Component Mode Synthesis Method Applied to Acoustic Resonators in Ducts for Structural Vibration Analysis

Tubular structural systems appear in many industrial applications, such as heating, ventilation, and air conditioning systems, which are responsible for making any enclosed environment remain within a temperature, humidity, and cleanliness range. This kind of system has its applications in the internal environmental comfort of industrial spaces, buildings, and vehicles. Several of these spaces have industrial processes that generate high sound frequencies and mechanical vibrations that need to be adequately controlled to meet both environmental and health norms. With the intention to analyze the structural vibration of tubular systems, the modal analysis technique is a classical methodology for the extraction of natural frequencies and vibration modes. Among the various techniques of modal analysis, numerical methodologies such as the finite element method, and also analytical methodologies such as the Component Mode Synthesis (CMS) can be found. CMS is one of the leading modeling tools for complex systems that are applied to large systems. The method uses a modal superset and consists of separately modeling individual components of a structure and coupling them into a single system. The objective of this work is to demonstrate the application of the CMS technique through the estimation of natural frequencies and vibration modes in a simplified tubular structural system formed by two substructures, using MATLAB and ANSYS. The validation of the results was done through numerical modeling using the finite element method using and ANSYS software. The results obtained were satisfactory, thus demonstrating the feasibility of applying the CMS technique to an analysis of structural vibration in tubular structural systems.

A Proposal of Mode Polynomials for Efficient Use of Component Mode Synthesis and Methodology to Simplify the Calculation of the Connecting Beams

Analytical method using Rayleigh–Ritz method has not been widely used recently due to intensive use of finite element analysis (FEA). However as long as suitable mode functions together with component mode synthesis (CMS) can be provided, Rayleigh–Ritz method is still useful for the vibration analysis of many local structures in a ship such as tanks and supports for an equipment. In this study, polynomials which combines a simple and a fixed support have been proposed for the satisfaction of boundary conditions at a junction. Higher order polynomials have been generated using those suggested by Bhat. Since higher order polynomials used only satisfy geometrical boundary conditions, two ways are tried. One neglects moment continuity and the other satisfies moment continuity by sum of mode polynomials. Numerical analysis have been performed for typical shapes, which can generate easily more complicated structures. Comparison with FEA result shows good agreements enough to be used for practical purpose. Frequently dynamic behavior of one specific subcomponent is more concerned. In this case suitable way to estimate dynamic and static coupling of subcomponents connected to this specific subcomponent should be provided, which is not easy task. Elimination of generalized coordinates for subcomponents by mode by mode satisfaction of boundary conditions has been proposed. These results are still very useful for initial guidance.