DAMPING CROSS-REFERENCE
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1 AMPING CROSS-REFERENCE There are at least eleven parameters commonly used to express damping. Cross-reference formulas are given in Tables A through C. The formulas are taken from Reference. Let be the natural frequency in units of radians per second. Note that is in units of Hertz. n π f n, where f n Table A. amping Reference Parameter 3 db Bandwidth (rad/sec 3 db Bandwidth (Hz (rad/sec π amping Frequency fd (Hz 4πfd Loss Factor (Hz amping Frequency fd (Hz Loss Factor Fraction of Critical amping π 4 π n n Quality Factor Q Q ecay Constant σ σ (/sec Time Constant τ (sec Reverberation Time RT 60 (sec ecay Rate (db/sec Logarithmic ecrement δ 3.8 RT π δ n π π Q π 4πfd πfd Q 4πfd π 4 π Q σ n σ π σ πfd π πfd RT 60 RT 60 RT 60 fd fd 4.34 δ π f n δ 4 π fd n δπ
2 Table B. amping Reference Parameter Fraction of Critical amping (rad/sec (Hz amping Frequency fd (Hz Loss Factor Fraction of Critical amping Quality Factor Q ecay Constant σ (/sec π π Quality Factor Q Q πq 4πQ Q Q Q σ σ Q ecay Constant σ (/sec σ σ π σ π σ σ n Q σ Time Constant τ (sec τ πτ πτ τ τ Q n τ σ τ Time Constant τ (sec Reverberation Time RT 60 (sec ecay Rate (db/sec Logarithmic ecrement δ 6.9 RT δ π Q 3.8Q RT Q π δ Q σ 6. 9 RT 60 σ 8. 68σ πσ δ RT τ 8.68 τ π δ τ
3 Table C. amping Reference Parameter Reverberation (rad/sec (Hz amping Frequency fd (Hz Loss Factor Fraction of Critical amping Quality Factor Q ecay Constant σ (/sec Time RT 60 (sec fd Q n σ 6. Time Constant τ (sec 90 Reverberation Time RT 60 (sec ecay Rate (db/sec Logarithmic ecrement δ δ ecay Rate (db/sec Q σ RT π δ 4.34 Logarithmic ecrement δ δ π δ π δ 4π δ π δ π π Q δ δ σ π π δ 43.4 RT 60 δ.38δ Reference. Svend Gade and Henrik Herlufsen, "igital Filter versus FFT Techniques for amping Measurement," Sound and Vibration, Bay Village, Ohio, March 990.
4 AMPING PROPERTIES OF MATERIALS The purpose of this tutorial is to give typical damping values for various materials and systems. The data in Tables and is taken from Reference. Table. Static Properties of Materials under Standard Conditions (approx. 0 C. Material ensity (kg/m 3 Elastic Modulus (N/m Shear Modulus (N/m Poisson s Ratio Aluminum (0 9 7 ( Lead,300 7 (0 9 6 ( Iron ( ( Steel ( ( Gold 9, (0 9 8 ( Copper ( ( Magnesium (0 9 7 ( Brass ( ( Nickel ( ( Silver 0, (0 9 9 ( Bismuth (0 9.3 ( Zinc (0 9 5 ( Tin (0 9.6 (
5 Table. ynamic Properties of Materials under Standard Conditions (approx. 0 C Material Propagation Velocity of Longitudinal Wave in a Rod Propagation Velocity of Torsional Wave Longitudinal Loss Factor Aluminum (meters/sec (meters/sec to 0 ( 0 5 Lead 5 to 30 0 Flexural Loss Factor 0 4 ( ( 0 (pure Lead (including to 4 ( 0 3 antimony Iron to 4 ( 0 4 to 6( 0 4 Steel to 3 ( 0 4 Gold ( Copper ( 0 3 ( 0 3 (polycrystalline Copper to 7 ( 0 4 (single crystal Magnesium Brass ( 3 0. to 0 < 0 3 Nickel < 0 3 Silver < 3 ( 0 3 Bismuth ( Zinc ( Tin ( Notes:. Some loss factors are unavailable.. The relationship between the loss factor and the viscous damping ratio ξ is: ξ.
6 The data in Table 3 is taken from Reference. Table 3. Representative amping Ratios System Viscous amping Ratio ξ Metals (in elastic range <0.0 Continuous Metal Structures 0.0 to 0.04 Metal Structure with Joints 0.03 to 0.07 Aluminum / Steel Transmission Lines Small iameter Piping Systems 0.0 to 0.0 Large iameter Piping Systems 0.0 to 0.03 Auto Shock Absorbers 0.30 Rubber 0.05 Large Buildings during Earthquakes 0.0 to 0.05 Prestressed Concrete Structures 0.0 to 0.05 Reinforced Concrete Structures 0.04 to 0.07 The data in Tables 4 through 6 is taken from Reference 3. Table 4. Material amping Ratios (Bare Structure System Reinforced Concrete Small Stress Intensity (uncracked Medium Stress Intensity (fully cracked High Stress Intensity (fully cracked but no yielding of reinforcement Viscous amping Ratio ξ to to to Prestressed Concrete (uncracked 0.04 to 0.07 Partially Prestressed Concrete (slightly cracked to 0.0 Composite 0.00 to Steel 0.00 to 0.00 C. 3
7 Table 5. Footbridge amping Construction Type Viscous amping Ratio ξ Min. Mean Max. Reinforced Concrete Prestressed Concrete Composite Steel Table 6. Building amping Construction Type Tall Buildings ( h > ~00 m Viscous amping Ratio ξ Min. Mean Max. Reinforced concrete Steel Buildings ( h ~ 50 m Reinforced concrete Steel The damping values in the tables should be used with caution. There are many types of damping, such as viscous, hysteresis, acoustic coupling, air pumping at joints, energy radiation to the soil, etc. Also, boundaries and bearings contribute damping. Furthermore, structures have many modes. Each mode may have a unique damping value. References. L. Cremer and M. Heckl, Structure-Borne Sound, Springer-Verlag, New York,
8 . V. Adams and A. Askenazi, Building Better Products with Finite Element Analysis, OnWord Press, Santa Fe, N.M., H. Bachmann, et al., Vibration Problems in Structures, Birkhauser Verlag, Berlin,
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