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Body loads in wave propagation..

ramdas chennamsetti's picture

Hi all,

[1] In solids, the wave propagation equation is obtained from stress equilibrium equations. We make use of constitutive and strain-displacement relations to convert these equations in terms of displacements

[2] In the above equations we assume that there are no body loads.

[3] The form of solution we assume for displacements is harmonic

[4] Plug these three displacements, u1, u2 and u3 in the equilibrium equations stated in [1].

[5] We end up with an Eigenvalue problem. This is nice.

[6] If body loads are present, then, it will no more an Eigenvalue problem. I haven't seen any test book /literature dealing with such problem.

Has anybody tried solving the wave equation with body loads. If so, you may please write me and suggest me some literature on this.

Thanks in advance.

- Ramdas

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ramdas chennamsetti's picture

R. Chennamsetti, R&DE(E), INDIA

Hi all,

In continuation with my earlier post, when the body loads are present, we will end up with system (three) of non-homogeneous algebraic equations, which can be solved for amplitudes of harmonic displacements.

I haven't seen any text book/literature dealing with body loads with wave propagation.

Are these body loads too small, so that one can neglect??

Thank you in advance,

- Ramdas

Ramdas,

I don't think the body force problem can be reduced to a straightforward eigenvalue problem.   The  body force acts as a forcing term.  For free vibrations you can ignore the body force term and that's what most analytical solutions are for. 

The body force term can be very important in applications such as large windmills or high-speed turbines and also in certain parts that move in strong magnetic fields such as MRI machines. People have tried to solve the problem using analytical methods for simple geometries (see e.g. Pan and Pan, Structural intensity of torsional vibration in solid and hollow cylindrical bars, The Journal of the Acoustical Society of America, 1998, Volume 103, Issue 3, pp. 1475-1482) or using numerical methods.

Perhaps Zhigang and others who teach elasticity and vibrations can further illuminate us on this issue.

ramdas chennamsetti's picture

R. Chennamsetti, R&DE(E), INDIA

Dear Sir,

Thank you. Yes, the body loads like force due to magnetic field, centrifugal force are important in high speed rotating machines. Compared to these, we may fairly neglect body load due to acceleration due to gravity.

With regards,

- Ramdas

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