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f = C * SQRT[(E.I/M.L^4)(1+Seff/Pcr+C.(d/D)^2]

C = Constant dependant on boundary conditions of span

E = Youngs modulus

I = Second moment of area (piping)

M = Mass

L = Span length

Seff = Axial force in piping

Pcr = Critical buckling load

d = deflection

D = piping diameter

The axial force in the piping is negative, due to the temperature and pressure, and I'm trying to perform a conservative calculation assuming the piping is fully restrained. This results in a negative term in the square root. Is it possible to have a negative natural frequency?

The natural frequency is coming out as -0.5 i Hz (i being sqrt(-1)).

Any help or guidance appreciated. Thanks