Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hz Figure 1: Single-degree-of-freedom system in Problem 1. Please compute the following considering the steady-state response of the SDOF system. Do not consider the transient response unless it is explicitly stated in the question. (a) The natural circular frequency and the natural period of the SDOF. (10 points) (b) The maximum displacement of the mass uo = max(|u(t)|) and the maximum shear force in the Space Launch System fso =max(|fs(t)|). (10 points) (c) The acceleration dynamic response factor of the SDOF. (10 points) 1(d) How would you calculate the maximum displacement of the mass if you had to consider both the transient and the steady-state part of the response of the SDOF system? You do not need to calculate a number; just describe the process. (10 points) (e) A linear viscous damper is attached between the mass and the rigid support as shown in Figure 1(c). The forcing function and the rest of the properties of the SDOF remain the same. What is the value of the damping ratio of the viscous damper that is required to reduce the maximum displacement of the mass by 10%. (10 points) (f) What is the coefficient of damping of the viscous damper mentioned above? What is the maximum force in the viscous damper? (10 points
Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of
freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless.
Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt)
acting on the mass. The known properties of the SDOF and the applied forcing function are given below.
• Mass of SDOF: m =120 kip/g
• Acceleration of gravity: g = 386 in/sec2
• Bending sectional stiffness of SDOF: EI = 1015 lbf×in2
• Height of SDOF: h = 2000 inches
• Amplitude of forcing function: po = 6 kip
• Forcing frequency: f = 8 Hz
Figure 1: Single-degree-of-freedom system in Problem 1.
Please compute the following considering the steady-state response of the SDOF system. Do not consider
the transient response unless it is explicitly stated in the question.
(a) The natural circular frequency and the natural period of the SDOF. (10 points)
(b) The maximum displacement of the mass uo = max(|u(t)|) and the maximum shear force in the Space
Launch System fso =max(|fs(t)|). (10 points)
(c) The acceleration dynamic response factor of the SDOF. (10 points)
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(d) How would you calculate the maximum displacement of the mass if you had to consider both the
transient and the steady-state part of the response of the SDOF system? You do not need to calculate
a number; just describe the process. (10 points)
(e) A linear viscous damper is attached between the mass and the rigid support as shown in Figure 1(c).
The forcing function and the rest of the properties of the SDOF remain the same. What is the value
of the damping ratio of the viscous damper that is required to reduce the maximum displacement of
the mass by 10%. (10 points)
(f) What is the coefficient of damping of the viscous damper mentioned above? What is the maximum
force in the viscous damper? (10 points
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