Mumbai University > Electronics Engineering > Sem 8 > MEMS Technology

Marks: 5M

Classical structural elements (axial rod, torsion rod, beam, plate, etc.) that can be used in combination to analyze more complex structures.

• A common metric for the analysis of structural elements separately or in combination is the stiffness coefficient, K, which has units of force or torque per deflection.
• • To combine stiffness elements to access the stiffness of more complex structures, the methods of combining stiffnesses in series or parallel are used (Figure 6.18).
• A series spring combination has the same force or torque in both spring elements and the deflection is the total deflection of both springs.
• A parallel combination of spring elements has the force split between the springs and the deflection is the same for all the springs in parallel.
• Note: the mathematical relationship for combinations of mechanical stiffnesses vs. electrical elements is opposite.
• The use of simple models and the ability to combine them to make estimates of the system response are immensely valuable in design.

Example based on stiffness:

Problem: An object is supported by two beams with fixed–fixed boundary conditions and deflected in the lateral direction as shown in Figure 6.20. Find the total spring constant for this suspension.

Solution: The support beams in this situation are connected in parallel because they have the same deflection and the force split between them. Therefore, the total spring constant of this suspension is simply the sum of the two

Individual stiffnesses: