Question

4-30. A torsional system consists of a shaft having a torsional spring constant kr = 12 800 N m /rad, a disk with a mass moment of inertia I = 8 kg.m, and a torsional damping device with a torsional damping constant Ct = 192 N.m s/rad. A harmonic torque with a maximum value of 480 N m produces a steady angular oscillation of 1.5-degree amplitude. (a) Determine the frequency of the impressed torque. (b) Obtain the maximum torque transmitted to the support

answer is

a)9.298 Hz

b) 445.6 N*m

but need steps

Answer 1

G. 2 K7 = 12800 Nmload To = 8kg me G = 192 Nmstred Mro = 480 Nm 27. -x1.5 = 0.0262 rad 360*1.5 We're, . - 12800 = 40 red's =480 = 0.0375 vcd 2 12800 5 - C 2 Jun = 192 = 0.3 2x8x40 For a Torsional system, The Jordan legyen squasing of taking the reciprocal, 2.0486 - (1-77? + 0.367°= 7*-1.647+1 or, 74 - 1.6402-110486 = 0 ? - 2.1318, -0.4918 - Scanned with

We runs V2.1318 x 40 = 58.47adls. fa hao -584 - 9.29 Hz 23 Maximum torque transmitted, M, CH = kr OCH+GÒ CH) = k ④ cosluet-d -e Que sin (wet-do Mt, me x = J Chy ) ² + (40 we) ² 162800X00262) + (1920.0262 758-4) = V112466.3 + 86 303.9 = 445.8 Nm