S. Sankar

Single unit impact damper in free and forced vibration

Abstract The single unit impact damper under free and forced vibrations is studied. The effects of mass ratio, coefficient of restitution, and gap size on the free vibrations are determined by simulating motion on the digital computer. Agreement of theoretical results with the present and previous experimental results in the free vibration state is good. In the study of forced motion, charts are developed, by using the closed form solution, showing optimum gaps and corresponding displacement amplitude reduction within the resonant frequency range. The optimum gap at resonance is not necessarily optimal at other frequencies.

Multiunit impact damper—Re-examined

The multiunit impact damper with Coulomb friction has been studied theoretically and by simulation on the digital computer. It is found that the performance of a single damper is retained when it is replaced by a multi-unit damper with a moderate number of units having the same total mass, coefficients of Coulomb friction and restitution, and gap. However, the velocity discontinuity of the damped system is reduced significantly. In periodic motion with identical units, each unit exhibiting two equispaced impacts/cycle motion, impacts occur in clusters and are not uniformly distributed in time. The effect of the number of units and Coulomb friction on the amplitude reduction, velocity discontinuity at impact and temporal distribution of impacts is considered.

Repeated impacts on a sinusoidally vibrating table reappraised

The traditional simplification for one commonly used example of repeated collisions is shown to be frequently erroneous for a wide range of coefficients of restitution. Bounded errors arise from an artificial speed constraint whose circumvention is largely but not exclusively unpredictable. Therefore exact equations, whose periodic solutions are detailed, should be generally used.

Semi-active force generators for shock isolation

Abstract Semi-active suspensions represent a compromise between active and passive suspensions. The isolator requires virtually no power and the forces in the damper are generated by modulating its orifices for fluid flow. The shock isolation characteristics of semi-active isolators based on two different control schemes are presented. In the first type the control depends on absolute and relative velocities of the sprung mass while in the second type it depends on relative displacement and relative velocity. Both employ continuous control of damper forces as opposed to on-off control. The semi-active isolator is incorporated in a one-degree-of-freedom quarter vehicle model. The base is subjected to rounded pulse and rounded step transient displacement inputs. The performance is evaluated in terms of the resulting acceleration of the sprung mass and the relative displacement across the isolator. The performance of the semi-active isolators is compared with that of passive and active isolators. It is seen that both the semi-active control schemes can simultaneously reduce the acceleration and the relative displacement, something passive linear isolators cannot do. They also achieve a performance close to that of a fully active isolator without requiring power, or complex and expensive instrumentation.

An extended transfer matrix-finite element method for free vibration of plates

Abstract A combination of extended transfer matrix and finite element methods is proposed for obtaining vibration frequencies of structures. This method yields the value of the frequency once a trial value is assumed. By using this technique, the number of nodes required in the regular finite element method is reduced and therefore a smaller computer can be used. Besides, no plotting of the values of the determinants corresponding to each assumed frequency is necessary. A worked example is given for the case of vibration of a cantilever plate. The results show fast convergence from the assumed value to the true natural frequency.

A discrete harmonic linearization technique for simulating non-linear mechanical systems

An efficient simulation technique referred to as DH linearization is presented. The non-linear damping mechanisms in vibration isolation systems are represented by an array of viscous damping coefficients which are functions of local values of excitation frequency, and amplitude. The non-linear system is thus represented by a number of algebraic expressions. In the DH linearization technique an iterative algorithm is used, with simulataneous solution of the algebraic expressions. Unique dynamic behaviour of the mechanical systems, specifically due to discontinuous non-linearities, is quite accurately represented. The simulation of a non-linear mechanical system is carried out by using statistical, harmonic, and DH linearization techniques. A comparison of the three technques reveals that the DH linearization technique provides non-linear system response close to the exact solution, throughout the entire frequency range. A number of examples are presented to demonstrate the effectiveness of DH linearization for harmonic as well as random inputs.

Performance of different kinds of dual phase damping shock mounts

A detailed performance analysis of six different kinds of dual phase damping shock mounts is presented. The conclusions of this study are of interest to engineers concerned with the design of shock mounts. The results also contain important clues which may be useful in guiding future research workers in the development of a theory of the optimization of non-linear damping.

A new approach for the calculation of response spectral density of a linear stationary random multidegree of freedom system

A new approach for the calculation of response spectral density for a linear stationary random multidegree of freedom system is presented. The method is based on modifying the stochastic dynamic equations of the system by using a set of auxiliary variables. The response spectral density matrix obtained by using this new approach contains the spectral densities and the cross-spectral densities of the system generalized displacements and velocities. The new method requires significantly less computation time as compared to the conventional method for calculating response spectral densities. Two numerical examples are presented to compare quantitatively the computation time.