S.K. Dwivedy

A review of the experimental estimation of the rotor dynamic parameters of seals

In this paper, we present a critical review of the experimental estimation of the rotor dynamic parameters (RDPs) of different types of seals. The main focus is on rotary seals for high-speed and high-pressure applications. These play an active role between the rotating and stationary parts of turbomachinery to prevent working fluid leakage; however, they can cause rotor instability. The main parameters that govern the instability are the RDPs of seals. This review includes a variety of rotary seals, a description of experimental rigs and measurement techniques, parameter estimation procedures, and uncertainty analysis. Based on the state of the art in the experimental estimation of the RDPs of seals, conclusions are made and future directions are suggested.

Non-linear dynamics of a slender beam carrying a lumped mass under principal parametric resonance with three-mode interactions

The non-linear response of a base-excited slender beam carrying a lumped mass subjected to principal parametric resonance is investigated. The attached mass and its location are so adjusted that the system exhibits 1:3:5 internal resonances. Method of multiple scales is used to reduce the second-order temporal differential equation to a set of first-order differential equations which is then solved numerically to obtain the steady-state response and stability of the system. The steady-state response thus obtained is compared with those found by single- and two-mode analyses and very significant differences are observed in the bifurcation and stability of the response curves. The effects of external and internal detuning, amplitude of excitation and damping on the non-linear steady state, periodic, quasi-periodic and chaotic responses of the system are investigated. Funnel-shaped chaotic orbits, fractal orbits, cascade of period-doubling, torus doubling and intermittency routes to chaos are observed in this system. A simple illustration is given to control chaos by changing the system parameters.

Fabrication and characterization of magnetorheological elastomer with carbon black

In this study, the isotropic magnetorheological elastomer samples are fabricated with and without addition of carbon blacks into the silicon rubber matrix and carbonyl iron particles in the absence of magnetic field. Microscopic and morphological analyses, thermo-gravimetric analysis, MH measurements, thermomechanical analysis, dynamic mechanical analysis, tensile test and magnetorheological test of magnetorheological elastomers are performed to characterize the fabricated magnetorheological elastomers. The experimental results demonstrate that the addition of carbon black improves the mechanical properties of the magnetorheological elastomer. The fabricated magnetorheological elastomers can be used in applications such as adaptive tuned vibration absorbers and vibration reduction in sandwich structures.

Simultaneous combination and 1:3:5 internal resonances in a parametrically excited beam–mass system

Abstract The nonlinear dynamics of a base-excited slender beam carrying a lumped mass subjected to simultaneous combination parametric resonance of sum and difference type along with 1:3:5 internal resonances is investigated. Method of normal form is applied to the governing nonlinear temporal differential equation of motion to obtain a set of first-order differential equations which are used to obtain the steady-state, periodic, quasi-periodic and chaotic responses for different control parameters viz., amplitude and frequency of external excitation and damping. Frequency response, phase portraits, time spectra and bifurcation diagram are plotted to visualize the system behaviour with variation in the control parameters. Here, two distinct zones of trivial instability, blue sky catastrophe phenomena, jump down phenomena, simultaneous occurrence of periodic and chaotic orbits, period doubling of the mixed-mode periodic orbits leading to chaos, attractor merging crisis, boundary crisis, type II and on–off intermittencies are observed. Bifurcation diagram is plotted to facilitate the designer to choose a safe operating zone.

Nonlinear Dynamics of a Cantilever Beam Carrying an Attached Mass with 1:3:9 Internal Resonances

In this paper the nonlinear response of a base-excited slender beam carrying an attached mass is investigated with 1:3:9 internal resonances for principal and combinationparametric resonances. Here the method of normal forms is used to reduce the second order nonlinear temporal differential equation of motion of the system to a set offirst order nonlinear differential equations which are used to find the fixed-point, periodic, quasi-periodic and chaotic responses of the system.Stability and bifurcation analysis of the responses are carried out and bifurcation sets are plotted. Many chaotic phenomena are reported in this paper.

