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Published byAmelia Sherburn Modified about 1 year ago

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2 Amplification of displacement amplitude (transmissibility of displacement amplitude) DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION (FROM BASE TO MASS) Relative / base Absolute / base X Z r

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k = 3125N/mk = 10000N/mk = 18000N/m m=100kg vib iso 01.SLDASM DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION (FROM BASE TO MASS) Absolute / base

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DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION (FROM BASE TO MASS) Problem 1 Mass 100kg Stiffness 10N/m Damping0% Base excitation at 120% of resonant frequency Design linear damper to reduce the amplitude of vibration of mass by 50%

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Problem 2 A 20kg lab experiment is to be mounted to a table that is bolted to the floor in a laboratory. Measurements indicate that due to the operation of a nearby pump that runs at 2000RPM (209.4 rad/s) the table has steady-state displacement 0.25mm. What is the maximum stiffness of an undamped oscillator, placed between the experiment and the table such that the experiment’s acceleration amplitude is less that 4m/s^2? Transmissibility ratio of acceleration is the same as transmissibility ratio of displacement : Transmissibility ratio: DISPLACEMENT TRANSMISSIBILITY IN BASE EXCITATION (FROM BASE TO MASS)

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FORCE TRANSMISSIBILITY IN BASE EXCITATION (FROM BASE TO MASS) kY = F 0

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FORCE TRANSMISSIBILITY IN FORCE EXCITATION (FORCE TRANSMITTED FROM MASS TO BASE) Force transmitted to base. Isolation (reduction of force transmitted to base) occurs only for r > √2 r

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8 Problem 3 What is the minimum static deflection of an undamped isolator to provide at least 75% isolation to a pump that operates at speed between 1500 and 2000RPM ( rad/s). Isolation is better for higher speeds, therefore if we ensure 75% isolation at 1500RPM it will be only better at 2000RPM No solution Relation between natural frequency and operating frequency ω = 157rad/s (1500RPM). This is the maximum natural frequency if we want 75% isolation. FORCE TRANSMISSIBILITY IN FORCE EXCITATION (FORCE TRANSMITTED FROM MASS TO BASE)

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Problem 4 A 150kg machine operates at 1200RPM. It has rotating unbalance 0.45kgm. What is the maximum stiffness of an undamped isolator such that the force transmitted to the machine’s foundation is less than 2000N FORCE TRANSMISSIBILITY IN FORCE EXCITATION (FORCE TRANSMITTED FROM MASS TO BASE)

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Problem 5 FORCE TRANSMISSIBILITY IN FORCE EXCITATION (FORCE TRANSMITTED FROM MASS TO BASE)

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