Dynamic analyses of liquid storage tanks

Theoretical and experimental investigations of the dynamic behavior of cylindrical liquid storage tanks are conducted to seek possible improvements in the design of such tanks to resist earthquakes. The study is carried out in three phases: 1) a detailed theoretical treatment of the liquid-shell system, 2) an experimental investigation of the dynamic characteristics of full-scale tanks, and 3) a development of an improved design-procedure based on an approximate analysis. Natural frequencies of vibration and the associated mode shapes are found through the use of a discretization scheme in which the elastic shell is modeled by finite elements and the fluid region is treated as a continuum by boundary solution techniques. In this approach, the number of unknowns is substantially less than in those analyses where both tank wall and fluid are subdivided into finite elements. A method is presented to compute the earthquake response of both perfect circular and irregular tanks; it is based on superposition of the free lateral vibrational modes. Detailed numerical examples are presented to illustrate the applicability and effectiveness of the analysis and to investigate the dynamic characteristics of tanks with widely different properties. Ambient and forced vibration tests are conducted on three full-scale water storage tanks to determine their dynamic characteristics. Comparison with previously computed mode shapes and frequencies shows good agreement with the experimental results, thus confirming the reliability of the theoretical analysis. Approximate solutions are also developed to provide practicing engineers with simple, fast, and sufficiently accurate tools for estimating the seismic response of storage tanks.