Viscoelastic Filler Research Articles

Stationary response of the system “Cylindrical shell – viscoelastic filler” to the effect of a moving load

The paper considers the stationary response of the system “cylindrical shell - viscoelastic filler” to the action of a moving load. The filler and the shell were assumed to be viscoelastic. Using the principle of analogy of viscoelastic and elastic problems (elastic-viscoelastic analogy), a stationary solution of the action of mobile loads on a shell with a viscoelastic filler is obtained. It is shown that this principle makes it possible to generalize the class of problems obtained for the case of viscoelastic media. Since the viscoelastic filler has damping properties, the inversion integrals have no singularities on the real axis, and the elements of the determinants in integrals become complex since in this problem in the image space, the Lame coefficients are complex and depend on the speed of the load movement, as well as the Fourier transform parameter. Numerical results are obtained, and an analysis is made.

Control of resonant oscillations of viscoelastic systems

Structures in the form of cylindrical ribbed shells and panels are widely used in engineering and construction. The problem of the action of moving loads on an infinitely long cylindrical shell, reinforced along the outer surface with longitudinal stiffeners and containing a viscoelastic inertial filler, is considered. The moving load is transferred to the shell only through the ribs, and there is no load outside the ribs. The discreteness of the location of the ribs is taken into account by writing the equations of motion of the beams, followed by the satisfaction of the conjugation conditions. The influence of the number and stiffness of ribs on the nature of the distribution of shell displacements and contact pressure at the boundary of a viscoelastic filler is shown. The movement of the shell is described by classic equations based on the Kirchhoff?Love hypothesis; for the filler, dynamic equations of the theory of visco-elasticity are used. It has been established that the reinforcement of shells with longitudinal ribs (oscillations of a cantilevered cylindrical shell) leads to a decrease in natural frequencies and damping coefficients in some shells, an increase in the density of the spectrum of natural frequencies, and the appearance of intermediate forms and forms with the same wave numbers, but with different frequencies. External forces increase natural frequencies and damping coefficients. It is found that the frequencies for the inner edges are lower than for the outer edges. In the high-frequency zone, any efforts reduce the natural frequencies and the damping coefficient. This means that additional mass plays a more significant role than additional rigidity. Consequently, the longitudinal strengthening of the shell worsens its dynamic properties.

Stationary deformation of cylindrical shells with viscoelastic filler

The task of determining the dynamic response of plates and shells to moving loads is very relevant. The purpose of this work is to study the stationary deformation of infinitely long cylindrical shells with viscoelastic filler when moving along the axis of the shell of a wave of normal pressure with up to resonant velocity under the influence of normal moving loads. The paper presents a mathematical formulation of the problem, developed methods of solution and obtained numerical results. The solution methods are based on the joint application of the integral Fourier transform in the axial coordinate and the decomposition of all given and desired values into Fourier series in the angular coordinate. An effective algorithm for solving the problem has been developed and implemented on a computer. It is established that with the distance from the point of application of force along the circumference of the voltage for all considered cases, the sign changes. If the connection is one-sided, then tensile stresses arise, and the shell will detach from the filler. It has also been found that changes in the stiffness and rheological properties of the filler in the considered range have little effect on the length of the contact zone.

Investigations of Non-Linear Viscoelastic Properties for Polypropylene/Clay-Nanocomposites through Melt Flow Birefringence and Damping Function

Rheological investigations are reported for pure polypropylene and its clay-nanocomposites to establish viscoelastic properties and filler concentration relationship. Flow birefringence is performed through a slit-die to obtain centerline principal stress difference during extensional flow. The centerline stress profile of clay-nanocomposite revealed additional viscoelastic nature even at low silicate concentrations whereas no exceptional strain hardening was reported. Effects of higher filler concentrations are further examined during the simple shearing flow to consider non-linear viscoelasticity in terms of damping function. The increase in damping coefficient with increasing clay concentration shows polymer-nanocomposites are more strain sensitive. The Wagner's exponential damping function could adequately describe the time-strain separability at all clay concentrations studied. The results of both investigations reveal that the polymers are time-strain separable at all clay concentrations studied during elongational and simple shearing flows, whereas filler orientations are found to be different for different melt flow behavior.

