[試題] 102上 柯文俊 振動學 期中考
課程名稱︰振動學
課程性質︰系必修
課程教師︰柯文俊
開課學院：工學院
開課系所︰工科海洋系
考試日期（年月日）︰102/11/06
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Give detailed responses to the following problems:[40%]
(a) Why is viscous damping used in most cases rather than other types of
damping?
(b) Impulse response function
(c) Logarithmic system
(d) Self-excited system
(e) Quality factor
(f) Force transmissibility
(g) Duhamel integral
(h) Give a physically explanation of why the magnification factor is nearly
equal to 1 for small value of r and is small for large values of r.
2. A simply supported beam with load at the middle of square cross section
a mm X a mm and length l m, carrying a mass of m kg at the middle, is found
to have a natural frequency of transverse vibration of f Hz. Determine the
Young's modulus of elasticity of the beam. [10%]
3. A spring-mass system is subjected to Coulomb damping. When a harmonic
force of amplitude F0 N and frequency f Hz is applied, the system is found
to oscilliate with an amplitude of α mm. Determine the coefficient of
dry friction if mass and stiffness are m kg and k N/m respectively. [15%]
4. An air compressor of mass m kg is mounted on an elastic foundation. It has
been observed that, when a harmonic force of amplitude A1 N is applied to
the compressor, the maximum steady-state displacement of β mm occured at a
frequency of R1 rpm. Determine the equivalent stiffness and damping
constant of the foundation. [15%]
5. Find the energy dissipated during a cycle of simple harmonic motion given
by x(t) = X sin(ωd t) m by a viscously damped single degree of freedom
system with mass, damping and stiffness constant are m kg, c N-s/m and
k N/m respectively. [10%]
6. A cantilever beam having a bending stiffness of k3 N/m supports a mass of
m3 kg at it free end. The mass is displaced initially by A0 mm and
released. If the amplitude is found to be A100 mm after 100 cycles of
motion, estimate the hysteresis damping constant β of the beam. [10%]
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