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

Forced nonlinear oscillations of an autoparametric system-Part 1: Periodic responses

Forced oscillations of a two degree-of-freedom autoparametric system are studied with moderately high excitations. The approximate results obtained by the method of harmonic balance are found to be satisfactory by comparing with those obtained by numerical integration. In the primary parametric instability zone, separate regions of stable and unstable harmonic solutions are obtained. In the regions of unstable harmonic solutions, depending on the forcing amplitude and frequency, the solutions may be amplitude modulated or completely nonperiodic. In the latter case the numerical integrations do not converge

Forced nonlinear oscillations of an autoparametric system-Part 2: Chaotic responses

Chaotic oscillations arising in forced oscillations of a two degree-of-freedom autoparametric system are studied. Statistical analysis of the numerically integrated nonperiodic responses is shown to be a meaningful description of the mean square values and the frequency contents of the responses. Some qualitative experimental results are presented to substantiate the necessity of performing the statistical analysis of the responses even though the system and the input are deterministic

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

Response of non-linear dissipative shock isolators

In this paper, a simple technique combining the straightforward perturbation method with Laplace transform has been developed to determine the transient response of a single degree-of-freedom system in the presence of non-linear, dissipative shock isolators. Analytical results are compared with those obtained by numerical integration using the classical Runge-Kutta method. Three types of input base excitations, namely, the rounded step, the rounded pulse and the oscillatory step are considered. The effects of nonlinear damping on the response are discussed in detail. Both the positive and negative coefficients of the nonlinear damping term have been considered. It has been shown that a critical value of the positive coefficient maximizes the peak values of relative and absolute displacements. This is true for any power-law damping force with an index greater than 1. On the other hand, the overall performance of a shock isolator improves if the nonlinear damping term is symmetric and quadratic with a negative coefficient

Performance of non-linear isolators and absorbers to shock excitations

To improve the performance of a non-linear shock isolator, four different alternatives are being considered and compared. These are (i) an isolator with a Coulomb damper, (ii) a three-element isolator, (iii) an isolator along with vibration absorber and (iv) a two-stage isolator. Three different types of shock inputs are considered as the base motion to be isolated. Three different indices are used to judge the overall performance characteristics of the isolator. Overall, it is seen that the three-element and two-stage isolators are preferable in the presence of a non-linear cubic damping