-of-freedom systems
    • Free vibration - Flexibility matrix, stiffness matrix, mass matrix, equations of motion, eigenvalue problem in vibration analysis, natural frequencies, natural modes, orthogonality of the natural modes, rigid body modes, generalized mass and stiffness matrices, response to initial conditions.
    • Approximate methods for estimating the fundamental frequency - Rayleigh’s method, inverse iteration, forward iteration.
    • Mode superposition - Mode displacement method for undamped systems, modal participation factor, systems with classical damping, response to support motions, response spectrum analysis, earthquake excitation.