An Investigation into the Mode Superposition Method for the Foreced Transverse Vibration Analysis of Structures subject to the Timoshenko Beam Analogy

기준진동형중첩법(基準振動型重疊法)에 의한 Timoshenko보 유추(類推) 구조체(構造體)의 강제횡진동해석(强制橫振動解析)

The mode superposition method(MSM) for the forced transverse vibration analysis of structures subject to Timoshenko beam analogy, which had originally been developed by Ormondroyd and McGoldrick, is reviewed to formulate it in more general form taking account of rotary inertia, dampings in separate terms of internal and external ones, and simultaneous action of exciting forces and moments. To investigate some general features of the method in practical utilizations, resonant maximum amplitudes of 4 high speed ships under concentrated sinusoidal excitation at the stern are calculated by both MSM and the finite difference method(FDM). For the FDM the hulls are discretized into 40 equal segments, and in utilization of MSM contributions of the first six modes are summed up to obtain responses up to the six-nodes resonant mode. The numerical results show that MSM gives slightly higher values, $4{\sim}10%$, than those by FDM. Since there is always uncertainty in the damping estimation of actual systems, influences of the damping magnitude on resonant amplitudes and a practical method to estimate modal damping coefficients are discussed.