Viscoelastic Rod Research Articles

Vibration transmissibility characteristics of reinforced viscoelastic pipes employing complex moduli master curves

Fibre and wire reinforced flexible viscoelastic pipes are used in situations where their static and dynamic characteristics provide much better performance than metallic pipes. Because of their vibration and shock attenuation characteristics, these viscoelastic pipes are used as flexible conduits in applications where it is desirable to minimize the transmission of vibration and structure-borne sound to the surroundings. In analyzing the vibration and structure-borne sound transmission and the vibrational power flow through systems that incorporate such pipes, knowledge of the mathematical models that satisfactorily predict the vibration transmissibility characteristics of the viscoelastic pipes is advantageous. It is shown that the use of the frequency and temperature dependent complex moduli of these pipes with the elementary and the more exact theories of the propagation of axial and flexural vibration through viscoelastic rods and beams provides satisfactory prediction of the vibration transmissibility characteristics of the reinforced viscoelastic pipes.

Some problems for viscoelastic rods

Using an approach proposed in [3], we consider some linear and nonlinear problems for viscoelastic rods. Results in [I] for linear case are affirmed more elamentarily and simply here. We also treat linear problem with damping term and nonlinear problem with power nonlinearity 819-1. Some new results are es tablished.

On the linearised theory of buckling for a compressed viscoelastic rod

SynopsisResults are obtained on the existence, multiplicity, blow-up and asymptotic behaviour of the solutions to the integro-differential equationwhich arises in the linearised, quasi-static theory of buckling for a viscoelastic rod.

Stability of annular plates of inhomogeneously ageing viscoelastic material

A thin-plate bending equation in a polar coordinate system is derived for an inhomogeneously ageing material using creep theory. This equation is used to prove the sufficient condition forthe stability of annular plates by an energy method. The case of rigid clamping of both plate edges and compressive forces of dissimilar intensities along these edges is examined. Stresses in the plane of the plate are estimated, whereupon a bound is obtained on the compressible force in explicite form. An extension is made to other kinds of plate support. Equations for the deflection and sufficient conditions for the stability of inhomogeneously ageing viscoelastic rods were obtained earlier in the one-dimensional case /1/.

Oscillatory Structured Shock Waves in a Nonlinear Elastic Rod With Weak Viscoelasticity

The propagation of longitudinal shock waves in a thin circular viscoelastic rod is investigated theoretically as the counterpart of the torsional shock waves previously considered in [1, 2]. Assuming a “nearly elastic” rod, the approximate equation is first derived by taking account of not only the finite deformation but also the lateral contraction or dilatation of rod. The latter gives rise to the geometrical dispersion, which is taken in the form of Love’s theory for an elastic rod. Taking two typical relaxation functions, the structures of the steady shock waves are investigated in detail, one being the exponential function type and the other the power function type. The effect of geometrical dispersion is emphasized. Finally a brief discussion is included on the simplified evolution equations for a far field behavior.

Forced and free longitudinal vibrations of a regular-structure viscoelastic rod

Forced and free longitudinal vibrations of a regular-structure viscoelastic rod

Torsional Shock Waves in a Viscoelastic Rod

The propagation of torsional shock waves in a thin circular viscoelastic rod is investigated theoretically. An analysis is carried out based on the approximate equations previously derived. Two typical viscoelastic models are considered, which possess, respectively, the discrete and continuous relaxation spectrum. One is the usual Maxwell- Voigt model and the other is a new model whose relaxation function is given by a power law with weak singularity. The structures of steady shock profiles are presented and compared for both types. Finally a brief discussion is included on the simplified evolution equations for a far field transient behavior.

