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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   Derivation of Miles Equation  Miles.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  Enveloping Data via the Vibration Response Spectrum  envelope.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

VRS Software  Description   Executable   Source Code Vibration response spectrum of a single-degree-of-freedom system subjected to base excitation.   vrs.exe   vrs.cpp Conversion of a vibration response spectrum to a power spectral density.  vrs_to_psd.exe vrs_to_psd.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  Miles.m  Vibration Response Spectra Matlab Code  VRS.m Functions: calculate_PSD_slopes.m vrs_engine.m AVRS_plot.m