User`s guide

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2. BACKGROUND
Health monitoring is the process of studying and assessing the integrity of structures,
which is crucial for preventing failure and for achieving reliable designs. Health monitoring can
be done by dynamic or static analysis, or a combination of both. In static analysis, deformations
or changes in the orientation of structures, due to application of loads, or unexpected damages,
are determined via comparisons with reference models. For dynamic analysis, dynamic
characteristics of the structures, including natural frequencies, modal shapes, and damping
factors, are determined via modal analysis.
In either static or dynamic health monitoring, the utilization of appropriate transducers is
required to provide accurate measurement of structural responses in both frequency and time
domains. Conventional devices utilized for health monitoring are based on piezoelectric
transducers. These transducers are usually large in size, require high actuation power, and have
narrow frequency bandwidths, which reduce their accuracy, versatility, and applicability to study
smaller structures. The advanced developments of IC microfabrication and
microelectromechanical systems (MEMS) have led to the progressive designs of small footprint,
low dynamic mass and actuation power MEMS inertial sensors. Due to their high natural
frequencies, these MEMS inertial sensors provide wide frequency bandwidths and high
measuring accuracies.
2.1 Static Analysis of a Simple Cantilever Beam
2.1.1 Stress, Strain, and Deflection Associated with Bending
A bending moment exists in a structural element when a moment is applied so that the
element bends. The bending moment at a section of a structural element is defined as the sum of
the moments about that the section of external forces acting to one side of the section. Moments
are calculated by multiplying the external vector forces by the vector distance at which they are
applied.
Bending occurs locally when a slender object is subjected to an external load applied
perpendicular to a longitudinal axis of the object. On a bending beam, compressive and tensile
forces develop in the direction of the beam axis under bending loads. The forces induce stresses
on the beam. The maximum compressive force occurs on at the lower edge of the beam, and the