《ABAQUS动力分析资料(台湾大学教学资料)》.pdf

LECTURE VII—DYNAMIC ANALYSIS When is needed? (不or 狀 1 (Excitation freq. ≥ Fundamental freq. / 3) Ω ≥ ω ex 3 1 Peak dynamic response / static response 1 Classification of Dynamics Problems Wave propagation problems Loading: impact Excitation structural response are rich in high frequencies Interests: stress wave effects Time duration of analysis: short (the order of a wave traversal time across a structure) Structural dynamics problems The inertia is important 1 Ω ≈ ω ex 3 1 Interests: (1) Natural frequencies of vibration and the corresponding mode shapes (2) Time-history analysis: how a structure moves with time STRUCTURAL DYNAMICS Equations of Motion .. ρu σ +ρb i ij,j i Weak Form .. ρu δu dV σ δu dV + ρb δu dV ∫ i i ∫ ji ,j i ∫ i i V V V 1424 434 (Gauss theorem ) .. ρu δu dV + σ δu dV ρb δu dV + t δu dS ∫ i i ∫ ji i,j ∫ i i ∫i i V V V S Damping Effects (Viscous Damping) .. . (ρu δu +κ u δu +D u δu )dV ρb δu dV + t δu dS ∫ i i d i i ijkl k ,l i,j ∫ i i ∫i i V V S Interpolation (Separation of Variables) N N N n . n . .. n .. ui ∑uiα(t)Nα(ξ,η,ξ)