Semi-infinite Rod Research Articles

Thermoelastic behavior of fractional order two temperatures heat flux of a semi infinite ceramic rod

Thermoelastic behavior of fractional order two temperatures heat flux of a semi infinite ceramic rod

Longitudinal elastic stress impulse induced by impact through a spring-dashpot system: Optimization and inverse problems for the spring stiffness

In the present paper, an exact analytical solution is obtained for the problem of a semi-infinite elastic rod struck by a rigid mass through a linear Kelvin–Voigt element. The optimization problem resulting in generating compressed pulses of minimum duration is addressed. The case of undamped impact has been studied in detail, and the optimal value for the spring stiffness is presented in a closed form. Inverse problems of recovery of the impact system parameters from the parameters of the strain wave impulse are also considered.

Numerical Solution of Wave Propagation in Viscoelastic rods (Standard Linear Solid Model)

The studies is about the propagation of waves through a short rod (or slug) of viscoelastic material. The viscoelastic material are modelled as standard linear solids which involve three (3) material parameters and the motion is treated as one-dimensional. In this study, a viscoelastic slug is placed between two semi-infinite elastic rods and a wave initiated in the first rod is transmitted through the slug into the second rod. The objective is to relate the transmitted signal to the material parameters of the slug. We solve the governing system of partial differential equations using Laplace transform. We invert the Laplace transformed solution numerically to obtain the transmitted signal for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. Finally, we discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the interface velocity discontinuities.

Mechanical wave motion due to the radiation pressure on gain or absorptive rods

The interaction of a light pulse with reflective and either a passive, lossy medium or an active medium with population inversion gives rise to elastic waves, already as a result of the change in the momentum carried by the incident light. We derived a 1D analytic displacement field that quantitatively predicts the shape and amplitude of such waves in semi-infinite and finite elastic rods in a half-space and infinite layer. The results are compatible with the conservation of momentum and energy of the light-matter system. They can be used as a signature for direct measurements of the radiation-pressure-induced elastic waves and to clarify the Abraham-Minkowski momentum dilemma.

Twistor theory of higher dimensional black holes: I. Theory

The correspondence between stationary, axisymmetric, asymptotically flat spacetimes and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples in higher dimensions has been the lack of a higher dimensional equivalent of the Ernst potential. This paper will propose such a generalized Ernst potential, point out where the rod structure of the spacetime can be found in the twistor picture and thereby provide a procedure for generating solutions to the Einstein equations in higher dimensions from the rod structure and other asymptotic data. An important result for the study of five-dimensional examples will be the theorem which relates the patching matrices on the outer semi-infinite rods.

Two Temperature Heat Flux of Semi Infinite Piezoelectric Ceramic Rod

The theory of two-temperature generalized thermoelasticity is used to solve the problem of heating a semi-infinite rod made of a piezoelectric ceramic material within the framework of generalized thermopiezoelasticity theory by supplying the rod a certain amount of heat uniformly distributed over a finite time period to the finite end of the rod. The Laplace transform formalism is used to solve the proposed model. Inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. The physical parameters (i.e., conductive temperature, dynamical temperature, stress, strain, and displacement distributions) are investigated graphically.

Propagation of longitudinal waves in non-homogeneous four-parameter viscoelastic rods

AbstractThe purpose of this paper was to study the propagation of longitudinal waves in non-homogeneous four-parameter viscoelastic rods of arbitrary thickness. The rods were initially supposed to be unstressed and at rest. Apart from a sudden rising traction uniformly applied over the boundary of the opening and parallel to the faces of the plates, which is steadily maintained thereafter, the rods are otherwise free from loading. Methods for treating reflection at the free end of the finite rod and reflection and transmission at an interface between two media in the semi-infinite bi-viscoelastic rod are also presented. Asymptotic techniques are used throughout, and formal asymptotic wave-front expansions of the solution functions are obtained.

One Dimensional Coupled Thermoelastic Problem Due To Periodic Heating In A Semi-Infinite Rod.

This paper is concerned with the determination of the distribution of temperature and displacement in a thin semi-infinite elastic rod when its free end is subjected to periodic heating. It has been pointed out by P.Chadwick(1960) that the rigorous approach,i.c. the approach by way of the coupled equations, to the thermal boundary value problem. In this paper the one dimensional problem of the periodic heating of the free surface of a semi-infinite rod has been solved by a perturbation procedure, approximations upto the first order being retained.

Complex resonance and localized vibrations at the edge of a semi-infinite elastic cylinder

The effect of the free edge of a semi-infinite elastic cylinder with circular cross section is considered. It is shown that there exists a complex resonance frequency associated with an axially symmetric localized vibration near the free edge for every value of the Poisson ratio v. For two particular values of v, v = 0 and v = 0.1267, the imaginary part of the complex resonance frequency is zero which corresponds to a trapped mode of the semi-infinite rod. This resonance is also shown to be associated with two eigenfrequencies of the finite length cylinder.

Heat flow in composite rods – An old problem reconsidered

The interface temperature of two rods with equal cross section joined at one end and with different initial temperatures, initially always acquires the value characteristic for two semi-infinite rods. This value, which is shown to be a consequence of conservation of energy is, in general, different from the thermal equilibrium temperature in finite rods. To illustrate this result, two particular cases are discussed.

Stresses and deformations in the rod under the action on the end of the dynamic load

The stresses and deformations of a semi-infinite rod located in an elastic medium are considered when the dynamic load acts on the end face. Using the respect to time Laplace transform, a system of two differential equations of motion of the theory of Timoshenko beams has been solved. The integrals obtained are determined numerically. The graphs of the change in deflection and bending moment along the longitudinal coordinate are given.

