A harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, proportional to the displacement. If a frictional force damping proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. If the system contained high losses is called overdamped.
Commonly, the mass tends to overshoot its starting position, and then return, overshooting again. With each overshoot, some energy in the system is dissipated, and the oscillations die towards zero.
This case is called underdamped. Between the overdamped and underdamped cases, there exists a certain level of damping at which the system will just fail to overshoot and will not make a single oscillation.
This case is called critical damping. The key difference between critical damping and overdamping is that, in critical damping, the system returns to equilibrium in the minimum amount of time.
The Critical damping coefficient is depended on the mass of the oscillated body. Dynamics Statics. External links Wikipedia. Solver Browse formulas Create formulas new Sign in. Critical Damping Coefficient. Solve Add to Solver. Description A harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, proportional to the displacement.
Related formulas. Categories Dynamics Statics External links Generator diamond. Recently viewed formulas.I need to solve a trouble with Ansys WB I have to do a damped modal analysis, and so I need to set the damping values somewhere.
I read in an official Ansys guide referred to However, if I try with the first option, an error message is generated:. Moreover, how can I introduce directly the Damping coefficient ratio that is funcion of alpha and beta coefficients? I have the R17 Dynamics lectures, so I used some of that at the top and added R18 snapshots at the bottom. Note that the coefficients are a function of frequency.
There is also Constant material damping that is independent of frequency.
One model can have both types of damping. The Analysis Settings provide the same ability to define damping as R17 when using materials that have not had damping added. When I left these values at zero, and added damping to the material, the solver gave me the same results. Hello,here I have another problem. Now have the value of modal damping ratio, which is 0. Sofirstly, the value of frequency how I should input.Calculate Damping Factor / Coefficient, Structural Dynamics for Damped Free Vibration Example 4
The Damping Ratio is not a constant, but a function of frequency. If you want a relatively constant damping ratio between two frequencies, then you select the coefficients according to the formula shown in my last post. Say in addition to 30 Hz, you also want 10 Hz to be at 0. Note: it is better for you if you start a New Discussion, rather than tack on to the bottom of an old discussion.
The reason is you will be notified of replies if you start the discussion. In this situation, you have to remember to check back to see if there is a reply. Autonewbie, you add damping to the model for harmonic response or transient structural using data acquired from experiments on the structure. If you know the first natural frequency of the structure, you can excite that with a hammer strike, and using the log-decrement method, calculate a damping ratio for that frequency.
Then you can make a hammer strike at a different location, in a different direction to excite the second natural frequency and record with an accelerometer the acceleration-time history and compute the damping ratio of the second natural frequency.Answer: Mass- and stiffness-proportional dampingnormally referred to as Rayleigh damping, is commonly used in nonlinear-dynamic analysis.
Suitability for an incremental approach to numerical solution merits its use. During formulation, the damping matrix is assumed to be proportional to the mass and stiffness matrices as follows:. Relationships between the modal equations and orthogonality conditions allow this equation to be rewritten as:.
Here, it can be seen that the critical-damping ratio varies with natural frequency.
According to the equation above, the critical-damping ratio will be smaller between these two frequencies, and larger outside.
When damping for both frequencies is set to an equal value, the conditions associated with the proportionality factors simplify as follows:. All rights reserved. Powered by Atlassian. Technical Knowledge Base. Page tree. Browse pages. A t tachments 4 Page History Scaffolding History.
Copy with Scaffolding XML. Dashboard Home Damping. Jira links. Created by Ondrejlast modified on May 30, What values should I use for mass- and stiffness-proportional damping? When damping for both frequencies is set to an equal value, the conditions associated with the proportionality factors simplify as follows: References Wilson, E.
Static and Dynamic Analysis of Structures 4th ed. Powered by Atlassian Confluence 6.Hot Threads. Featured Threads. Log in Register. Search titles only. Search Advanced search…. Log in. Forums Engineering Mechanical Engineering.
