1. Resonance meters for viscoelasticity measurement
Department of Biophysics and Physical Chemistry, Faculty of Pharmacy, Heyrovskeho 1203, Hradec Kralove, Czech Republic
DELTER v.o.s. Lohenice 43, Prelouc, Czech Republic

2. Introductory remarks
Quantification of relations between strains and stresses in dynamic loading is one of the key tasks of biomechanics.
In contrast to static loading, in dynamic loading energy losses play a relevant role. Viscoelasticity must thus be taken into account.
Rheological viscoelastic models are currently applied on this field. Nevertheless, they do not ensure a satisfactory approximation.
There are two main sources of discrepancy between the behavior of rheological models and the behavior of real viscoelastic structures.
The first issue is the problematic disregard of the influence of inertial forces.
The second lies in the fact that the current rheological models use lumped parameters which are incongruous with the distributed parameters in real bodies.
Complex moduli or, more generally, complex stiffness's, provide adequate tools for satisfactory characterizing dynamic behavior of linear mechanical systems.

3. Principle of resonance apparatuses (RMA)
RMA measure complex stiffness and complex moduli. RMA are based on the measurement of mechanical resonance of samples of biological materials.
Resonance methods represent an alternative to direct measurements of frequency characteristics (DMA apparatuses). Crucial advantage of resonance meters consists in the high sensitivity of measurements and the elimination of errors resulting from the effect of the mass of the sample and the mass of the moving part of the meter on measurement results. Moreover, its design enables contactless sensing, which further improves the accuracy and precision. Application of this principle leads to a reduction of costs and elimination of some errors.

4. Inverse problem solutions
inertial body
sample F
Fundamental equations: l0
Complex stiffness definition:
Complex modulus definition:
Complex stiffness of system sample-inertial body in periodic mode:
Loss modulus of sample:
Storage modulus of sample:

5. RMA – tensile measurements

6. RMA – measurements in bending loading

7. RMA – measurements of surface stiffness

8. Solutions of problems of mechanical compatibility
Potential application of measurement of viscoelasticity in biomechanics
Solutions of problems of mechanical compatibility
Origin of additional stresses in mechanically incompatible bodies.
Tangent stresses in tensile loading.
Condition of mechanical compatibility is the same complex stiffness in all bodies in contact.

9. Solutions of problems of complex mechanical systems
Potential application of measurement of viscoelasticity in biomechanics
Solutions of problems of complex mechanical systems
Knowledge of stiffness's of partial bodies enables calculation of stiffness of whole system F
Serial systems
body1
body2
body n
body 3 L1 L2 L3
Parallel systems F 1 2 n F1 F2 F3 L