What precaution may be taken in developing and operating mec

What precaution may be taken in developing and operating mechanical system, in order to reduce system nonlinearities?

Solution

Answer :

Non-linear dynamical structures depending on control parameters are encountered in many areas of science and engineering. In the study of non-linear dynamical systems depending on a given control parameter, the stability analysis and the associated non-linear behaviour in a near-critical steady-state equilibriumpoint are two of the most important points; they make it possible to validate and characterize the non-linear structures. Stability is investigated by determining eigenvalues of the linearized perturbation equations about each steady-state operating point, or by calculating the Jacobian of the system at the equilibrium points. While the conditions and the values of the parameters which cause instability can be investigated by using linearized equations of motion, studies of the nonlinear behaviour of vibration problems, on the other hand, require the complete non-linear expressions of systems. Due to the complexity of non-linear systems and to save time, simplifications and reductions in the mathematical complexity of the non-linear equations are usually required. The principal idea for these non-linear methods is to reduce the order of the system and eliminate as many non-linearities as possible in the system of equations. In this artical, a study devoted to evaluating the instability phenomena in non-linear models is presented. It outlines stability analysis and gives a non-linear strategy by constructing a reduced order model and simplifying the non-linearities, based on three non-linear methods: the centre manifold concept, the rational approximants and the Alternating Frequency/Time domain method. The computational procedures to determine the reduced and simplified system via the centre manifold approach and the fractional approximants, as well as the approximation of the responses as a Fourier series via the harmonic balance method, are presented and discussed. These nonlinear methods for calculating the dynamical behaviour of non-linear systems with several degrees-of-freedomand non-linearities are tested in the case of mechanical systems with many degrees-of-freedom possessing polynomial non-linearities. Results obtained are compared with those estimated by a classical Runge-Kutta integration procedure. Moreover, an extension of the centre manifold approach using rational approximants is proposed and used to explore the dynamics of non-linear systems, by extending the domain of convergence of the non-linear reduced system and evaluating its performance and suitability.

Following precaution are must be taken :

1. High-risk situations

Do not start up or shut down equipment or installations without using the appropriate written operating procedure.

Any situation where the risk level is temporarily increased is reported. Induced risks are identified and analyzed and compensatory measures are implemented.

2. Traffic: Machine/vehicle/cyclist/pedestrians

Do not exceed the speed limits.

Traffic rules apply inside and outside sites.

3. Body mechanics and tools

Do not carry out work if you do not have the right tools for the job and the environment.

Adopting an inappropriate posture when handling objects or using tools can cause physical harm.

4. Protective equipment

Do not access installations and perform work without wearing general or task-specific personal protective equipment (PPE).

Collective protection is preferred. Individual protection completes preventive measures already taken.

5. Work permits

Do not perform work without a valid work permit.

Any work performed on site requires a permit.

6. Lifting

Do not walk under a load while lifting is taking place.

For any work involving a crane, hoist or other mechanical system, a preliminary risk analysis is required. Equipment must be in good condition. Personnel must be qualified and access to the area must be restricted.

7. Work on powered systems

Do not perform work without checking that the power and product source supply has been rendered inoperative.

Some works require the energy to be safely discharge or the equipment to be purged and vented. In such cases a lockout system is set up to isolate the energy or product according to a specific method.

8. Confined spaces

Do not enter a confined space until isolation has been verified and the atmosphere checked.

Do not enter a confined space (container, tank, well, etc…) without supervision and only after the atmosphere and isolation have been checked.

9. Excavation work

Do not perform excavation work without a valid work permit comprising a map of all underground hazards.

Manual or mechanical excavation work, including dragging rivers and seabeds, can only start after a risk analysis has been performed to identify all hazards in the zone and related precautions have been taken.

10. Working at heights

Do not work at heights without a safety harness when there is no collective protective equipment.