Coupled free vibrations of liquid in a three-dimensional rectangular container with an elastic cover

The coupled free vibration of liquid and its elastic cover, such as a plate or membrane, in three-dimensional rectangular tank is investigated through an analytical scheme based on the velocity potential theory for flow linear cover. For fluid domain, expanded into double cosine series along longitudinal transverse directions, respectively, with corresponding eigenvalues determined from impermeable conditions side walls. vertical modes are obtained Laplace equation. deflection cover same to match potential, together additional terms satisfying edge conditions. polynomials used these terms, which then series. expansions higher-order derivatives deflection, polynomial directly, rather than being differentiating avoid non-convergent Through imposing boundary fluid–plate interface conditions, infinite matrix equation unknown coefficients can be established. natural frequencies when determinant zero. In practical computation, truncated finite size. Results first provided frequencies. This followed by mode shapes principal strains distribution underlying physics results provided.