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Vibration Response Spectrum Page

INTRODUCTION

Mechanical shock pulses are often analyzed in terms of shock response spectra. The shock response spectrum assumes that the shock pulse is applied as a common base input to an array of independent single-degree-of-freedom systems. The shock response spectrum gives the peak response of each system with respect to the natural frequency. Damping is typically fixed at a constant value, such as 5%, which is equivalent to an amplification factor of Q=10.

A similar tool is available for vibration. This tool is the vibration response spectrum. This function gives the root-mean-square response of each system to an acceleration base input. The base input is an acceleration power spectral density.

The vibration response spectrum is particularly suited for random vibration inputs.

The vibration response spectrum has many uses, such as deriving and evaluating test specifications.

This page offers tutorials which explain the vibration response spectrum, as well as software tools for implementing this function.

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Vibraton Response Spectrum Tutorials

Introduction to the Vibration Response Spectrum	vrs.pdf
Use of the Vibration Response Spectrum to Evaluate Flight Data Compliance with Test Specification Levels	VRS_case_history.pdf
Derivation of Miles Equation for Base Excitation	Miles.pdf
Robert L. Towner, NASA Practical Approach for Random Load Factors PowerPoint Presentation, FEA model, and Hand-calculation notes.	RLF.pdf RandomLoadFactors.pdf
Derivation of Miles Equation for Relative Displacement Response to Base Excitation	Miles_rel_disp.pdf
Derivation of Miles Equation for Applied Force	Miles_force.pdf
Simmons, Miles Equation	Simmons_MilesEquation.pdf
Application of Miles Equation to Multi-degrees-of-freedom Systems (Refer to Section 3.2.1.2 of this Document)	mdof_miles.pdf
Robin Ferebee & Jess Jones, Comparison of Miles' Relationship to the True Mean Square Value of Response for a Single-degree-of-freedom System	Ferebee_Miles.pdf
Enveloping Data via the Vibration Response Spectrum	envelope.pdf
Deriving a Random Vibration Maximum Expected Level with Consideration for Kurtosis	envelope_kurtosis.pdf
Optimizing a Circuit Board Natural Frequency with Respect to Random Vibration. The optimization is achieved using the vibration response spectrum.	cb_opt_fn.pdf
Equivalent Shock and Vibration Tests for Quasi-static Acceleration	quasi_static_accel.pdf
Methods for Converting a Power Spectral Density to a Shock Response Spectrum	psd_srs.pdf
Equivalent Static Load for Random Vibration. The static load is taken from the three-sigma vibration response.	eqstatic.pdf
Partial Fractions in Shock and Vibration Analysis	partial.pdf

VRS Software

Description	Executable	Source Code
Vibration response spectrum of a single-degree-of-freedom system subjected to base excitation.	vrs.exe	vrs.cpp
VRS for a fixed frequency domain. This program is useful if the lower and upper natural frequency bounds of the component are known.	vrs_range.exe	vrs_range.cpp
Conversion of a shock response spectrum to a power spectral density	New method envelope_srs_psd.ex e Old method srs_to_psd.exe	New method envelope_srs_psd.cpp Old method srs_to_psd.cpp
Conversion of a vibration response spectrum to a power spectral density.	vrs_to_psd.exe	vrs_to_psd.cpp
Vibration response spectrum of an acceleration time history.	th_vrs.exe	th_vrs.cpp
Response of an individual single-degree-of-freedom system to base excitation PSD.	sdof_ran.exe	sdof_ran.cpp
Response of an individual single-degree-of-freedom system to an applied force PSD.	sdof_ran_force.exe	sdof_ran_force.cpp
Response of an individual single-degree-of-freedom system to base excitation via Miles equation.	miles.exe	miles.cpp
Peak SDOF response from the Rayleigh distribution	peak_response.exe	peak_response.cpp

Matlab Scripts
Miles Equation for Base Excitation	Miles.m
Miles Equation for Applied force	Miles_force.m
Vibration Response Spectra Matlab Code	VRS.m Functions: calculate_PSD_slopes.m vrs_engine.m AVRS_plot.m interpolate_PSD.m
Enveloping Data via the Vibration Response Spectrum	envelope.m Functions: env_vrs_best.m env_interp_best.m env_generate_sample_psd.m env_generate_sample_psd2.m env_compare.m env_grms_sam.m env_make_input_vrs.m env_vrs_sample.m env_interp_sam.m env_vrms_sam.m env_drms_sam.m env_checklow.m

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