TRANSVERSE VIBRATION OF TWO AXIALLY MOVING BEAMS CONNECTED BY AN ELASTIC FOUNDATION

ABSTRACT Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The system is a model of paper and paper-cloth (wire-screen) used in paper making. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. Due to the effect of translation, the dynamics of the system displays gyroscopic motion. The Euler-Bernoulli beam theory is used to model the deflections, and the governing equations are expressed in the canonical state form. The natural frequencies and associated mode shapes are obtained. It is found that the natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at the critical velocity; and, the frequency-velocity relationship is similar to that of a single traveling beam. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams, as well as the effects of the elastic foundation stiffness are investigated

2003TRIB-269 A CYLINDRICAL CONTACT MODEL FOR TWO DIMENSIONAL MULTIASPERITY PROFILES

ABSTRACT In practice, multi-asperity contact problems are often solved as two dimensional (2D) plane problems rather than true three dimensional (3D) problems. This is accomplished by assuming that each peak on a 2D scanned profile is the pinnacle of a half sphere. Hertz contact equations are then used to solve for the radius of contact and pressure profile. In reality, the local maximum in the plane may not be the maximum in the unmeasured depth direction, creating inherent errors in the contact model. This error is shown to be significant in contact problems when estimating the area of contact and total contact force over a single asperity. The pressure corrected SternbergTurteltaub model is introduced, in which a cylinder is used to model a sphere in a plane. This model is shown to improve the contact area and total force estimates for a range contact parameters. INTRODUCTION Typically, multi-asperity contact problems are solved by assuming that each asperity is a perfect sphere. Hertz's equations for contacting spheres gives good estimates of the contact pressure profile, if the radius of the sphere is know

ANALYTICAL AND EXPERIMENTAL NATURAL FREQUENCIES OF TRANSVERSE VIBRATION OF SANDWICH BEAMS INTERCONNECTED BY WINKLER ELASTIC FOUNDATION

ABSTRACT The free transverse vibration of an elastically connected axially loaded double beam system for different materials and geometry were measured experimentally and analyzed theoretically. The theory predicts that natural frequencies of the system are composed of two infinite sets, describing in-phase and out-of-phase vibrations. It is observed, for the case of identical beams, that the in-phase frequencies are independent of the elastic foundation stiffness and its frequencies are identical to a single beam with the same boundary conditions. To compare and verify the accuracy and reliability of theoretical models, experimental measurements of natural frequencies of free vibration of axially tensioned, double beams interconnected by a silicone rubber foundation with fixed-fixed supported conditions are conducted. The first four synchronous natural frequencies were measured, and they were found to increase with increasing tension. The experiments showed that the synchronous natural frequencies of axially tensioned double beam system with fixed-fixed end conditions are in excellent agreement with those for a tensioned single beam with the same end conditions. The asynchronous mode frequencies are not observed, and believed to be due to the existence of damping properties in the elastic foundation, which suppressed the outof-phase (asynchronous) mode frequencies

Lateral Vibration of Two Axially Translating Beams Interconnected by a Winkler Foundation

ABSTRACT Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. The natural frequencies and associated mode shapes are obtained. The natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at a critical velocity and a critical tension; and, divergence and flutter instabilities coexist at post-critical speeds, and divergence instability takes place pre-critical tensions. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams are presented

2003-TRIB-262 FRICTION INDUCED TRANSVERSE VIBRATIONS OF AN AXIALLY ACCELERATING STRING

ABSTRACT The purpose of this study is to investigate the dynamic response of axially translating continua undergoing both the effect of friction and axial acceleration. The axially moving continuum is initially modeled as a string, neglecting its flexural stiffness; the response, with particular interest given to transverse vibrations and dynamic stability, is studied through numerical methods. A finite element method is employed to discretize the space domain and an implicit α−method is employed to integrate the resulting matrix equation in the time domain. Results are given through time history diagrams and stability considerations

On the elastic-plastic shrink fit with supercritical interference

Shrink fits with perfectly elastic-plastic hub material cannot be treated with the help of Tresca's yield criterion, if the ratio of outer and inner diameter as well as the interference exceed certain limits. For linear hardening material, however, a solution exists for all radii ratios. It is shown that, for small hardening, the material in the neighbourhood of the interface undergoes a twofold change of the yield condition

Lateral Vibration of Two Axially Translating Beams Interconnected by a Winkler Foundation

ABSTRACT Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The system is a model of paper and paper-cloth (wire-screen) used in paper making. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. Due to the effect of translation, the dynamics of the system displays gyroscopic motion. The EulerBernoulli beam theory is used to model the deflections, and the governing equations are expressed in the canonical state form. The natural frequencies and associated mode shapes are obtained. It is found that the natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at the critical velocity; and, the frequency-velocity relationship is similar to that of a single traveling beam. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams, as well as the effects of the elastic foundation stiffness are investigated