Decay of waves in a rod owing to the hysteresis-type loss of energy in a material

Decay of waves propagating in a semi-infinite rod owing to the hysteresis-type loss of strain energy in the material is studied. Results of numerical calculations are given.

Axial impact on a semi-infinite elastic rod

An approximate theory for treating the axial collision of a rigid mass against an elastic rod was proposed by Saint–Venant more than 150 years ago. The method works only for short bars, under the assumption that the elastic axial displacement instantaneously propagates from one end to the other after the impact. Moreover, this hypothesis is unrealistic for long rods. Here we suggest an extension of the method which is able to treat the axial impact on the initial cross-section of a semi-infinite rod.

Free-field calibration of microphones: theoretical and experimental determination of the acoustic center

The concept of acoustic center is closely linked to the free-field calibration of microphones and have a great influence on the final results for the free-field sensitivity of the calibrated microphones. The international standard IEC 1094-3 defines the acoustic center of a reciprocal transducer as the point from which spherical waves seem to be diverging when the transducer is acting as a source. In the literature, the principal procedure used to measure the acoustic center of a reciprocal transducer is based on the measurement of the modulus of electrical transfer impedance at various distances of three pairs of microphones coupled by a free field. This paper presents a new procedure to determine the acoustic center of a reciprocal transducer assuming a source without any acoustic center and measuring the modulus of the electrical transfer impedance at various distances between this source and the transducer to be tested. Finally, the position of the acoustic center is deduced from the inverse distance law. Experimental values are presented and compared with theoretical values obtained using a theoretical model of the laboratory standard microphones (mounted on a semi-infinite rod) derived from those available in the literature.

Waves in a rod under pulsed loading

Wave processes in a semi-infinite rod located in an elastic medium under pulsed loading by an external distributed force are considered. A system of two differential equations of motion of Timoshenko’s beam theory is solved with the use of the Laplace transform in time. The resultant integrals are determined numerically. The changes in bending and bending moment over the longitudinal coordinate at different times are demonstrated.

The state of stress induced by ring dislocations in a semi-infinite stepped shaft

The state of stress induced in an axi-symmetric solid formed from a half-space and a bonded semi-infinite rod, by a family of ring dislocations of arbitrary Burgers vector is found. Particular care is given to the interaction between the Cauchy singularity near the dislocation core and the geometric singularity at the rod/half-space junction.

Elastic waves in a fluid-loaded, semi-infinite axisymmetric rod

In a fluid-loaded, semi-infinite axisymmetric rod, a free shear stress boundary condition on the circular cross-sectional end introduces complicated, nondispersive waves in the solid. They are composed of a pulse wave, which has the same waveform as the transmitted one and travels at speed c1, and different kinds of pulse trains, each of which travels along the rod at the speed of either c1 or square root of 2c2, where c1 and c2 are the propagating speeds of the longitudinal and transversal bulk waves, respectively. Furthermore, one can conclude from the solutions to the boundary conditions that c1 and square root of 2c2 are the only phase speeds of nondispersive waves. Frequency equations associated with these waves are established, and the solutions are solved and discussed analytically and numerically. The acoustic field in the fluid is also fully discussed, and it is more complicated than a single outgoing Hankel function as described for an infinite rod. The acoustic energy coupling between the solid and the fluid and the end reflection and transmission are quantified as well. In the end, experimental examinations of the echo spectra, using an aluminum rod immersed in the water and air, fully confirm the numerical solutions to the frequency equations.

Stress waves in a rod subjected to a moving load

The wave processes in a semi-infinite rod located in an elastic medium and subjected to a point load moving at a constant velocity are considered. The system of two differential equations of motion of Timoshenko beam theory is solved using the Laplace transform in time. The integrals obtained are determined numerically. Variation of the bending moment on the longitudinal coordinate behind the elastic-wave front and the region of action of the point force at various times is shown. The results of the solution are influence functions.

Micromagnetic simulation of the distribution of magnetization in semiinfinite single crystals

A method for calculating magnetization distribution in a single crystal in the form of a semiinfinite rod is suggested. The method is based on the division of the single crystal into two regions one of which, adjacent to the butt end of the rod, is finite and has a three-dimensional field of magnetization, and the remaining one (semiinfinite), in which the magnetization field is assumed to be two-dimensional. When computing the magnetization in the finite region, the effect of the magnetostatic field of the semiinfinite part of the rod is taken into account. An example of the calculation for a Co single crystal with a transverse orientation of the easy axis is given. This example shows that in the one and the same sample there are possible equilibrium states such that the magnetization distribution is virtually the same in any transverse section of the rod and differs qualitatively at the surface of the butt end of the rod from the distribution in the bulk of the rod.

Propagation of Discontinuities in Thermopiezoelectric Rod

ABSTRACT A model of the equations of generalized linear thermoelasticity theory for piezoelectric media is given. The formulation is applied to the generalized thermoelasticity theories—Lord-Shulman, Green-Lindsay, and Chandrasekharaiah and Tzou—as well as to the dynamic coupled theory. The state space approach is adopted for the solution of the one-dimensional problem of a semi-infinite piezoelectric rod. The Laplace transform technique is used. The expansions of the stress component, the temperature increment, the electric field, and the displacement, in Laplace transform domain, in power series, and the exact inversions for arbitrary time are given. The jump discontinuities are calculated for the four theories and the kinematical conditions of compatibility are verified. Numerical results are given and illustrated graphically by employing the numerical method for the inversion of the Laplace transforms. Comparisons are made with the results predicted by the four theories.