Q_2+Solution

# Q_2+Solution - 51 25 The response of a system excited at...

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51 25. The response of a system excited at its base by y ( t ) = Y sin !t is given by x ( t ) = X sin( ! b t ) ; with X Y = 1 + (2 ±! b =! n ) 2 (1 ! 2 b =! 2 n ) 2 + (2 ±! b =! n ) 2 ± 1 = 2 : Use Figure 3.29 for displacement transmissibility in answering the following questions, but do not solve any equations. (a) Assume that the maximum amplitude of the base load is Y = 1 cm. A design for a rotating machine with the above base load and with natural frequency ! n = 3 rad/s is required such that X ± 2 cm across all frequencies ! b . Which ± value should be chosen? (b) Suppose that instead of the criteria in (a), we require X ± 1 cm and ± < 1 : 0 . The machine operates at ! b = 9 rad/s. What are the options for satisfying this criterion? (c) What is the equation for the maximum force transmitted to the base in terms of ±; ( ! b =! n ) ;k; and Y ? For ± = 1 : 0 , what is the force transmissibility ( F T =kY ) when the machine is running at ! b

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Q_2+Solution - 51 25 The response of a system excited at...

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