A.K. Mallik

Variational approach for singularity-free path-planning of parallel manipulators

This paper addresses the problem of singularity-free path-planning for parallel manipulators. Unlike in serial manipulators, where there are only boundary singularities, parallel manipulators also possess singular configurations within the workspace where the manipulators are uncontrollable. Therefore, it is imperative that the generated paths are singularity-free. In this paper, we use a variational approach for planning singularity-free paths for parallel manipulators, based on a Lagrangian incorporating both a kinetic energy term which keeps the path short, and a potential energy term which ensures that the obtained path is singularity-free and the actuator lengths remain within their prescribed limits. The approach is applied to several parallel manipulators to evaluate the performance of this method.

Non-linear vibrations of a harmonically excited autoparametric system

Harmonic forced vibration of a spring-mass-damper system with a parametrically excited pendulum hinged to the mass is investigated. Two types of restoring forces on the pendulum are considered. The method of harmonic balance is used to evaluate the system response. The results are also verified by numerical integration. Non-periodic system responses are possible if the excitation parameter is large. The performance of the pendulum as an absorber is also studied.

Non-linear vibration of a travelling beam

Free and forced responses of a travelling slender beam including the non-linear terms are studied. A simple method of calculating the non-linear, non-stationary, complex normal mode is presented. The hardening characteristic and intercoupling of linear modes during the non-linear modal vibration are clearly brought out. The response of the beam, excited by a point harmonic load, is calculated using the non-linear normal modes. A stability analysis is provided to delineate the stable and unstable roots of the response.

Dynamics of a weakly non-linear periodic chain

Harmonic wave propagation in an infinite, non-linear periodic chain is investigated. Both hardening and softening types of non-linearity are considered. A perturbation approach is used to obtain both propagation and attenuation constants which are amplitude dependent for such a non-linear system. Only the first-order non-linear effect is retained in the analysis. Special attention is given to the bounding frequencies of the propagation zone. Propagation constants are used to obtain the non-linear natural frequencies and the associated non-linear modes of both finite chains with homogeneous boundary conditions and endless cyclic chains. The computational effort is shown to be independent of the number of elements present in the chain. The interaction of two opposite-going primary waves in semi-infinite or finite chains are seen to generate secondary waves. The non-linear normal modes are found to consist of atmost two linear modes and for some boundary conditions exhibit restricted orthogonality properties. Some explicit numerical results are included to validate the wave-propagation approach for studying free vibration of such non-linear periodic chains.

Hard duffing-type vibration isolator with combined Coulomb and viscous damping

The steady-state, harmonic response of a vibration isolation system with a cubic, hard non-linear restoring force and combined Coulomb and viscous damping is presented. The results have been obtained by using the method of harmonic balance. It has been assumed that the motion is continuous without any stop. An anomalous jump in the response, similar to the one obtained in earlier studies on certain soft systems, is observed when the isolation system is subjected to a base excitation. Linear stability analysis is carried out to determine the status of the anomalous jump. The effect of the damping parameters on the jump in the response is investigated. Transmissibility curves are plotted for various parameter values to study the performance characteristics. The obtained results extend the previous works of Den Hartog and Ruzicka who considered a linear restoring element.

An approximate theory for the sound radiated from a periodic line-supported plate

An approximate method is presented for estimating the sound power radiated by an infinite plate, supported elastically along parallel, equi-spaced lines and subjected to a simple pressure field convecting uniformly over the plate in a direction perpendicular to the supports. Suitable complex modes are assumed for the induced plate flexural wave motion, and an energy method is used to estimate the plate response and the radiated sound power. The effect on the plate response of the acoustic loading is taken into account. The influence of the convection velocity (which may be subsonic) and of certain plate parameters is investigated.

Mechanical error of a four-bar linkage coupler curve

Mechanical error in the coupler curve of a four-bar linkage is estimated in terms of translational and rotational components of the position error. Cognate linkages, theoretically capable of generating identical coupler curves, are seen to have different sensitivity to the errors in the link lengths. Numerical results are included to identify the most critical link of a given mechanism. The maximum translational and rotational errors are found to be proportional to the errors in link lenght when all the links have the same but small error.

Improvement of damping characteristics of structural members with high damping elastic inserts

The major objective of this work is to investigate theoretically the possibility of improving the damping capacities of structural members with the help of inserts of special high damping materials. The inserts have been considered to be both welded and press-fit to the members. It has been observed that the effectiveness of the press-fit inserts is much more than that of the welded inserts. In case of the welded inserts there exists an optimum size whereas for shrink-fit inserts best results are expected when the inserts are solid. It has been found that with such a method the damping capacity of a member can be considerably increased with no significant loss in static rigidity.

Wave propagation and vibration response of a periodically supported pipe conveying fluid

Propagation of free harmonic waves, in a periodically supported infinite pipe, has been studied. The presence of the Coriolis term in the equation of motion renders the phase velocity different for the positive and the negative going waves. Hence no classical normal modes (in the sense of standing modes) exist. Natural frequencies of a periodically supported finite pipe have been obtained by using the wave approach. The response of the infinite pipe to a convected harmonic pressure field has also been obtained. Owing to the difference in the phase velocities of the positive and the negative going free waves, the coincidence frequency depends on the direction of the convected loading. The static buckling or the divergence instability of such pipes has also been considered from the wave approach.

Elastomeric Damper Model and Limit Cycle Oscillation in Bearingless Helicopter Rotor Blade

The authors investigate the phenomenon of limit cycle in bearingless rotor blades by studying the transient response of the blade with two different elastomer models. Even though both models fit the experimental data fairly well, the response characteristics of the blade exhibit a totally different nature. These results show that the phenomenon of limit-cycle oscillation is highly dependent on elastomer model. It is recommended that care must therefore be exercised in modeling the elastomer.