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The application of chaos theory to forces inducing rolling maneuvers by acting on linear or nonlinear temperature dependent viscoelastic wings with actual widely scattered random material properties is investigated in detail. Published experimental data shows widely scattered 1-D viscoelastic moduli and small excursions from average or beginning values - the basis for chaos theory - is realistically inapplicable and would simply constitute a purely academic exercise excursion. While conventional approaches have been associated with applied forces, such as probability theory, to characterize these deterministic and stochastic properties, chaos theory is offered as an additional alternate generalized protocol to characterize viscoelastic responses to chaotic flight loads. At this time unfortunately no deterministic, stochastic or chaotic experimental data seems to be available, nor experimental data on aero-viscoelastic structural responses to flight vehicle maneuvers at any temperature. [ABSTRACT FROM AUTHOR]

The hereditary and/or convolution integrals associated with linear viscoelastic material constitutive relations based on Prony series [1] characterization are recast into ordinary nonconvolution time integrals, which can be more efficiently evaluated analytically and numerically. Application of this protocol greatly reduces computational time, CPU usage and memory requirements used to solve linear temperature dependent and/or independent viscoelastic problems involving integral-differential equations with variable coefficients. The formulation includes temperature dependent materials with time and space dependent temperatures as well as stresses due to thermal expansions. Approximate approaches for dealing with time dependent temperatures are derived and solutions to non-convolution integral equations as well as to differential equations with variable coefficients are formulated. Relaxation time consistent relations are derived for isotropic viscoelastic materials. Applications of Galerkin and Runge-Kutta methods to viscoelastic solutions are discussed and evaluated. These protocols include solutions to IODEs and IPDEs with variable coefficients. An illustrative algorithm to be used in conjunction with differential equation solvers such as MATLAB's™ ODE45 has been developed which allows for numerical solutions simultaneously in both real and reduced time spaces without approximations of linear and nonlinear integral differential equations with variable or without coefficients. Similar protocols could be readily extended to other software such as MATHEMATICA™, MAPLE™, etc. [ABSTRACT FROM AUTHOR]

Analytical and experimental deterministic and statistical protocols are formulated for the constitutive linear relations that characterize viscoelastic media. These proceedings are achieved in the real time space in terms of moduli and/or compliances without any inclusion of viscoelastic Poisson's ratios. Independent experimental determinations of linear viscoelastic material properties of three distinct polymers include single conditions of creep, relaxation, and constant strain and extensometer time rates - except for starting transients. Statistical dynamic data for the instantaneous modulus and quasi-static data for relaxation moduli are analytically and numerically merged to produce relaxation modulus and creep compliance expressions containing properly evaluated parameters. The combined actual starting load and displacement transient and subsequent time histories are tracked, recorded and incorporated into the analyses to produce moduli and compliances based on actual continuous loading-time sequences. Prony series and generalized continuous relaxation time spectral modulus and compliance functions are derived and discussed. Four distinct probability models of material properties and temperature are postulated and evaluated for two sets of real viscoelastic materials (polymers). Statistical sufficiency considerations are included in the analyses. [ABSTRACT FROM AUTHOR]

This paper presents two characterization methods that are used to describe viscoelastic behavior. In the Prony series method, a discrete representation of the generalized Kelvin model is used, whereas the spectral method uses a continuous distribution. The Prony series coefficients are determined through the linear least squares technique. The Elastic-Viscoelastic Correspondence Principle and the Laplace transform are used in the spectral function approach, which utilizes a selected distribution function that has the potential to describe a wide range of viscoelastic material behavior. Characterization exercises from both methods used strain histories from short-term unidirectional tensile creep experiments that were obtained at three temperatures below the glass transition temperature of a vinyl ester polymer. Experimental strains in both the longitudinal and transverse directions were measured using the digital image correlation technique and linear viscoelastic material properties were obtained without using Poisson's ratios. The measured data was subsequently used to determine the tensile creep compliance function for each test configuration. The potential and limitations of each modeling approach are discussed. [ABSTRACT FROM AUTHOR]

Two separate sets of nonlinear 3-D constitutive relations are modeled in terms of (1) elastic strain invariants and (2) viscoelastic strain and strain rate invariants each assembled in their own multidimensional Maclaurin series. Characterization of material properties is formulated and evaluated. Fundamental difficulties associated with the nature of the nonlinear functions defining the stressstrain relations are examined. Several protocols for joint analytical and experimental viscoelastic material characterization and wave motion analyses are presented. As an illustrative problem, the 1-D wave propagation phenomenon is studied in detail. It is shown that the wave front velocities in linear elasticity and viscoelasticity are invariant with respect to the magnitude and character of the forcing function. In nonlinear elastic and viscoelastic media, the specific characteristics of the constitutive relation nonlinearities also do not influence the wave front velocity, but impact stresses and strains. Both must be evaluated on a case by case basis for each specific material properties and impact load-time functions. The nonlinear analyses are carried out using Poincare's successive approximation method (SAM). The use of SAM successively leads to linear elastic PDEs and to linear viscoelastic IPDEs respectively for each and every unknown approximation term of the stress and displacement wave series as well as the series representing the propagation velocity. The influences of the impact force loading pattern and of the nonlinear elastic and viscoelastic contributions on responding wave motions and wave front velocities and amplitudes are analyzed and evaluated. In particular, both the classical and distributed Dirac delta function impact loads are analyzed in detail and found to be incompatible models compared to the real world in certain areas in bothlinear and nonlinear elastic and viscoelastic media. An actual impact force pattern is then modeled and analyzed in the same medium and it was found to also work well with the SAM. [ABSTRACT FROM AUTHOR]

Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated. [ABSTRACT FROM AUTHOR]

An analytical study is undertaken to ascertain the effects on elastic and viscoelastic flutter of (1) starting transients due to changes in flight velocity, (2) boundary conditions and (3) unsteady aerodynamic force definitions (spatial deflection derivatives). Lifting surface and panel flutter are considered in the steady-state velocity range after transient effects and varied boundary condition influences are also studied. In addition to the various unsteady aerodynamic theories, the effects due to the presence or absence of spatial deflection derivatives on pressure distributions are also examined. Necessary and sufficient conditions for the onset of flutter in the form of simple harmonic motion are also formulated and evaluated. [ABSTRACT FROM AUTHOR]

Analytical and numerical formulations and simulations are presented in order to conduct sensitivity studies of physical parameters affecting thermal stress control of viscoelastic structures during cure through designer materials tailored to alleviate or outright eliminate undesirable thermal stress states. Numerical simulations in terms of critical parameters are carried out to evaluate system responses. [ABSTRACT FROM AUTHOR]