Oscillations Of Rod Research Articles

Longitudinal and torsional oscillations of a rod in an Oldroyd-B fluid with suction or injection

The axisymmetric flow of a homogeneous Oldroyd-B fluid due to the longitudinal and torsional oscillations of an infinite circular rod is studied. At the surface of the rod, suction or injection velocity is applied. The motion and the constitutive equations from a system of P.D.E.s solved numerically. Only in few cases can the numerical results be compared with some known analytical solutions. Numerical experiments show the effect of the non-Newtonian dimensionless parameters on the velocity and on the shear stresses.

超磁歪発電機の創作 逆磁歪効果の適応

A new application of giant magnetostrictive materials (GMM) is proposed. In most application using GMM, transduction from magnetic energy to mechanical energy is utilized. As an interesting potential application, unlike the conventional ones, a reverse phenomenon of GMM is applied to an electric generator. Longitudinal oscillations of GMM rod give rise to a varying flux which induces a current in the coil surrounding the rod. This report deals with a fabrication of electric generator, accompanied by some experiments for generation and storage of electric energy. The experimental results imply that this method may be utilized for the effective use of the mechanical energy which will be wasted otherwise such as wind, running water, mechanical vibration, and so on.

Conditional stability of solitary waves propagating in elastic rods

The problem of dynamic stability of solitary wave solutions of the equations describing bending oscillations of inextensible elastic rods is treated. The governing equations describe sufficiently large displacements (though we are restricted to small strains). We show that under the condition of well-posedness of the initial value problem (in some specific sense) the family of solitary wave solutions of the mentioned equations is stable for the planar elastic rod. The framework of the analysis is largely based on the spectral properties of the “linearized Hamiltonian” H. We show that for planar oscillations H is positively semidefinite subject to a certain constraint, which implies the stability.

Dipole Moment of the Lowest Π Bending State of (HCN)2

The dipole moment of the lowest Π bending state of (HCN)2 has been determined by tunable far-infrared Stark spectroscopy to be 6.023(31) D. This represents a reduction in dipole moment of 0.54(5) D relative to the ground state, which is over five times too large for simple harmonic oscillations of uncoupled rods. Although qualitative comparison with related systems suggests the possibility of a secondary minimum near the T-shaped configuration, electrostatic modeling does not support the existence of such a feature.

Determination of characteristics of damping capacity for rods formed from several materials oscillating at different amplitudes and frequencies

Results of experimental study of the damping capacity of steel St. 3, glass-cloth-base laminate VFT-S, and beech wood by the method of damping oscillations during the transverse oscillations of cantilevered prismatic specimens within a broad range of stress amplitudes and vibration frequencies are presented. The experiments were conducted on the first three forms of transverse rod oscillations. Variation in vibration frequency was achieved by successive shortening of the specimens. An amplitude dependence of the logarithmic vibration decrement, which was adopted as a characteristic of the damping capacity, was obtained for all materials tested. The influence exerted by vibration frequency on the magnitude of the vibration decrement in the frequency range under consideration is established for specimens formed from the glass-cloth-base laminate VFT-S and beech wood, and is virtually undetected for steel St. 3 specimens. Empirical expressions that make it possible to describe the frequency dependencies of the vibration decrement of the materials under investigation with allowance for stress amplitude are proposed.

Many oscillations of a rigid rod

The many oscillations of a rigid rod—pendular, bifilar, torsional, coupled, nonlinear (including pure x3), and chaotic—provide interesting opportunities for experimental and theoretical investigations in introductory, intermediate, and advanced mechanics courses. Because of the rod’s simple geometry, precise expressions for the periods of its oscillations can be calculated, allowing comparisons between theory and experiment to within 0.5%. At this level of precision, the finite diameter of the pin upon which the rod oscillates has an observable effect on the period. A derivation is given of this effect, and applied to a ring oscillating on rods of various diameters. The large-angle oscillations of the bifilar pendulum are shown to depart by a measurable amount from the large-angle oscillations of the physical pendulum. The unequal-arm bifilar pendulum couples torsional and pendular modes in a calculable way. The vertical bifilar pendulum is a double pendulum with calculable coupled oscillations for small amplitudes and chaotic oscillations for large amplitudes. Other oscillators that can be built from a rigid rod, including an x3 oscillator, are described.

