Mechanical Characterization of Materials and Wave Dispersion
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Conclusion 7. Bibliography 7. Appendix 7A. Line integral of complex function and Cauchy's integral 7A. Analyticity of a function f z of complex variable z 7A. Appendix 7B. Hilbert transform obtained directly by Guillemin's method Chapter 8. Introduction 8. Overview of various methods used to evaluate damping ratios in structural dynamics 8. Measurement of structural damping coefficient by multimodal analysis 8. The Hilbert envelope time domain method 8. Detection of hidden non-linearities 8.
How to relate material damping to structural damping? Concluding remarks 8. Introduction 9. Industrial torsion test bench 9. Parasitic bending vibration of rod 9. Shear moduli of transverse isotropic materials 9. Elastic moduli obtained for various materials 9. Experimental set-up to obtain dispersion curves in a large frequency range 9. Experimental results obtained on short samples 9. Experimental wave dispersion curves obtained by torsional vibrations of a rod with rectangular cross-section 9. Frequency spectrum for isotropic metallic materials aluminum and steel alloy 9.
Impact test on viscoelastic high damping material 9. Concluding remarks 9. Bibliography 9. Appendix 9A.
Choice of equations of motion 9A. Circular cross-section 9A. Square cross-section 9A. Rectangular cross-section 9A.
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Ratio of Young's modulus to shear modulus 9A. Special experimental studies of wave dispersion phenomenon 9.
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Complementary information concerning formulae used to interpret torsion tests 9B. Quick overview of Saint Venant's theory applied to the problem of dynamic Torsion 9. Compliments concerning the solution of equations of motion with first order theory 9D. Displacement field 9D. Relations between two sets of coefficients 9D.
Equations giving the two sets of coefficients Aa, Ba, Ca, Da deduced from the four boundary conditions 9D. Evaluation of coefficients in [9D. Introduction Realization of an elasticimeter How to conduct bending tests Concluding remarks Useful formulae to evaluate the Young's modulus by bending vibration of rods 10A. Bernoulli-Euler's equation 10A.
Enhanced Wave Absorption and Mechanical Properties of Cobalt Sulfide/PVDF Composite Materials
Timoshenko-Mindlin's equation 10A. Boundary conditions and wave number equation 10A. Important parameters in rod bending vibration 10A. Expression of the wave number 10A. Young's modulus Bernoulli's theory 10A. Young's modulus Timoshenko-Mindlin's equation Chapter Mechanical set-up Electronic set-up Estimation of phase velocity Short samples and eigenvalue calculations for various materials Experimental results interpreted by the two theories Influence of slenderness?
Experimental results obtained with short rod Bibliography Appendix 11A. Eigenvalue equation for rod of finite length Appendix 11B. Additional information concerning solutions of Touratier's equations 11B. Eigenequation with elementary theory of motion Chapter Principal mechanical parts of the double pendulum system Instrumentation Experimental precautions Details and characteristics of the elasticimeter Some experimental results Damping ratio estimation by logarithmic decrement method Equations of motion for the set pendulums, platform and sample and Young's modulus calculation deduced from bending tests 12A.
Equations of motion 12A. Solutions for pendulum oscillations 12A. Relationship between beating period? Young's modulus calculation Appendix 12B. Evaluation of shear modulus by torsion tests 12B. Energy expression Chapter Choosing the samples based on material symmetry Ultrasonic benches Experimental results and interpretation List of symbols Determination of inertia moment of a solid by means of a three-string pendulum 13B. Principle of the method 13B.
Calculations Appendix 13C. Necessary formulae to evaluate Young's modulus of a straight beam Chapter Ultrasonic transducers The stress contours of FEM simulation are shown in Fig.
Stress—strain curve by tensile tests and FEM simulation: a tensile test, b FEM simulation, c comparison between measured and calculated elastic modulus. The elastic modulus calculated by the FE model is These results show that the elastic modulus increases with the cobalt sulfide mass fraction. In this research, two-phase composites comprising cobalt sulfide and PVDF were synthesized and studied in terms of their microstructures and characterization, and the wave absorption and mechanical properties were explored.
This intensity can be tuned by regulating the thickness and the content levels of the cobalt sulfides. Moreover, the elastic modulus is increased with the cobalt sulfide mass fraction. Therefore, cobalt sulfide is conducive to the improvement of the mechanical properties of composites. Ren, Y. Xia, T.
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Mechanical Characterization of Materials and Wave Dispersion
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