The multibody system transfer matrix method (MSTMM), a novel dynamics approach developed during the past three decades, has several advantages compared to conventional dynamics methods. Some of these advantages include avoiding global dynamics equations with a system inertia matrix, utilizing low‐order matrices independent of system degree of freedom, high computational speed, and simplicity of computer implementation. MSTMM has been widely used in computer modeling, simulations, and performance evaluation of approximately 150 different complex mechanical systems. In this paper, the following aspects regarding MSTMM are reviewed: basic theory, algorithms, simulation and design software, and applications. Future research directions and generalization to more applications in various fields of science, technology, and engineering are discussed.

https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/msd2.12037

Multibody system transfer matrix method: The past, the present, and the future

Flexible multibody system dynamics (MSD) is one of the hot spots and difficulties in modern mechanics. It provides a powerful theoretical tool and technical support for dynamic performance evaluation and optimization design of a large number of complex systems in many engineering fields, such as machinery, aviation, aerospace, weapon, robot and biological engineering. How to find an efficient accurate dynamics modeling method and its stable reliable numerical solving algorithm are the two core problems of flexible MSD. In this paper, the research status of modeling methods of flexible MSD in recent years is summarized first, including the selection of reference frames, the flexible body’s kinematics descriptions, the deductions of dynamics equation, the model reduction techniques and the modeling methods of the contact/collision, uncertainty and multi-field coupling problems. Then, numerical solution technologies and their latest developments of flexible MSD are discussed in detail. Finally, the future research directions of modeling and numerical computation of flexible MSD are briefly prospected.

Theoretical modeling and numerical solution methods for flexible multibody system dynamics


 Absolute nodal coordinate formulation (ANCF) is a non-incremental nonlinear finite element procedure that has been successfully applied to the large deformation analysis of multibody systems for more than two decades. Although a comprehensive review on ANCF was conducted by Gerstmayr et al. in 2013, significant theoretical developments have been made since then at a much faster pace to improve the element accuracy and computational efficiency. In order to overview recent advances in ANCF simulation capabilities that are not covered in the first review paper, this paper aims to conduct a comprehensive review of 259 papers concerning ANCF published from 2012 through 2020. It is shown that the ANCF element library has grown substantially for beam, plate/shell, solid elements, eliminating drawbacks of ANCF elements developed earlier. The application areas have extended, especially in the aerospace field, and the enhanced ANCF simulation capabilities have been demonstrated in solving challenging engineering problems. Research efforts have been made continually to integrate computer-aided design (CAD) and analysis with ANCF elements. Furthermore, computational improvements and multiphysics simulations have become major research topics for ANCF. It is also demonstrated that the accurate ANCF geometry description can be exploited to facilitate structural optimization of multibody systems.

https://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/17/8/080803/6871780/cnd_017_08_080803.pdf

Recent Advances in the Absolute Nodal Coordinate Formulation: Literature Review From 2012 to 2020

Static equilibrium configuration and nonlinear dynamics of slightly curved cantilevered pipe conveying fluid

Fatigue is inevitable in pipes conveying fluid due to unwanted vibration. Internal resonance occurs in such pipes due to pre-pressure. For the first time, the effects of vibration on the fatigue of fluid-conveying pipes are investigated in this paper. The influences of the internal resonance and the axially functionally graded materials on the fatigue of the pipes are analyzed, aiming at improving mechanical properties and increasing fatigue life. The Galerkin method and the direct multi-scale method are used to construct the solvability condition for the primary resonance and 1:3 internal resonance. Approximate analytical solutions are derived for presenting the nonlinear dynamics of the pipes. The tensile, bending, and resultant stress distribution of the axially functionally graded pipe in internal resonance is determined. The results of the fatigue analysis demonstrate that internal resonance can shorten the fatigue life of axially functionally graded pipes. Reducing the distribution coefficient of functionally graded pipe is beneficial for reducing the resonance response and maximum stress of the pipe conveying fluid. The numerical integration results support the analytical results.

Nonlinear vibration effects on the fatigue life of fluid-conveying pipes composed of axially functionally graded materials

Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

Based on the absolute nodal coordinate (ANC) formulation and transfer matrix method (TMM), a novel efficient Riccati ANC–TMM is applied to nonlinear dynamics analysis of pipe conveying fluid with large deformations. By deducing the new transfer equations of pipe elements in the ANC frame and introducing Riccati transform technology into the dynamics solution algorithm, the nonlinear dynamics of pipe conveying fluid can be calculated highly efficient and stable. An illustrative comparison simulation of a cantilever pipe conveying fluid by using this method and ordinary ANC method is presented, and its critical fluid velocity and other nonlinear dynamics behavior are analyzed. Compared with ordinary ANC method, this method avoids the higher-order global differential or differential-algebra equations of the system, therefore, its computational efficiency could be improved essentially. It may be further extended to study nonlinear dynamic characteristics of a pipe conveying fluid under the condition of arbitrarily large overall motions and commonly elastic supports easily.

Nonlinear dynamics analysis of pipe conveying fluid by Riccati absolute nodal coordinate transfer matrix method

Dynamics analysis and wave compensation control design of ship’s seaborne supply by discrete time transfer matrix method of multibody system

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Papers

Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

Nonlinear dynamics analysis of pipe conveying fluid by Riccati absolute nodal coordinate transfer matrix method

Dynamics analysis and wave compensation control design of ship’s seaborne supply by discrete time transfer matrix method of multibody system