Source/Cause of a second-order response

Lingfeng Su · November 6, 2018, 03:14

Hi guys, I have a question here.

When I generate a linear wave to excite a floating body, the wave-induced loads acting on the body present not only the first-order resonance frequency but also another peak at the second-order frequency through FFT method. So I want to know what may be the causes of this second order response, or what may be the sources of the second order response.

Cheers!

FMDenaro · November 6, 2018, 12:46

Quote:

Originally Posted by Lingfeng Su

Hi guys, I have a question here.

When I generate a linear wave to excite a floating body, the wave-induced loads acting on the body present not only the first-order resonance frequency but also another peak at the second-order frequency through FFT method. So I want to know what may be the causes of this second order response, or what may be the sources of the second order response.

Cheers!

You should provide more details about your flow problem and the set of equations you are using.
Also some results would be useful.

Lingfeng Su · November 6, 2018, 20:18

Quote:

Originally Posted by FMDenaro

You should provide more details about your flow problem and the set of equations you are using.
Also some results would be useful.

Hi,

What I questioned is about fluid mechanics or hydrodynamics, not only about computational fluid dynamics.

I generated linear wave by wave makers in physical wave tank, force transducer is installed and monitored the wave-induced loads acting on the floating body excited by the generated wave. But after analyzing the measured loads, it presents a first-order and a second-order frequency shown in frequency plot.

There is nothing about the equations that describe the flow and any other environmental condition.

Cheers

agd · November 6, 2018, 22:13

FMDenaro's point still stands even if you leave out the CFD aspect. The explanation of the physics is contained in the equations of motion. For example, is the governing equation of the body in motion truly linear? Is the disturbance you input represented by a single harmonic, or can the linear input (not sure what that means for a wave, since there are several ways to interpret that) be decomposed into a sum of harmonics? There are a number of possible answers to your query, but they all start with the mathematical description of your problem.

Lingfeng Su · November 6, 2018, 23:14

Quote:

Originally Posted by agd

FMDenaro's point still stands even if you leave out the CFD aspect. The explanation of the physics is contained in the equations of motion. For example, is the governing equation of the body in motion truly linear? Is the disturbance you input represented by a single harmonic, or can the linear input (not sure what that means for a wave, since there are several ways to interpret that) be decomposed into a sum of harmonics? There are a number of possible answers to your query, but they all start with the mathematical description of your problem.

Hi there

Thank you for your reply. My point is what could be the reason that may trigger a nonlinearity of the loads due to a regular linear wave excitation. E.g. may be the nonlinear body motion (nonlinear damping/restoring, even though here the motion is regarded as linear), or asymmetric geometry of immersed part of the body, or coupled motion among 6 DOFs, etc.

Brainstorming......

Cheers

FMDenaro · November 7, 2018, 02:22

There is nothing of linear in a real experiment. Again, the mathematics of the equations can explain the physics you observe. If you consider the 1D Burgers equation and start from a single wave at a unique wavenumber, the solution evolves producing more waves at increasing wavenumbers.
Your case is simply not linear

blackjack · November 7, 2018, 13:52

Whenever I perform an oscillatory potential-flow analysis, I observe a double-frequency response.

For example, consider a symmetric, non-moving airfoil at zero angle of attack subject to a low-frequency, sinusoidal gust normal to the chord.

When the gust velocity is most up, the normal force is positive, and (because the drag is small and the lift normal to the velocity) the force along the chord is in the direction of the leading edge.

When the gust velocity is most down, the normal force is negative, but the force along the chord is again in the direction of the leading edge. In fact, the oscillatory chordwise force is at twice the frequency of the gust and directed toward the leading edge. A fourier analysis of the pressure distribution clearly shows the double-frequency harmonic in the pressure.

When I am becalmed on my sailboat I can propel the boat forward by shifting my weight from side to side to make the boat roll, the wing keel is then "flapping" from side to side and generates thrust. I will also add that the rotation of the earth is once per day, but the tidal response of the ocean is twice per day (two high tides and two lows).

A double-frequency response can be obtained because it is the product of two fundamental frequency quantities (wave velocity*body motion) or a double-frequency pressure distribution.

November 6, 2018, 03:14	Source/Cause of a second-order response	#1
Lingfeng Su New Member Join Date: May 2015 Posts: 13 Rep Power: 10	Hi guys, I have a question here. When I generate a linear wave to excite a floating body, the wave-induced loads acting on the body present not only the first-order resonance frequency but also another peak at the second-order frequency through FFT method. So I want to know what may be the causes of this second order response, or what may be the sources of the second order response. Cheers!

November 6, 2018, 22:13		#4
agd Senior Member Join Date: Jul 2009 Posts: 353 Rep Power: 18	FMDenaro's point still stands even if you leave out the CFD aspect. The explanation of the physics is contained in the equations of motion. For example, is the governing equation of the body in motion truly linear? Is the disturbance you input represented by a single harmonic, or can the linear input (not sure what that means for a wave, since there are several ways to interpret that) be decomposed into a sum of harmonics? There are a number of possible answers to your query, but they all start with the mathematical description of your problem. FMDenaro likes this.

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November 7, 2018, 02:22		#6
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	There is nothing of linear in a real experiment. Again, the mathematics of the equations can explain the physics you observe. If you consider the 1D Burgers equation and start from a single wave at a unique wavenumber, the solution evolves producing more waves at increasing wavenumbers. Your case is simply not linear

November 7, 2018, 13:52		#7
blackjack Member james nathman Join Date: May 2011 Posts: 62 Rep Power: 14	Whenever I perform an oscillatory potential-flow analysis, I observe a double-frequency response. For example, consider a symmetric, non-moving airfoil at zero angle of attack subject to a low-frequency, sinusoidal gust normal to the chord. When the gust velocity is most up, the normal force is positive, and (because the drag is small and the lift normal to the velocity) the force along the chord is in the direction of the leading edge. When the gust velocity is most down, the normal force is negative, but the force along the chord is again in the direction of the leading edge. In fact, the oscillatory chordwise force is at twice the frequency of the gust and directed toward the leading edge. A fourier analysis of the pressure distribution clearly shows the double-frequency harmonic in the pressure. When I am becalmed on my sailboat I can propel the boat forward by shifting my weight from side to side to make the boat roll, the wing keel is then "flapping" from side to side and generates thrust. I will also add that the rotation of the earth is once per day, but the tidal response of the ocean is twice per day (two high tides and two lows). A double-frequency response can be obtained because it is the product of two fundamental frequency quantities (wave velocity*body motion) or a double-frequency pressure distribution.