Approximate equations for torsional waves in a nonlinear elastic rod with weak viscoelasticity

Approximate equations are derived for nonlinear torsional waves propagating along a thin circular viscoelastic rod. Ignoring the thermal effect, ‘nearly elastic’ compressible viscoelastic solids are considered in which a weak dependence of stresses on a history of strain is assumed. With the assumption that the rod is subjected to a finite angle of torsion, but that the rod is thin, the displacement is sought in a power series of the radial coordinate. The effects of geometrical and material nonlinearity give rise to the normal stress effect, which introduces deformations in the cross sectional and longitudinal dimensions of rod. Taking account of both the effect of nonlinearity and that of viscoelasticity, one dimensional approximate equations are obtained for the angle of torsion coupled with the longitudinal deformation.

The motion of a heavy symmetrical body with flexible rods about a fixed point

The motion of a symmetrical solid about its centre of mass is considered in the case, when four mutually orthogonal flexible rods are fixed to it in the equatorial plane of the body ellipsoid of inertia. The deformations of rods is defined by the linear theory of the bending of thin viscoelastic rods, and lead to the evolution of the motion of the solid, i.e. the solid approaches steady rotation about the vertical. the approximate equations in Andoyer variables that define the system evolution are obtained by the method of averaging. The stability of the steady rotations obtained is investigated.

A linear integro-differential equation for viscoelastic rods and plates

It is proved that the resolvent kernel of a certain integrodifferential equation in Hilbert space is absolutely integrable on ( 0 , ∞ ) \left ( {0,\infty } \right ) . The equation arises in the linear theory of isotropic viscoelastic rods and plates.

Dynamic strain of a longitudinally vibrating viscoelastic rod with an end mass

The dynamic strain of a viscoelastic rod excited into longitudinal simple harmonic vibration, a constant amplitude displacement being maintained by a shaker at one end and a mass terminating the other end, is theoretically investigated in this paper. The general equation of the strain distribution in the rod is derived by solving the one-dimensional wave equation. It is shown that the strain in the rod is the largest at the excited end, at the antiresonant frequencies. Simplified approximate equations are derived for the low loss case to calculate the largest strain in the rod with knowledge of the loss factor.

On Nontrivial Solutions for a Compressed Linear Viscoelastic Rod

On Nontrivial Solutions for a Compressed Linear Viscoelastic Rod

Approximate equations for the oscillations of viscoelastic rods and plates

Approximate equations for the oscillations of viscoelastic rods and plates

Apparent complex Young's modulus of a longitudinally vibrating viscoelastic rod

Longitudinal vibration of a viscoelastic rod with a finite lateral dimension is theoretically analyzed on the basis of the approximate Love theory. The frequency range where the Love theory gives good approximation and its accuracy in that range are determined. The theory predicts that the wave propagation in a viscoelastic rod is not governed solely by the complex Young's modulus of the material at higher frequencies, due to the lateral motion, but by its apparent value. It is shown that the apparent dynamic Young's modulus is smaller and the apparent loss factor is larger than the corresponding actual values for the material. The differences between the apparent and actual values depend on the lateral dimension to wavelength ratio and on the complex elastic constants as well.

Effect of thermomechanical coupling on the stability of viscoelastic rods under the influence of a sliding force

Effect of thermomechanical coupling on the stability of viscoelastic rods under the influence of a sliding force

Transient waves in finite viscoelastic rods

Transient waves in finite viscoelastic rods

Parametrically excited oscillations of viscoelastic rods with a nonlinear elasticity relation and nonlinear internal friction

Parametrically excited oscillations of viscoelastic rods with a nonlinear elasticity relation and nonlinear internal friction

Stability of viscoelastic rods and shells under the action of loads that decrease with time

Stability of viscoelastic rods and shells under the action of loads that decrease with time

On the stability of nonuniformly aging viscoelastic rods: PMM vol. 43, No. 4, 1979, pp. 709–721

The stability of a nonuniformly aging viscoelastic rod is investigated. The critical force is determined in terms of parameters of the rod in the case of infinite time interval. Critical time estimates are presented for the problem covering a finite time interval.

Oscillations of a viscoelastic rod taking thermomechanical coupling into account

The effect of thermomechanical coupling on the forced longitudinal oscillations of a viscoelastic rod is investigated.