Free vibration analysis of liquid-filled open rectangular containers

•Analytical method to calculate the natural frequencies of partially liquid-filled open container with flexible bottom were developed.•The comparison showed excellent agreement between the results from the proposed theoretical method with the results.•The effect of the liquid level on the natural frequencies of the liquid-filled open container is investigated.

The analytical method to calculate the natural frequencies of an open rectangular container partially filled with water is suggested. The wet dynamic displacements of the U-shaped container are approximated by combining the orthogonal polynomials. The liquid displacement potentials describing the Laplace equation are deduced so that the liquid boundary conditions can be satisfied. The relationship between the structure and liquid is derived by the compatibility requirement using the finite Fourier transform. An eigenvalue problem based on the Rayleigh–Ritz method is derived to extract the natural frequencies of the wet rectangular container. The predictions from the proposed analytical method show an excellent agreement with the finite element analysis results.