Measuring and Calculating the Dynamic Response of Simple Structures AOE 3054 E. Nikolaidis

Outline 1Introduction 2Analysis of Dynamical Behavior of Structures 3Dynamic Testing of Structures 4Summary/Concluding Remarks

1 Introduction a. Dynamic loading Dynamic means time varying Examples: Aircraft wing-gust loads Offshore platform-waves Car on rough pavement Earthquake loads

Terminology Vibration: ?

b. Static versus dynamic analysis Static Constant load, response No inertia forces Dynamic ? Inertia forces

c. Steps in a dynamical investigation Design Analysis Testing/correction of model Redesign

2 Analysis of Dynamical Behavior of Structures Define ? model Derive ? model Solve for dynamical behavior

3 Dynamical Testing of Structures Why dynamical testing: ?

Full-scale structure Reduced scale physical models (use in early design stages)

Frequency response function Basic property of linear systems: Sine in-Sine out S cos(  t) ?

Beam that can be modeled as a SDOF system

Observations  =0 then ? At resonance: Amplitude ratio=Q=AK=1/2  Phase angle= ? For frequencies of excitation much higher than natural frequency the response amplitude is close to zero

Example: Large space structures

4 Summary/Concluding Remarks Dynamic loading Steps in dynamical investigation Test Motivation Examples