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International audience; Relevant for engineering a wide range of technological systems, Property Model Methodology (PMM) is applied in this paper to the development process of a helicopter function in the frame of the ARP4754A/ED79A. After a short presentation of the method, the case study is presented: "to retract and to extend airborne the landing gear system". Then, each stage of the PMM development process is illustrated by examples from the case study: (1) Modeling the top level requirements specification, (2) Validating the requirements specification by proof and simulation, (3) Modeling the architectural design, Refining the top level requirements into requirements specified to the different subsystems contributing to the function and Modeling the terminal subsystems detailed designs (4) Validating the requirements specified to the contributing subsystems by proof or simulation, (5) Verifying the design models by simulation and finally (6-8) Verifying physical implementations by test on the basis of all validation and verification scenarios accumulated throughout the development. At end, lessons learnt and industrial perspectives are summarized highlighting how PMM is a methodology adapted to the challenges facing to systems engineering by the globalization of development processes and showing how PMM can provide a powerful conceptual framework to support digital continuity within globalized Design Organizations. Modeling, simulation, proof and test generation activities are supported by the MATLAB and Simulink products. Introduction The aeronautic industry has to deliver more and more complicated systems in term of functions while maintaining high level of quality and safety/reliability. In the same time, competition is driving aircraft manufacturers to strongly improve their costs (including non-recurring costs) and development lead time. At the age of globalization, these systems are designed and produced by large, multicultural, geographically distributed teams belonging to different industrial organizations. This evolution introduces additional complexities (the complexity of a goal-oriented process refers to its propensity to fail [Suh, 2005]). To face these challenges, classical systems engineering approaches

The finite element method for stochastically inhomogeneous structures is now under active development. Very often the conventional finite element is used in conjunction with the Monte Carlo method. It appears imperative, therefore, to have benchmark solutions for the deterministic problems. This paper is devoted to fill the gap. The old (but not obsolete) method of successive approximations is newly interpreted to yield closed-form solution for vibrating beams.

New closed-form solutions for the natural frequency of a clamped–guided beam are derived in this investigation. By postulating the mode shape of the clamped–guided beam, whose material density and stiffness are taken as polynomial functions, one is able to calculate the closed-form solution for its natural frequency. A remarkable property of the suggested method is its extreme simplicity.

In this study, the method of successive approximations is turned around so as to obtain closed form solutions for vibrating inhomogeneous bars. In particular, the method recently developed by the first author for the homogeneous beams is extended for bars.