Longitudinal and torsional oscillations of a rod in a third-grade fluid

The flow of a third-grade fluid due to the torsional and longitudinal oscillations of an infinite circular rod is discussed. The non-linear coupled partial differential equations resulting from the momentum equations are solved numerically and the result is compared with that of a regular perturbation solution. The velocity field, the axial shear force, and the torque acting on the rod are computed. The stress power is found to be negative at particular times, but that expended in a cycle turns out to be positive.

A magnetostrictive electric generator

An electric generator based on the magnetostrictive effect is presented. Longitudinal oscillations of a Terfenol-D rod give rise to a varying flux which induces a current in a coil wound around the rod. A small prototype of such a device is discussed, and both calculations and experiments are performed. The problem of eddy current losses is addressed. >

Free oscillation of a curvilinear rod

A method and finite-element algorithm are presented for determining the frequencies and form of free oscillations of elastic curvilinear rods with finite rigidity under deflection. Numerical examples are introduced in order to investigate the dependence of the precision of the calculated frequencies and the form of the oscillations on the method of division into finite elements.

The use of generalized functions in the problem of elastic oscillations of a composite rod

The motion of a multicomponent anthropomorphic model is described by the equation of degenerate transverse oscillations of a one-dimensional system of rods with distributed mass and bending stiffness parameters and with concentrated inclusions into these parameters. The concentrated inclusions can be introduced into the analytic expression for the distributed parameters using impulse functions of the first and higher orders (the delta-function and its derivatives). The solution of the equation is found by the operational method. Krylov's generalized functions make it possible to obtain an analytic solution of the equation, which can be realized on a computer, and is written for the whole multicomponent structure at once in the framework of the direct and inverse problems of mechanics. Some optimization problems for a model of the motion of a sportsman are solved in the framework of the direct problem of mechanics.

Oscillations of an elastic rod with nonlinear boundary conditions

We study the dynamics of a building with a nonlinear seismic insulation system whose motion is described by the equation of transverse oscillations of a rod. We obtain the connection between the displacement of the lower section of the rod and the forces and moments in the section. We propose a numerical procedure for solving a nonlinear Volterra integral equation of second kind with dry friction damping. We determine the region of variation of the parameters of the building and the seismic insulation system in which it is possible to use the rigidbody model of the building. Two figures.

Oscillations of an elastic rod with nonlinear boundary conditions

Oscillations of an elastic rod with nonlinear boundary conditions

Transverse oscillations of rods, cables, and wires loaded with axial tensile forces is derived and experimentally verified : Soviet Journal of Nondestructive Testing, Vol. 26, No. 10, pp. 696–702 (Jun. 1991)

Transverse oscillations of rods, cables, and wires loaded with axial tensile forces is derived and experimentally verified : Soviet Journal of Nondestructive Testing, Vol. 26, No. 10, pp. 696–702 (Jun. 1991)

A more precise definition of relationships of the Kol'skii-Hopkinson composite-rod method

More precisely defined relationships of the composite-rod method in which attention is focused on distortion of the deformation pulse as a result of dispersion are derived. The Rayleigh equation of longitudinal rod oscillations is used in constructing these relationships [1]. It is proposed to measure the acceleration on the surface of the rod in one of the sections: this makes it possible to improve the correspondence between the parametrically assigned stress-strain function, determine the strain rate of the specimen easily, and establish the stresses in the specimen with allowance for the inertial component.

Oscillations of tubular helical cylindrical spirals with an internal flow of liquid

The results of determination of the natural and forced oscillations of the tubular rods of heat exchanger coils in the form of helical cylindrical spirals are given. The spectrum of natural oscillations of the spiral tubes is calculated and the modes of oscillations corresponding to it are constructed. It is noted that the presence of an internal flow of liquid leads to a change in the frequencies of natural oscillations of the system, as the result of which the zones of resonant conditions of movement and the amplitudes of oscillations in vibrations of the base change significantly.

