Nomenclature
A s= cross-sectional area of suction line, m 2 A th = nozzle throat area, m 2 C f = thrust coefficient, dimensionless g = standard gravitational acceleration, m=s 2 h s = height of propellant in suction line, m h t = height of propellant in tank, m I s = inertance of propellant in suction line, s 2 =m 2 K = effective stiffness of accumulator which is defined as K a K p =K a K p , 1=m 2 K a = stiffness of the accumulator, 1=m 2 K p = stiffness of pump cavitation, 1=m 2 k = the ratio between effective stiffness and stiffness of accumulator defined as K =K a , dimensionless L = length, m M s = modal mass of structure mode, kg i, j, n = index, dimensionless m 1 = pump gain, dimensionless N = number of thrust chambers, dimensionless p = oscillatory pressure, Pa R c = linearalized combustion resistance for propulsion flow perturbation, s=m 2 w = weight displacement of flow, N = mass flow gain factor of a pump, s = the propulsion modal damping coefficient, dimensionless = dimensionless mass flow gain factor of a pump defined as , dimensionless = couple strength between the structure mode and the propulsion system, dimensionless = frequency ratio between the propulsion mode and the structure mode, dimensionless = the structure damping ratio, dimensionless = density of the propellant, kg=m 3 ' = structural mode gain, dimensionless = circular natural frequency of the structure mode, 1=s ! = circular natural frequency of the propulsion mode, 1=sSubscripts c = combustion chamber p = pump s = suction line t = tank
