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Modal Testing & Statistical Energy Analysis Page

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MODAL TESTING
An Introduction to Frequency Response Functions:  frf.pdf
The Impulse Response Function: impulse_response_function.pdf
Response of a Single-degree-of-freedom System Subjected to an Impulse Force: force_impulse.pdf

The Impulse Response Function for Base Excitation:  impulse_response_function_base.pdf
Nyquist and Nichols Plots: Nyquist_plot.pdf

The Steady-State Frequency Response Function of a Multi-degree-of-freedom System Subjected to Harmonic Base Excitation: mdof_FRF_base.pdf
Structural Dynamics Testing using an Impulse Force:  structd.pdf
This tutorial also covers use of the exponential window.

Exponential Windows: expw.pdf. Guest tutorial submitted by
G. Weber.

Effective Modal Mass & Modal Participation Factors: ModalMass.pdf

The Fundamentals of Modal Testing: modal_fund.pdf

Frequency Response Function Measurements: FRF_measurements.pdf


Kijewski and Kareem, Analysis of full-scale data from a tall building in Boston: damping estimates: boston.pdf

Richardson, Derivation of Mass, Stiffness and Damping Parameters From Experimental Modal Data: derivation_modal.pdf

Okuma, Heylen, Sas, Identification of Rigid Body Properties of 3-D Frame Structure by MCK Identification Method:  ident_MCK.pdf

See also:  Transfer_Functions
MODAL DENSITY
Modal Density:  mdens.pdf
Matlab Script: modal_density.m
STATISTICAL ENERGY ANALYSIS
Radiation & Driving Point Impedance of a Thin, Isotropic Plate: dp_impedance.pdf
Vibroacoustic Critical and Coincidence Frequencies of Structures: critical_frequency.pdf
Vibration Response of a Thin Cylindrical Shell to External Acoustic Pressure via Statistical Energy Analysis: SEA_cylindrical_shell.pdf
Matlab Scripts:
SEA_cylinder.m
SEA_plot.m
progressbar.m
Transmission loss through a single partition: single_partition.m
Transmission loss through a single partition using the plane wave method: single_partition_plane_wave.m
Fill factor for a payload fairing
fill_factor.m
octaves.m
Vibration Power Measurement using a Plate as a Reverberant Structure: VPthesis.pdf
Byam & Radcliffe, Statistical Energy Analysis Model and Connectors for Automotive Vibration Isolation Mounts: IsolMount.pdf
See also: Vibroacoustics
 Bruel & Kjaer Booklets
Structural Testing 1: Mobility Measurement
Structural Testing 2: Modal Testing

Software

Executable

Source
Digital filtering using a Butterworth 6th order filter. The user must supply an input time history file. Both lowpass and highpass options are available.
filter.exe
filter.cpp
Fast Fourier transform (FFT) of a time history. The transform operates on a time series with 2^n points, where n is an integer.
Also, corresponding inverse FFT.
fft.exe

invfft.exe
fft.cpp

invfft.cpp
Conventional Fourier transform of a time series with an arbitrary number of points.
fourier.exe
fourier.cpp
Zoom FFT of a time series.
zoomFFT.exe
zoomFFT.cpp
Cross-spectrum of two time histories. The output files may be used for modal test data analysis.
cross_spectrum.exe
cross_spectrum.cpp
Cross-spectrum of two time histories. The program generates H1 and H2 frequency response functions (FRFs), the coherence function, and the corresponding impulse response functions.
cross_spectrum_modal.exe
cross_spectrum_modal.cpp
This program generates a power transmissibility function for a single-degree-of-freedom subjected to a force input.
The transmissibility dimension is: ( accel^2 / force^2 )
 force_trans_modal.exe
 force_trans_modal.cpp
This program performs a curve-fit on an acceleration spectral function resulting from an applied force.

The main purpose is to determine the damping ratio.

The spectral function may be:
1. acceleration PSD
2. acceleration Fourier magnitude
3. transfer function magnitude (accel/force)
 
 bandwidth_damp.exe
 
bandwidth_damp.cpp
Driving point impedance of a thin plate, bending waves
dp_impedance.exe
-
Driving point impedance of a beam, longitudinal waves
dpi_beam.exe
-
Critical and Ring Frequencies of a Cylinder.
SEA_cylinder_parameters
-

Matlab Script
Calculate frequency & impulse response functions from an input force and response amplitude time history. frf_from_th.m

Supporting Functions:

fix_size.m

frf_median_filter.m
 Recommended Books
1. D.J. Ewins, Modal Testing: Theory and Practice
2. Lyon and Dejong, Theory and Application of Statistical Energy Analysis
3. L. Cremer and M. Heckl, Structure-Borne Sound
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