Fundamentals of Dynamics
    Lecture 5
    Arch 721, Structural Design for Dynamic Loads, University of Virginia
     Copyright © 1996-2006 Kirk Martini. 05-Nov-2007 9:05     		Table of
    Contents
    Today's Topics

    • Pre-lab 3 Discussion
    • Photographs of the U-building

    • Fundamentals of Dynamics: Single Degree of Freedom Systems
      • Motion: displacement, velocity, and acceleration
      • Mass, stiffness, and period of vibration
      • Free vibrations and damping
      • Forced vibrations and resonance

    Single Degree-of-Freedom Systems

    A restoring force returns an object to its original position
         In a pendulum, the restoring force is provided by gravity. In a structure, it is provided by the tendency of material to return to its original shape.
    A system with mass and a restoring force will oscillate when loaded.
         The oscillation results from the interaction of the restoring force and the inertia of the mass
    The simplest oscillating system is a Single Degree of Freedom System (SDOF)
         In a single degree of freedom system, the deformation of the entire structure can be described by a single number equal to the displacement of a point from an at-rest position.


    EERC
    EERC

    KM

    Concepts and Terms

    Displacement
    Motion from one point to another, described by a vector of distance and direction, with units of length (e.g. feet or meters).
    Velocity
    The rate that displacement changes with time, described by a vector of speed and direction, with units of length per time (e.g. feet per second).
    Acceleration
    The rate that velocity changes with time, described by a vector of speed-change rate and direction, with units of length per time per time (e.g. feet per second per second; this can also be viewed as units of velocity per time).
    Period
    The duration of one cycle of motion.
    Natural period of vibration
    The time required for a freely vibrating structure to complete one cycle of motion.
    Frequency
    The number of cycles of motion completed during a unit time interval (i.e. cycles per second). Frequency is the inverse of Period (i.e. a structure with a natural period of 0.2 seconds has a natural frequency of 5 cycles per second).
    Amplitude
    The maximum value of a periodic function (which may be displacement, velocity, acceleration, etc.)
    Free vibration
    When a structure vibrates without any externally applied forces, such as when it is pulled out of position, and then released.

    KM
    Forced vibration
    When a structure vibrates under the influence of an external force.

    KM
    Periodic load
    A loading pattern that repeats over a regular period of time.
    Impulse load
    A very short-term load (e.g. heel drop, or blast).
     
    Damping
    The dissipation of energy that causes the amplitude of motion of a freely vibrating structure to decrease with each cycle, with the motion eventually dying out. The term damping is broadly applied to energy dissipation mechanisms that are not associated with structural damage. (e.g. friction and microcracking)
    Resonance
    The amplification of response that occurs under forced vibration when the period of the applied force is close to the natural period of the structure.
    Arch 721, Structural Design for Dynamic Loads, University of Virginia
     Copyright © 1996-2006 Kirk Martini. 05-Nov-2007 9:05    		 Table of
    Contents