Size-dependent linear rheology of silica filled poly(2-vinylpyridine)

Nanoparticles reinforcement of polymers has been of great interest to researchers for the better part of a century. However, researchers are in confusion in describing the role of filler network. Herein we report a framework to solve both reinforcement and dissipation of nanocomposites with respect to strain amplification effect of dynamically retarded bulk polymer phase and jamming of nanoparticles in the filler phase, disclosing a new mechanism differing from previously established ones. We show how the viscoelastic filler phase impacts on the terminal flow of the matrix. Our finding, which counters the conventional understandings of nanoparticles reinforcement, provides a unique description of linear rheology of nanocomposites comprised by fillers of different sizes and polymers of different molecular weights.

Increasing Gas Turbine Blade Damping Through Cavities Filled with Viscoelastic Materials

To evaluate the effectiveness of high-damping materials as candidate fill materials for hollow fan blades, test specimens in the form of flat trapezoidal plates were designed and mounted as cantilevers. An open-ended cavity of uniform thickness comprised 71% of the planform area. Two viscoelastic materials were developed and used as fillers. Each was modified for reduced density and then aged after application to simulate the influence of 4000 service hours at a characteristic mission profile. Values of the loss factor (reciprocal of the system quality factor) determined from the resonant responses of the filled plates in the first bending, first torsion, and second bending modes at 75° C (170°F) were found to be in the range of q = 0.025-0.045 (Q = 22-40), η = 0.06 (Q = 16), and q = 0.09-0.11 (Q = 9-11) for the three modes, respectively, which is an improvement of 1.5 to 2 orders of magnitude over values measured with the unfilled specimens. A finite element analysis, using temperature and frequency dependent properties of the filler material as determined by separate tests, showed satisfactory agreement with the observed values for temperatures up to 120° C (250°F). This study confirmed that the addition of viscoelastic filler to a hollow plate can increase damping significantly and that the system response could be predicted by finite element analysis. Through appropriate selection of the filler material, such systems can be designed to have maximum damping at a desired specific combination of temperature and frequency.

Vibration isolation using buckled or pre-bent columns—Part 2: Three-dimensional motions of horizontal rigid plate

This is a continuation of previous work to investigate the use of pairs of pre-bent columns, bonded with a viscoelastic filler, as vibration isolators. In this paper, four of these devices support the corners of a square, rigid plate. When the system is in equilibrium, small harmonic vibrations are applied vertically to the base of the isolators, and the steady-state response of the system is determined. First, the system is analyzed for the fully symmetric case, i.e., the center of mass of the plate coincides with the geometric center. Then, the system is analyzed for various cases in which the center of mass has some eccentricity. The eccentric weight introduces rotational motions of the plate. The governing equations are formulated and then numerically solved in Mathematica using a shooting method. The displacement transmissibility is plotted over a range of excitation frequencies, and the mode shapes are shown for the first few resonant frequencies. Free vibration of the system is also considered. For this three-dimensional system, the pre-bent columns can be effective at isolating vibrations for a wide range of excitation frequencies.

Vibration isolation using buckled or pre-bent columns—Part 1: Two-dimensional motions of horizontal rigid bar

The use of buckled columns, or pairs of pre-bent columns bonded with a viscoelastic filler, as vibration isolators is analyzed. They support a horizontal rigid bar at its ends, and harmonic vertical motion is applied at the base of the isolators. The displacement transmissibility is analyzed for both symmetric and asymmetric bars. In the latter case, the bar exhibits rotational as well as translational motion. Each column is modeled as an elastica, allowing for large deflections. Small steady-state vibrations about the equilibrium configuration of the system are analyzed. After formulation of the governing equations, a shooting method is utilized to obtain numerical solutions in Mathematica. The transmissibility is plotted as a function of the excitation frequency, and vibration shapes associated with peaks in the transmissibility plots are shown. For the buckled single-column isolators, the effect of the amount of asymmetry of the bar is examined. For the bonded two-column pre-bent isolators, the effects of the filler stiffness, amount of initial curvature, and supported weight are determined. The isolators can be effective for a large range of excitation frequencies.

