Basic mechanics of beam and diaphragm structures part 2

Basic mechanics of beam and diaphragm structures part 2 -...

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SEN2MET Chapter 2, part 3 1 SEN2MET Sensors and actuators Basic mechanics of beams and diaphragm structures hans.j.alker@hive.no 1. Stress and strain fundamentals (review) 2. Stress and strain of beam structures (review) 3. Vibration frequency by energy method, the Rayleigh- Ritz method 4. Damped and forced vibration 5. Basic mechanics of diaphragms
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SEN2MET Chapter 2, part 3 2 Vibration frequency by energy method Spring-mass system System equations: General solution : Vibration frequency ω depending only on structural parameters By energy conservation: E P,max =E K,max
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SEN2MET Chapter 2, part 3 3 Vibration frequency by energy method Beam with an end mass Recovery force at beam end: Equivalent spring constant k Applying energy conservation: (Ref. slide 6, lecture #3) M>>M b
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SEN2MET Chapter 2, part 3 4 • So far, only concentrated masses and springs are considered • How about distributed masses and springs? • Rayleigh-Ritz method takes this into account • We will only analyze uniform beams with rectangular cross sections • Adoption to MEMS structures implies some small modifications of the method Vibration frequency by energy method Rayleigh-Ritz method
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5 Rayleigh-Ritz method For pure bending in the x-z plane: Normal forces at each end: The potential energy stored due to bending deformation: Elongation: For the kinetic energy: (Ref. slide 3, lecture #3) How to determine w(x,t) ?
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This note was uploaded on 05/30/2011 for the course SEN 2MET taught by Professor Ulrikhanke during the Spring '11 term at VCU.

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Basic mechanics of beam and diaphragm structures part 2 -...

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