Nashif vibration damping pdf

The popularity of sports involving sporting implements, such as golf, tennis, hockey, and racquet ball, continues at a strong pace. Better engineering, better materials, lighter, stronger implements with larger heads and more power have improved the play of games with these implements and thereby increased the enjoyment associated therewith.

Although these implements have worked well, they suffer from the disadvantage that despite improvements in other areas the unwanted vibratory phenomena generated upon an impact with a ball which is not dead center in the "sweet spot" of the implement remains. Lighter implements have allowed players to swing harder at the ball. Larger implements, while increasing the "sweet spot" on the face thereof, have also increased the area outside the "sweet spot", providing increased opportunity for imperfect or offset contact with the ball.

Vibrations are introduced into the implement due to the impact the ball creates on the face of the implement. At impact, the velocity of the ball transfers its energy into the face and the face, in turn, pass it onto the handle of the implement. The sweet spot of the implement is the point of minimum vibration. When the ball is hit perfectly, in the center of the sweet spot, the vibrations generated do not negatively affect the player and even give a distinctive, pleasant sound confirming the quality of the player's stroke.

On the other hand, when the ball is hit off center, this condition creates imbalanced forces and generates vibrations. Ideally, and in the absence of a damping medium, the vibrations would continue for an infinite time. Unfortunately, the human arm, which grasps the implement, is a good damping medium and absorbs this energy. The energy absorbed by the human arm is dissipated in the form of pain and tiredness. Commercial dampers presently available primarily help in reducing noise generated in connection with an off center contact with the ball but contribute little to the reduction of vibrations in the implement which are ultimately damped by the human arm.

It is, therefore, one object of the present invention to provide a vibration damping device for a sporting implement. It is another object of the present invention to provide a vibration damping device for a sporting implement which effectively cancels the vibration generated by unbalanced forces due to an off center contact with a ball. To achieve the foregoing objects, the present invention is a vibration damping device for a sporting implement including a base member and a mass mounted to the base member and cantilevered relative to the base member.

The device is tuned such that it vibrates at the same frequency as the sporting implement but out of phase therewith. One advantage of the present invention is that a vibration damping device is provided for a sporting implement in which the device itself is a vibrating system.

Another advantage of the present invention is that the vibration damping device vibrates at the same frequency as the sporting implement. Yet another advantage of the present invention is that the sporting implement and vibration damping device vibrate at the same frequency and in a phase opposite to each other to cancel out each other and the resultant responses in the sporting implement are reduced by a significant amount.

A further advantage of the present invention is that the vibrations transmitted into the sporting implement are greatly reduced and the human arm tends to absorb much less energy and effectively increases the sweet spot areas of the implement significantly. Other objects, features and advantages of the present invention will be readily appreciated as the same becomes better understood after reading the subsequent description taken in conjunction with the accompanying drawings.

Referring to the drawings and in particular to FIG. The vibration damping device 10 may be employed to reduce vibrations in any stringed racquet but is particularly adapted for use with tennis or racquetball racquets. While the vibration damping device 10 is shown in connection with a tennis racquet 12, it should be appreciated that this is by way of illustration and not by way of limitation.

Such racquets 12 generally include a racquet frame 13 having a head 14, strings 16, a throat 18 and a handle 20 as is known in the art. Referring to FIGS. The viscoelastic member 22 is ideally mounted low on a face of the racquet 12 near the throat However, it should be appreciated that the vibration damping device 10 may be mounted at any position on the face of the racquet 12 which would not otherwise interfere with play. The vibration damping device 10 also includes at least one movable mass or member, generally indicated at 24, carried on the viscoelastic member The moveable member 24 is movable relative to the viscoelastic member 22 in response to vibrations induced by an impact on the strings 16 of the racquet 12 such that the vibration damping device 10 vibrates over the same frequency range but out of phase with the racquet 12 to dampen vibrations in the racquet The viscoelastic member 22 includes a body 26 which is made of a viscoelastic material with appropriate modulus and damping values.

The body 26 has a pair of opposed flat sides 28 and a pair of slots 30 disposed opposite one another on the body 26 and interposed between the flat sides Newnham and T. Uchino and T. CAS Google Scholar. Hagood and A. Von Flotow , J. Luo , P. Rossiter , G. Sinmon , L. Koss and J. Unsworth , ibid. Jaffe , W. Jaffe and H. Van Randeraat and R. Download references. You can also search for this author in PubMed Google Scholar. Reprints and Permissions.

It is obvious that the vertical position of the test sample might show influence on frequencies of free vibration due to the absence of environmental chamber the gravitational forces. This effect depends on the free length of test specimen. To estimate this effect, series of numerical analysis are carried out on vertically clamped cantilever beam model.

These findings are also supported by comparing the test results of flexural vibrations for horizontally and vertically arranged test samples. The standard also states that fixation conditions of test specimen plays important role in damping and for fixed edge conditions, it is recommended to use base beams with root section properly clamped in test fixture Fig 4a. Variants of end conditions for the test-specimen.

In the proposed variant of the experimental setup, fixed support end condition is provided by the placing the test-specimen between two rigid plate and then is fixed with mechanical connection as whole Fig. To confirm the correctness of the use of this type of arrangement as a rigid support another experimental verification has been carried out. In this study, a dual lever cantilever test sample is placed between two calibrated cylinders Fig.

Figure 5. Test of dual lever cantilever on shaker This verification study showed that the difference between the first flexural mode resonance fre- quencies in the two different fixing schemes Fig.

Aerodynamic external damping The preliminary experimental research with the proposed method [13] revealed a significant de- pendence of the damping parameters on specimen width, which can only be explained by the pres- ence of external aerodynamic damping. Neglecting identification of aerodynamic damping con- stituent can make a substantial error in the assessment of the internal material damping properties and requires comprehensive study to reveal its contribution.

In Fig. These test results are evidence of significant influence of aerodynamic drag on the damping properties. This change in the dynamic modulus of elasticity shall to be taken into account not only for further evaluation of stiffness and damping properties of soft materials in accordance with the standard [12], but also in the dynamic analysis of structures made of this material. Dependence of dynamic elastic modulus of Al on vibration frequency At the second stage, decay curve of damped flexural vibrations is processed to determine the damping properties of the base material.

Here, LD curve obtained from experimental data of test specimen is illustrated in 1st curve, aero- dynamic damping is calculated according to analytical formulae from [14] is presented by 2nd curve and internal damping LD of investigated base material, which is obtained by subtracting the sec- ond from the first, shown in 3rd curve.

Presented dependencies are in good agreement with the experimental results shown in Fig. Noise control. Muszynska, A. Internal damping in mechanical systems. Dynamika Maszyn. Polish Academy of Science — Lazan, B. Damping of materials and members in structural mechanics. New York: Pergamon Press. Karnovsky, I. Advanced methods of structural analysis. New York: Springer. CrossRef Google Scholar. Strelkov, S. Introduction to the theory of vibrations.

Goodman, L. Analysis of slip damping. Journal of Applied Mechanics, 3. Protection of radio-electronic equipment and precision equipment from the dynamic excitations. Moscow: Radio. Henderson, J. Babakov, I. Theory of vibration.

Free vibrations of beams and frames. Eigenvalues and eigenfunctions. Oberst, H. Acustica, 4, — Harris, C. Editor in Chief Shock and vibration Handbook 4th ed.

Ross, D. Damping of plate flexural vibrations by means of viscoelastic laminate. Collar, A.