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Tham khảo tài liệu 'applied structural and mechanical vibrations 2009 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | displacement of the mass relative to a fixed frame of reference. Equation 4.55 can be rearranged to mi ex kx cy ky 4.56 Using complex algebra we let the support motion be of the form and the y i Ye iujt complex motion transmissibility is found to be X 1-2 ffl y 1 - - 2i 3 4.57 with magnitude and phase angle ộxy given by l 2 2 2 y 1 - 2 2 m tanộxy 1 -02 4C2 32 which are exactly the same as the magnitude and phase angle of the force transmissibility T of equations 4.53 and 4.54 . Graphs of eqs 4.53 and 4.54 are shown in Figs 4.10 and 4.11 for the two values of damping Í 0.05 and í 0.2. Fig. 4.10 Transmissibility magnitude versus p. Copyright 2003 Taylor Francis Group LLC By subtracting the quantity my from both sides of eq 4.55 we obtain mw cw kiv - my feffit 4.59 where we can see that the base motion has the effect of adding a reversed inertia force my to the equation of relative motion. Equation 4.59 is useful because in many applications relative motion is more important than absolute motion and also because the base acceleration is relatively easy to measure. The quantity feff t is the effective support excitation loading i.e. the system responds to the base acceleration as it would to an external load equal to the product mass X base acceleration . The minus sign indicates that the effective force opposes the direction of the base acceleration this has little importance in practice since the base motion is generally assumed to act in an arbitrary direction. 4.3.3 Resonant response of damped and undamped SDOF systems Immediately after the driving force is turned on it is not reasonable to expect that the oscillator response is given by eq 4.43 . In fact the force has not been acting long enough even to establish what its frequency is and it takes a while for the motion to settle into the steady state. The mathematical counterpart to this statement is as we have seen before that the general solution is the sum of two parts the transient complementary function and
