Wire Rope Cable Damping

Wire rope damping depends on:

1. Material
2. Diameter
3. Length
4. Number of strands
5. Number of turns per length
6. Initial tension or preload
7. Displacement amplitude

The damping can be very nonlinear, particularly depending on displacement amplitude.

The flexing of wire rope involves both coulombic and viscous damping. At very low vibration levels, the wire strands stick together and little sliding occurs. The damping is low and the behavior is viscous.

With higher displacements, coulomb damping predominates as the wires break free and start to slide against each other, absorbing large amounts of energy.

At large displacements the bending and stretching of the wire strands overshadows the sliding friction and viscous behavior again starts to show.

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Here are some viscous damping values for straight cables.

Longitudinal Vibration for 10 mm (0.39 inch) diameter:
Damping = 0.7% to 2.0% (ref 1)

Transverse Vibration for 3/8 inch diameter:
Damping = 0.3% to 0.5% (ref 2)

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For the case of wire rope used in helical isolators, the damping can vary from 5% to 22% (ref 3).

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Wire Rope Isolation of a Camera Video

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1. Feyrer, Wire Ropes: Tension, Endurance, Reliability

2. Vanderveldt, Chung and Reader, “Some Dynamic Properties of Axially Loaded Wire,” Experimental Mechanics, 1973.

3. http://www.enidine.com/Industrial/WireFAQmain/#14

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See also:

Initial investigations into the damping characteristics of wire rope vibration isolators

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– Tom Irvine

FRF Substructuring

This post is a work-in-progress…

Frequency Response Function based substructuring (FBS) predicts the dynamic behavior of a coupled system on the basis of free interface FRFs of the uncoupled components.

Here is a tutorial paper:  Frequency Response Function Substructuring 

Modal damping requires special consideration:  Notes on Damping in FRF Substructuring

This script sets up the initial mass and stiffness matrices for the systems in the tutorial paper: spring_mass_series.m

See also:

Transfer Functions from Normal Modes

Joint Receptance for Rigid & Elastically Coupled Subsystems

Matlab script: joint_receptance.m

Reference Papers

K. Cuppens, P. Sas, L. Hermans, Evaluation of the FRF Based Substructuring and Modal Synthesis Technique Applied to Vehicle FE Data:   Download

Dr. Peter Avitabile, Impedance Modeling & Frequency Based Substructuring:  Download

Matthew S. Allen, Randall L. Mayes, Comparison of FRF and Modal Methods for Combining Experimental and Analytical Substructures: Download

Randy L. Mayes, Patrick S. Hunter, Todd W. Simmermacher, Matthew S. Allen , Combining Experimental and Analytical Substructures with Multiple Connections:  Download

Mladen Gibanica, Experimental-Analytical Dynamic Substructuring, A State-Space Approach:  Download

Convert Modal Damping to a Damping Coefficient Matrix

Here is a method for converting modal damping to a damping coefficient matrix for all modes.  It is based on a pseudo inversion of the modal damping matrix.

The resulting coefficient matrix will be fully populated. The damping terms will not necessary corresponding to physical dashpots, but the modal damping will be fully represented. This is useful for the case where a direct solution method will be used, such as the Newmark-beta method.


Here is a Matlab script: c_matrix.zip

– Tom Irvine

Vibration Absorbers & Tuned Mass Dampers


A vibration absorber is a tuned spring-mass system which reduces the vibration of a harmonically excited system.

Here is a paper for an applied force:  Vibration Absorber

Here is a Matlab script and its supporting function:  vibration_absorber_trans.m


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Here is a paper for base excitation: Vibration Absorber Base Excitation

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See also:

The London Millennium Bridge Vibration

Taipei 101 Building Tuned Mass Damper

The Citicorp Building Tuned Mass Damper

– Tom Irvine

Tall Building Natural Frequencies and Damping


The Transamerica Pyramind has a Fundamental Frequency of 0.3 Hz

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Here are some papers which give natural frequencies and damping values for sample tall buildings:

Damping in Tall Buildings and Towers: tall_building_damping.pdf

The Damping Characteristics of Bolted and Welded Joints: bolted_joint_damping.pdf

Transamerica Pyramid Design: pyramid.pdf

NESC Academy Audio/Visual File: Building Natural Frequencies

– Tom Irvine

Fluid Structure Coupling Damper

Here is a project that my NASA colleagues have been working on:  FSC_damper.pdf

The original goal of the project was to use the Ares I second stage as a LOX damper to mitigate the first stage  thrust oscillation.

See also:


– Tom Irvine

Half-Power Bandwidth Method

The half-power bandwidth method can be used to estimate the damping ratio and corresponding Q value from the frequency response function of a structure which has been excited by base motion or an applied force.  The structure may be a multi-degree-of-freedom (MDOF) system as long as the modal frequencies are separated by a sufficient frequency margin so that the spectral peaks are distinct.

Here are some resources.



An Introduction to Frequency Response Functions: frf.pdf
(Download and then reopen to see full equations.)

Keyword:  frequency, resolution, damping, modal, FRF

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Matlab GUI scripts:

Force or Base Excitation, with Frequency Response Function Magnitude: half_power_bandwidth.zip

Force Excitation, with Complex Frequency Response Function:  half_power_bandwidth_fc.zip

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Here is a Matlab script that will perform a modal curve-fit for a multi-degree-of-freedom system. The script extracts modal frequencies and damping from a complex FRF. mdof_frf_curvefit.m

Supporting function: mdof_frf_curvefit_phase1.m

The method in these scripts is described in: mdof_frf_curvefit.pdf

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See also:

Damping Value Conversion Calculator

Vibrationdata Signal Analysis Package – modal FRF option

Vibration Isolation Basics

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Here is a newsletter with an example of the half-power bandwidth method applied to the Ares-1X roll-out: May2010_NL.pdf

– Tom Irvine

Contact Form:

Damping Value Conversion Calculator

Here is a Matlab GUI script which converts between various damping metrics:  damping.zip

The supported metric include:

quality factor Q
fraction of critical damping [zeta]
loss factor [eta]
3 dB Bandwidth [delta omega]
3 dB Bandwidth [delta f]
damping frequency [fd]
decay constant [sigma]
time constant [tau]
reverberation time [RT60]
decay Rate D
logarithmic decrement [delta]

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See also:

Damping, Isolation & Vibration Absorbers Page

Half-Power Bandwidth Method

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– Tom Irvine

Piezoelectric Shunt Damping

Piezoelectric shunt damping systems reduce structural vibration by shunting an attached piezoelectric transducer with an electrical impedance. Current impedance designs result in a coupled electrical resonance at the target modal frequencies.

Piezoelectric transducers (PZTs), in conjunction with appropriate circuitry, can be used as a mechanical energy dissipation device. If a simple resistor is placed across the terminals of the PZT, the PZT will act as a viscoelastic damper. If the network consists of a series inductor–resistor R–L circuit, the passive network combined with the inherent capacitance of the PZT creates a damped electrical resonance. The resonance can be tuned so that the PZT acts as a tuned vibrational energy absorber.

Here is a paper:


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– Tom Irvine