Ordinary differential equations of the first order linear differential equations complex numbers and linear algebra simultaneous linear differential equations numerical methods the descriptive theory of nonlinear differential equations mechanical systems and electric circuits Fourier series Fourier integrals and Fourier transforms the Laplace transformation partial differential equations Bessel functions and Legendre polynomials applications and further properties of matrices vector analysis the calculus of variations analytic functions of a complex variable infinite series in the complex plane the theory of residues conformal mapping.

Advanced Engineering Mathematics. By C. R. Wylie. Pp. xiv, 813. 1966. (McGraw-Hill.)

The present state-of-the-art article is devoted to the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics. This review involves the papers dealing with study of dynamic behavior of linear and nonlinear 1DOF systems, systems with two and more DOFs, as well as linear and nonlinear systems with an infinite number of degrees of freedom: vibrations of rods, beams, plates, shells, suspension combined systems, and multilayered systems. Impact response of viscoelastic rods and plates is considered as well. The results obtained in the field are critically estimated in the light of the present view of the place and role of the fractional calculus in engineering problems and practice. This articles reviews 337 papers and involves 27 figures. DOI: 10.1115/1.4000563

Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results

1. Our Frame of Reference A COMPREHENSIVE approach called the decision support problem technique" is being developed and implemented at the University of Houston to provide support for human judgment in designing an artifact that can be manufactured and maintained. Decision support problems (DSPs) provide a means for modeling decisions encountered in design, manufacture, and maintenance. Multiple objectives that are quantified using analysis-based "hard" and insight-based "soft" information can be modeled in the DSPs. For real-world, practical systems, not all of the information will be available for modeling systems comprehensively and correctly in the early stages of the project. Therefore, the solution to the problem, even if it is obtained using optimization techniques, cannot be the optimum with respect to the real world. However, this solution can be used to support a designer's quest for a superior solution. In a computerassisted environment, this support is provided in the form of optimal solutions for decision support problems. Formulation and solution of DSPs provide a means for making the following types of decisions:

The compromise decision support problem and the adaptive linear programming algorithm

A tunable high-static–low-dynamic stiffness vibration isolator

http://www.ikb.poznan.pl/roman.lewandowski/Passive/jabartosz.pdf

Identification of the parameters of the Kelvin-Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers

Three simple constitutive relationships are studied for application to viscoelastic materials. Experimental results for both a rubbery and a glassy viscoelastic material are fit by the three schemes. The Kelvin-Voigt scheme is shown to be adequate in only limited frequency ranges. A three-parameter fractional order constitutive relationship provides a substantially better model over a much larger bandwidth. A four-parameter fractional model improves on the accuracy in materials with significant glassy regions

Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials

A variable stiffness device selection and design tool for lightly damped structures

A novel vibration experiment consisting of a free-free boundary condition, an electromagnetic excitation source, a vacuum chamber, and a laser vibrometer based surface measurement system has been developed that permits high levels of excitation on highly damped specimens with a minimal amount of unwanted systematic error. While some of the aspects of this experiment are not unique, when combined with a processing technique that accounts for the nonlinearities present in the system, this experiment permits, accurate measurement of strain dependent stiffness and damping properties of hard coatings at high strain levels. This procedure has been demonstrated using a titanium beam that has been coated with a free-layer damping treatment of Magnesium Aluminate Spinel. The results indicate that Magnesium Aluminate Spinel has both nonlinear stiffness and damping properties. The stiffness asymptotes to a minimum value around 650 microstrain while the damping is a maximum around 100 microstrain. Additionally, the data contained herein cover a larger strain range for this material than previously reported.

/pdf/an-experimental-technique-for-the-evaluation-of-strain-4qzew7az0o.pdf

An Experimental Technique for the Evaluation of Strain Dependent Material Properties of Hard Coatings

[1] A nondestructive technique for determining the complex permittivity and permeability of a perfect electric conductor backed magnetic shielding material using a dual waveguide probe is presented. The dual waveguide probe allows for the simultaneous collection of reflection and transmission coefficients which distinguishes it from single probe methods common in the literature. Theoretical development of these coefficients, which is accomplished through a coupled magnetic field integral equations formulation using Love's equivalence principle and solved via the method of moments (MOM), is discussed. Evaluation of the resulting MOM impedance matrix elements is performed using complex plane integration leading to enhanced computational efficiency and physical insight. Comparison of the theoretical and measured reflection and transmission coefficients using a root finding algorithm leads to the desired permittivity and permeability. Measurement results of a magnetic shielding material are presented and compared to traditional methods for the purpose of validating the new technique. The probe's sensitivity to aperture alignment, sample thickness, and flange thickness is also investigated.

/pdf/nondestructive-electromagnetic-material-characterization-335u1xa6q4.pdf

William P. Baker

Papers

Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials

A variable stiffness device selection and design tool for lightly damped structures

An Experimental Technique for the Evaluation of Strain Dependent Material Properties of Hard Coatings

Nondestructive electromagnetic material characterization using a dual waveguide probe: A full wave solution

Numerical application of fractional derivative model constitutive relations for viscoelastic materials