Evaluating the second coefficient of viscosity from sound dispersionor absorption data

T HERMAL response of a viscoelastic rod subject to high- frequency cyclic loading is studied. The material con- sidered models a solid rocket propellant with temperature- dependent thermal conductivity. The mathematical model takes the form of a set of nonlinear, coupled partical differen- tial equations. An algorithm based on an iterative finite- difference method and an averaging technique have been developed to solve these coupled equations directly. The results indicate that the temperature of a material with temperature-dependent thermal conductivity is higher than that of one with constant thermal conductivity. This shows that noticeable errors can occur, especially at the thermal reso- nant frequencies where thermal conductivity is considered constant. Viscoelastic materials are dissipative in nature. They dissipate large amounts of mechanical energy in the form of heat when subjected to high-frequency loading. Solid pro- pellant, which is used as the rocket fuel, is also a viscoelastic material. Due to the high speed of the rocket, the solid fuel is subjected to high-frequency vibration. Heating due to vibra- tion near a resonance frequency may lead to melting or material failure. Tormey and Britton conducted vibration tests on solid fuel. They found that the heating due to vibraReceived Feb. 1, 1988; revision received Feb. 20, 1989. Copyright © 1989 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. *Assistant Professor, Mechanical Engineering Department. Member AIAA. tGraduate Student, Mechanical Engineering Department. tion increased the material temperature significantly to the ex- tent that it even flowed out of the motor. Henter derived a set of coupled partial differential equations for the propagation of stress, strain, and temperature distribution in a viscoelastic media. Huang and Lee studied longitudinal oscillations of viscoelastic rods. They solved the nonlinear coupled equations by iteration, thus determining stress and temperature distribu- tions along the rod. Mukherjee solved the same problem by a simpler method. He substituted a partially linear equation for the nonlinear differential equation and then solved this equa- tion by the finite-difference method. In all the papers cited certain parameters such as thermal conductivity and specific heat, which are weak functions of temperature, are assumed to be constants. This assumption, however, can lead to signifi- cant errors, especially at higher temperatures and critical fre- quencies.' This is due to the strong temperature dependence of the mechanical properties, which makes the system of equa- tions very sensitive to temperature variations. In this paper the effects of temperature-dependent thermal conductivity on the temperature distribution of a viscoelastic rod subjected to cyclic loading are discussed. Numerical solutions are obtained by the finite-difference method over a wide range of frequen- cies. The effects of frequency on the temperature and dis- sipated energy are studied. This leads to a critical frequency at which the temperature is maximum. Heating due to vibration near a critical frequency may cause the solid fuel to soften and melt the material. Therefore, accurate evaluation of these critical frequencies is vital. To simulate the solid rocket pro- pellant, a viscoelastic rod of length 1 insulated on its lateral surface, as shown in Fig. 1, is considered. The left end is free, while the right end is attached to a vibrator that has a pre- scribed stress given by a = a0 cosotf where a0 is the stress amplitude, co the frequency, and / the time. The temperature of the vibrator is assumed constant at T0, a convective boun- dary condition is assumed at x = 0, H is the surface conduc- tance, and K is the thermal conductivity of the material. It is also assumed that the solid rocket propellant is a ther- mohelogically simple material. The objective is to find the temperature distribution along the rod. Solving the governing equations (the energy balance equation, equation of motion, and stress-strain relationship), they reduce to the form

Thermal response of a dynamically loaded viscoelastic rod with variable properties