Hi, I have been looking for formulae for the damping coefficient, and I found two different formulae for it. Related Mechanical Engineering News on Phys. Hesch Gold Member. Is there a fixed definition for damping coefficient, or are both definitions acceptable?
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According to the equation, I need to know what k is and what the mass is What am I overlooking? Your equations are either confusing or wrong. What is k? Have you been given anything other than those?
Since its a hard problem, I assume its a physics class that assumes calculus knowledge, especially since you're required to find damping coefficient. Usually such a problem leads to damped exponential SHO. Do you know solutions for differential eqns? Mindscrape, I wasn't offered any equations for this problem, I am just trying to use the info from my text book to solve for this problem. I found an equation that might be helpful.
Last edited by a moderator: May 2, Is the n the number of oscillations? Should the coefficient, or rather can the coefficient be negative? Also, my answer is considered wrong, so that is why I am wondering if its the sign or if I did something wrong.
Yes, I got a positive value. However, I forgot to mention that the problem wants the damping coefficient in Hz.Specify damping for modal dynamic analysis. This option is used to specify damping for mode-based procedures. Type History data. Level Step. Include this parameter to select structural damping, which means that the damping is proportional to the internal forces but opposite in direction to the velocity.
The value of the damping constant, sthat multiplies the internal forces is entered on the data line. The data lines after the keyword line specify the modal damping values to be used in the analysis. Frequency ranges can be discontinuous. Mode number of the highest mode of a range. If this entry is left blank, it is assumed to be the same as the previous entry so that values are being given for one mode only. Scaling factor for the mass weighted fraction of composite critical damping calculated in the frequency analysis.
If omitted, the default value is 1. If the mass weighted fraction is excluded from the analysis, enter a value of 0. Only relevant in SIM -based analyses. Scaling factor for the stiffness weighted fraction of composite critical damping calculated in the frequency analysis. If the stiffness weighted fraction is excluded from the analysis, enter a value of 0.
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up. Where c is the 'viscous damping coefficient' of the spring, according to Wikipedia.
How is the value of c calculated though? Is it a constant for the air through which the spring is moving or does it depend on the spring itself? I'm just looking at the oscillation of a spring vertically, and I have data for its decreasing amplitude, and the velocity of the spring at all points. I have the value of the damping ratio, and I'm trying to find the value of 'c' in order to prove the above equation in an investigation.
Damping coefficient formulae
Or plot log amplitude versus time on linear--linear graph paper. Then extract the slope. If it is a spring in air, then it is likely to be proportional both to the viscosity of the air and to the relevant area of the the spring leading to the damping. For low speeds in air you can probably use Stokes' approximation. Structural Damping. As the material flexes in cycles, there is internal losses that occur due to a hysteresis effect on the force-deflection relationship.
This is a small but noticeable effect. Contact friction. The spring is not floating in space by itself, but is in contact with other objects like spring retainers and tappets.
Where there is contact there is energy loss due to friction. If it is dry friction there is an equivalent damping coefficient calculated that depends in the frequency and amplitude of the oscillation any vibrations book has it. If it is viscous friction then the damping coefficient depends on the laminar shearing of the fluid any fluid dynamics book at some point relates viscous coefficient to damping based on geometry.
An finally as you mentioned there is aerodynamic drag that contributes to damping. This is the most difficult to calculate as you need to run a CFD simulation as the spring moves. The combined effect can be measured and tested with a log decrement method. Hit the spring hard and measure the amplitude as a function of time. If you count the relative decrease and the of cycles you can use that to calculate and overall effective damping coefficient.
This was first mentioned by other answers already. You can't "prove" the equation since the equation is actually the definition of zeta, which is not a physical parameter. M, c, and K are all physical parameters that could actually be measured for a simple harmonic oscillator with a lumped mass, a massless spring, and an ideal dashpot.
In some messy real world situations with springs that have mass and damping, it might be easier to use something like the aforementioned log decrement method, or some other method, to estimate the decay rate, and from that get a value directly for zeta.