Nonlinear Vibrations and Frequency Response Analysis of a Cantilever Beam Under Periodically Varying Magnetic Field

In this paper, nonlinear vibration of a cantilever beam with tip mass subjected to periodically varying axial load and magnetic field has been studied. The temporal equation of motion of the system containing linear and nonlinear parametric excitation terms along with nonlinear damping, geometric and inertial types of nonlinear terms has been derived and solved using method of multiple scales. The stability and bifurcation analysis for three different resonance conditions were investigated. The numerical results demonstrate that while in simple resonance case with increase in magnetic field strength, the system becomes unstable, in principal parametric or simultaneous resonance cases, the vibration can be reduced significantly by increasing the magnetic field strength. The present work will be very useful for feed forward vibration control of magnetoelastic beams which are used nowadays in many industrial applications.

Nonlinear Response of a Parametrically Excited System Using Higher-Order Method of Multiple Scales

Two fundamentally different versions of the method of multiple scales (MMS) are currently in use in the study of nonlinear resonance phenomena. While the first version is the widely used reconstitution method, the second version is proposed by Rahman and Burton [1]. Both versions of the second-order MMS are applied to the differential equation obtained for a parametrically excited cantilever beam with a lumped mass at an arbitrary position. The bifurcation and stability of the obtained response show the difference between the two versions. While the Hopf bifurcation phenomena with no jump is found in the case of second-order MMS version I, both jump-up and jump-down phenomena are observed in second-order MMS version II, which closely agree with the experimental findings. The results are compared with those obtained by numerically integrating the original temporal equation.

Vibration analysis of a three-layer magnetorheological elastomer embedded sandwich beam with conductive skins using finite element method:

In this article, the free and forced vibration analyses of a three-layered magnetorheological elastomer embedded viscoelastic cored sandwich beam with conductive and non-conductive skins have been carried out using finite element method. The finite element method formulation is validated by conducting experiments for a viscoelastic cored sandwich cantilever beam. For an adaptive magnetorheological elastomer embedded viscoelastic cored sandwich beam, results have been compared with those obtained from analytical method. The natural frequencies and loss factors of the magnetorheological elastomer embedded viscoelastic cored sandwich beam have been determined for various system parameters. The forced vibration responses of the magnetorheological elastomer embedded sandwich beam are also evaluated under harmonic force excitations. The results suggest that the natural frequencies and transverse displacement response of the magnetorheological elastomer embedded sandwich beams are strongly influenced by the strength of the applied magnetic field, the location, the length of the magnetorheological elastomer patch and the magnetoelastic loads due to the conductive skins.

Nonlinear response of a soft magneto elastic cantilever beam with end mass under static and dynamics magnetic field

In this work, the nonlinear vibration of a cantilever beam with end mass subjected to both static and alternating transverse magnetic field has been studied. The governing temporal equation of motion of the system which contains nonlinearities of geometric and inertial type along with parametric excitation and non-linear damping terms due to the body force and couple generated by the magnetic field has been derived. Method of multiple scales (MMS) is used to determine the instability region and frequency response curves of the system. The influences of the damping, amplitude of static and dynamic magnetic field strength, and tip mass on the instability regions and frequency response curves for simple and principal parametric resonance conditions have been investigated. These results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion.

Dynamic Modeling and Effect of Dehydration on Segmented IPMC Actuators Following Variable Parameter Pseudo-Rigid Body Modeling Technique

An ionic polymer-metal composite actuator has been analyzed following the variable parameters pseudo-rigid body modeling (VPPRBM) technique in order to assess the effect of dehydration on bending resistance and bending response. An experiment is conducted with a single patch IPMC actuator and the dehydration factor is obtained following the Cobb-Douglas production method. An energy-based dynamic model of the patches has been derived after developing the forward kinematics incorporating loss due to dehydration. Simulation has been performed for two segmented IPMC patches to demonstrate the change in bending resistance, bending response, and end-tip positioning for various input voltages.