Steady-state reaction to the effect of a moving load in a system consisting of a cylindrical shell and a viscoelastic filler

Steady-state reaction to the effect of a moving load in a system consisting of a cylindrical shell and a viscoelastic filler

Vibrations of prestressed three-layer shells with viscoelastic filler when heat generation is taken into account

In the present article we give a thermomechanical theory of three-layer shells which takes account of the initial stress and of the effects of the heat generation in the filler. The derivation of the resolving mechanical equations is based on thebroken-line hypotheses of (2). The material of the layers is considered in the general case to be anisotropic. The surface layers are elastic, while the viscoelastic material of the filler is thermo- rheologically simple and has properties which depend on the temperature and the frequency of the vibrations. i. We consider a three-layer shell positioned in an orthogonal coordinate system ~x, ~2, z with the origin situated in the middle surface of the filler. The layer lying on the side of the outer normal will be called the first layer, the one on the side of the inner normal will be called the second, and the filler will be called the third. We denote by hi(h3 = 2c) the thickness of the layer; At, A2 and kl = I/Rx, k2 = I/R2 are the Lam~ coeffi- cients and the principal curvatures of the coordinate surface; the uikz are the components of the displacement of an arbitrary point of the k-th layer in the direction of the coordi- nates ~(i = i) and ~2(i = 2), respectively; m = m(~, ~2) is the normal deflection of the initial surface, which is the same for all layers and is independent of z because of the hy- pothesis that the layers are incompressible in the transverse direction. The method used in deriving the nonlinear equations of motion and the boundary condi- tions for three-layer prestressed shells is analogous to the method of (2). We use the most general nonlinear relations between the strain and displacement components in the form

Thermomechanical theory of three-layer orthotropic shells with a viscoelastic filler

Thermomechanical theory of three-layer orthotropic shells with a viscoelastic filler

Optimization of a cylindrical shell from a composite having a viscoelastic filler, operating for long-term stability

Optimization of a cylindrical shell from a composite having a viscoelastic filler, operating for long-term stability

Bulging of a cylindrical shell with viscoelastic filler during axial compression

The problem of static stability during axial compression of an orthotropic cylindrical shell reinforced by a continuous filler is solved. The filler is considered to be a three-dimensional isotropic linear-viscoelastic body, fixed at its outer surface to the shell. Transverse shear in the shell is taken into account. The loss of stability of the structure is related to the time-dependent development of initial defects, following application of a load, which is smaller than the instant critical load.

On rheological properties of polydisperse polymers

An investigation has been carried out into the effect of the fractional composition on the rheological (flow and elastic) properties of a system, using mixtures of polybutadienes with narrow molecularweight distribution (MWD). For mixtures of high-molecular-weight components, the initial Newtonian viscosity is determined by the weight-average molecular weight: η 0 ∼ M α w ; when low-molecular weight components are introduced, it is also determined by the MWD moment ratio. The characteristic relaxation time of a system is determined by the z-average molecular weight: θ 0 ∼ M α 1 z , and in the general case α 1 ≠ α. A new model has been proposed to explain the non-Newtonian phenomenon as a consequence of the existence of a molecular-weight distribution. According to this model, as the shear rate increases the high-molecular-weight components gradually (at their critical rates) pass over to the high-elastic state. Therefore, at high shear rates, their contribution to viscous losses of a polydisperse polymer is associated with their behaviour as a viscoelastic filler in a viscous liquid.

Stability of a cylindrical shell with viscoelastic filler

Stability of a cylindrical shell with viscoelastic filler

Axisymmetric reinforced viscoelastic cylindrical shell

Available methods for determining the mechanical properties of a reinforced material in terms of the mechanical properties of the constituents are discussed. A solution is then presented to the problem of an axisymmetric thin cylinder formed by reinforcing a viscoelastic filler with elastic reinforcement.