Analytical sloshing studies for rectangular container, how fourier series of x how they got it?

27 February 2017 0 8K Report

can any one help me,?

i have attached two images, in image b, i have highlighted one equation 2.110. how they get this equation from Fourier expansion.

and how from this equation and boundary condition can obtain the equation (phi) i,e 2.111. any idea can anyone tell me, or any paper can suggest me for this derivation step by step

thanks

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