SHOCK AND VIBRATION STRESS AS A FUNCTION OF VELOCITY Revision D By Tom Irvine Email: tomirvine@aol.com December 11, 2012 ______________________________________________________________________________ Variables Distance to neutral axis Area moment of inertia = I = c = Wave speed in the material K = Shear factor thickness Length h = L = Spring stiffness or wave Bending moment k = M = number depending on context u = Displacement U = Total energy v = Velocity V = Shear force Longitudinal Displacement Base acceleration x = = z = Transverse Displacement = Normal stress A = Cross section area = Shear stress Constant of proportionality Mass per volume = = Plate stiffness factor Mass per length D = = E = Elastic modulus = Phase angle G = Shear modulus = Natural frequency (rad/sec) n Note that the characteristic impedance is Introduction Shock and vibration environments produce dynamic stresses which can cause material failure in structures. The potential failure modes include fatigue, yielding, and ultimate stress limit. F.V. Hunt wrote a seminal paper on and Stress Limits on the this subject, titled “Stress Attainable Velocity in in 1960 in Reference 1. This paper Mechanical Vibration,” published gave the relationship between stress and velocity for a number of sample structures.
SHOCK AND VIBRATION STRESS AS A FUNCTION OF VELOCITY Revision D By Tom Irvine Email: tomirvine@aol.com December 11, 2012 ______________________________________________________________________________ Variables = Distance to neutral axis I = Area moment of inertia c = Wave speed in the material K = Shear factor h = thickness L = Length k = Spring stiffness or wave number depending on context M = Bending moment u = Displacement U = Total energy v = Velocity V = Shear force x = Longitudinal Displacement = Base acceleration z = Transverse Displacement = Normal stress A = Cross section area = Shear stress = Constant of proportionality = Mass per volume D = Plate stiffness factor = Mass per length E = Elastic modulus = Phase angle G = Shear modulus n = Natural frequency (rad/sec) Note that the characteristic impedance is Introduction Shock and vibration environments produce dynamic stresses which can cause material failure in structures. The potential failure modes include fatigue, yielding, and ultimate stress limit. F.V. Hunt wrote a seminal paper on this subject, titled “Stress and Stress Limits on the Attainable Velocity in Mechanical Vibration,” published in 1960 in Reference 1. This paper gave the relationship between stress and velocity for a number of sample structures.
sv_velocity_revD.docx