T HERMAL response of a viscoelastic rod subject to highfrequency cyclic loading is studied. The material considered models a solid rocket propellant with temperaturedependent thermal conductivity. The mathematical model takes the form of a set of nonlinear, coupled partical differential equations. An algorithm based on an iterative finitedifference method and an averaging technique have been developed to solve these coupled equations directly. The results indicate that the temperature of a material with temperature-dependent thermal conductivity is higher than that of one with constant thermal conductivity. This shows that noticeable errors can occur, especially at the thermal resonant frequencies where thermal conductivity is considered constant. Viscoelastic materials are dissipative in nature. They dissipate large amounts of mechanical energy in the form of heat when subjected to high-frequency loading. Solid propellant, which is used as the rocket fuel, is also a viscoelastic material. Due to the high speed of the rocket, the solid fuel is subjected to high-frequency vibration. Heating due to vibration near a resonance frequency may lead to melting or material failure. Tormey and Britton conducted vibration tests on solid fuel. They found that the heating due to vibraReceived Feb. 1, 1988; revision received Feb. 20, 1989. Copyright © 1989 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. *Assistant Professor, Mechanical Engineering Department. Member AIAA. tGraduate Student, Mechanical Engineering Department. tion increased the material temperature significantly to the extent that it even flowed out of the motor. Henter derived a set of coupled partial differential equations for the propagation of stress, strain, and temperature distribution in a viscoelastic media. Huang and Lee studied longitudinal oscillations of viscoelastic rods. They solved the nonlinear coupled equations by iteration, thus determining stress and temperature distributions along the rod. Mukherjee solved the same problem by a simpler method. He substituted a partially linear equation for the nonlinear differential equation and then solved this equation by the finite-difference method. In all the papers cited certain parameters such as thermal conductivity and specific heat, which are weak functions of temperature, are assumed to be constants. This assumption, however, can lead to significant errors, especially at higher temperatures and critical frequencies.' This is due to the strong temperature dependence of the mechanical properties, which makes the system of equations very sensitive to temperature variations. In this paper the effects of temperature-dependent thermal conductivity on the temperature distribution of a viscoelastic rod subjected to cyclic loading are discussed. Numerical solutions are obtained by the finite-difference method over a wide range of frequencies. The effects of frequency on the temperature and dissipated energy are studied. This leads to a critical frequency at which the temperature is maximum. Heating due to vibration near a critical frequency may cause the solid fuel to soften and melt the material. Therefore, accurate evaluation of these critical frequencies is vital. To simulate the solid rocket propellant, a viscoelastic rod of length 1 insulated on its lateral surface, as shown in Fig. 1, is considered. The left end is free, while the right end is attached to a vibrator that has a prescribed stress given by a = a0 cosotf where a0 is the stress amplitude, co the frequency, and / the time. The temperature of the vibrator is assumed constant at T0, a convective boundary condition is assumed at x = 0, H is the surface conductance, and K is the thermal conductivity of the material. It is also assumed that the solid rocket propellant is a thermohelogically simple material. The objective is to find the temperature distribution along the rod. Solving the governing equations (the energy balance equation, equation of motion, and stress-strain relationship), they reduce to the form

Bending-torsional oscillations of a rod with mass

Bending-torsional oscillations of a rod with mass

Dispersion of nonlinear spatial waves in a rod

A nonlinear generalization of the dispersion equations of three-dimensional oscillations is constructed for an inextensible rod. The dispersion equation is obtained for waves of any amplitude in the closed form,containing a solution of a certain system of two transcendental equations. For small amplitudes the final relationships are given in explicit form, taking into account the nonlinearity in the first approximation. The dispersion relation contains, just as in the linear case, the mean tensile force, the wave number and frequency, as well as the parameters defining the oscillation amplitudes. From the dispersion relation it follows that the larger the oscillation amplitude, the greater the wave velocity. The interaction of the transverse oscillations at different planes, absent in the linear case, is described, the characteristics of the “effective” rod computed and the corresponding averaged equations constructed. A nonlinear generalization of the dispersion equation was constructed earlier in /1/ for the plane oscillations of a compressible rod, for the case of small finite amplitudes. An analogous problem was studied in /2/ for the oscillations of an inextensible rod for the case of finite amplitudes, and in addition a concept of an “effective” rod was introduced, its characteristics computed, and the corresponding averaged equations constructed. The present paper generalizes the results of /2/.

Approximate equations for the oscillations of viscoelastic rods and plates

Approximate equations for the oscillations of viscoelastic rods and plates