Engineering Mechanics for MEMS MEMS are 3 dimensional

Engineering Mechanics for MEMS • MEMS are 3 -dimensional structures that often involve heat transmission as well as solid/fluid interactions. Most MEMS components are micro-scale machine components, e. g. , gears, springs, bearings, linkages. This necessitates the need for engineering mechanics. • Engineering mechanics for MEMS involves solid, fluid, and thermo mechanics. – Solid mechanics and dynamics are frequently applied in the design and operation of accelerometers, pressure sensors etc. – Fluid mechanics is involved in the design of microvalves and microfluidics. – Thermomechanics is used to study the stress state in MEMS components and in assessing the temperature field in MEMS structure.

Solid Mechanics : Static Bending of Thin Plates • Micro pressure sensors work on the principle of converting strain in a thin Si diaphragm. • The d. e. for deflection, w, • Ref : Timoshenko and Woinowsky-Krieger (1959).

Bending Moments Bending Stresses

Circular Diaphragm • A circular diaphragm of radius a and thickness h with edge fixed. • The maximum radial stress (srr), and maximum tangential stress (sqq) occur at the edge. • At the center of the plate

Rectangular Diaphragm • Rectangular diaphragm with length a, width b, and thickness h with all edges fixed • Maximum stress occurs at the center of the longer edges • The maximum deflection at the centroid

a/b 1 1. 2 1. 4 1. 6 1. 8 2. 0 a 0. 0138 0. 0188 0. 0226 0. 0251 0. 0267 0. 0277 b 0. 3078 0. 3834 0. 4356 0. 4680 0. 4872 0. 4974

Square Diaphragm • A square diaphragm of side a and thickness h with all edges fixed. • The maximum stress occurs at the center of each edge • The maximum deflection occur at the center of the diaphragm

Mechanical Vibration - The theory of mechanical vibration is the basis for microaccelerometer design. - The simplest mechanical vibration system is the mass-spring system. Free vibration of mass-spring - The equation of motion - Solution

Damped Free Vibration : Mass-Spring-Dashpot • Equation of motion • Overdamping case: • Critical damping case: • Underdamping case:

Overdamping

Underdamping

Critical Damping

Forced Vibration • Equation of motion • Solution • X(t) 0 when wo = a • Applying L’Hopital’s rule for wo = a (resonant vibration) where X(t) ∞ in a short time.

Rapid increase of amplitude in resonant vibration