Recent advances in nonlinear passive vibration isolators

Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study.

The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview

Proper orthogonal decomposition and its applications—part i: theory

Control of chaos: Methods and applications in engineering

A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic

The present invention relates to a blade arrangement with damping elements and to a method of damping vibrations of a blade arrangement. The blade arrangement comprises a rotor and blades arranged on the circumference of the rotor. Damping elements (2, 3) are arranged between the blades and are in contact with the blades due to a centrifugal force, acting in the radial direction, during rotation of the rotor. In this case, at least two damping elements (2, 3) are arranged one behind the other in the circumferential direction of the rotor between adjacent blades, which damping elements (2, 3), during rotation of the rotor, come into contact with one another via a contact surface (6), and of which a first damping element (2) comes into contact with a first friction surface (4) of one of the blades and a second damping element (3) comes into contact with a second friction surface (5) of the other blade. A multiplicity of different vibration states can be effectively damped with the blade arrangement.

Blade arrangement with damping elements

The use of under-platform friction dampers is a common practice for the elimination of high cycle fatigue failures of turbomachinery blading. Damper performance curves and damper optimization curves are used for the design of friction dampers. It is establishedAAfrom the previous work that apart from damper mass, the contact stiffness between damper and the blade platform is an important parameter in achieving a good damper design. Several methods for the estimation of damper stiffness have been proposed in the literature. Some of them include: 1. Curve fitting approach to a measured frequency response function, 2. Compliance measurement, 3. Measurement of hysteresis loop etc. However, it is not possible to carry out extensive sets of experiments to observe the influence of various parameters on the contact stiffness. Numerical and/or analytical models for contact stiffness evaluation are the present needs for a damper designer. This paper addresses a detailed investigation of the contact stiffness computation. Finite element modeling of the damper and the platform is carried out to study the effect of various parameters such as friction coefficient, centrifugal load, material properties etc. on the contact stiffness. The role of surface roughness and wear are neglected in the present analysis. The reliability of the applied finite element meshes is verified by simulating Hertz’s contact problems. The parametric study indicates that the contact stiffness builds up with increase in friction coefficient, centrifugal force and elastic modulus of the damper material. The results received from a pilot experiment are also presented for further evaluation of the computed results. Finally, a very good agreement between the numerical and experimental performance curves (resonance response amplitude of the blade versus excitation amplitude for the constant damper mass; Cameron et. al, 1987) of the blade with the damper is found for the tangential contact stiffness obtained from the finite element calculation. The present work extends the quest for a rational approach to damper design.© 2001 ASME

B. Ravindra

Papers

Blade arrangement with damping elements

Estimation of Contact Stiffness and its Role in the Design of a Friction Damper

Comments on “on the physical interpretation of proper orthogonal modes in vibrations”

Chaotic response of a harmonically excited mass on an isolator with non-linear stiffness and damping characteristics

Stability Analysis of a Non-Linearly Damped Duffing Oscillator