The transfer matrix method for multibody system takes into account the accuracy of the equations of motion and the efficiency of the algorithm. Especially if a system is composed of flexible and rigid components, transfer matrix method for multibody system reduces the dynamics problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundary are made up of rotation angles, displacements, shear forces, and bending moments, which are normally half known and half unknown. The proposed transfer matrix method for multibody system of multibody system dynamics to determine the vibration characteristics is easy to formulate, systematic to apply, and simple to code. The purpose of this study is to introduce a modeling and simulation idea of beam with attachments based on transfer matrix method for multibody system. Numerical results for several examples of beam with attachments are presented to demonstrate the validity of this method.
AbbasLKBestleDRuiXT (2013a) Transfer matrix method for the determination of the free vibration of two elastically coupled beams. Applied Mechanics and Materials372: 301–304.
2.
AbbasLKMin-JiaoLXiao-TingR (2013b) Transfer matrix method for the determination of the natural vibration characteristics of realistic thrusting launch vehicle-part I. Mathematical Problems in Engineering2013: 1–16.
3.
AbbasLKZhouQBestleD, et al. (2017) A unified approach for treating linear multibody systems involving flexible beams. Mechanism and Machine Theory107: 197–209.
4.
AkessonBA (1978) PFVIBAT-a computer program for plane frame vibration analysis an exact method. International Journal for Numerical Methods in Engineering10(6): 1221–1231.
BanerjeeJRPapkovSOLiuX, et al. (2015) Dynamic stiffness matrix of a rectangular plate for the general case. Journal of Sound and Vibration342: 177–199.
7.
BestleDAbbasLRuiX (2013) Recursive eigenvalue search algorithm for transfer matrix method of linear flexible multibody systems. Multibody System Dynamics32(4): 429–444.
8.
ChenDYAbbasLKRuiXT, et al. (2017a) Dynamic modeling of sail mounted hydroplanes system-part I: modal characteristics from a transfer matrix method. Ocean Engineering130(15): 629–644.
9.
ChenDYAbbasLKRuiXT, et al. (2017b) Dynamic modeling of sail mounted hydroplanes system-part II: hydroelastic behavior and the impact of structural parameters and free-play on flutter. Ocean Engineering131(1): 322–337.
10.
EberhardPNeerpaschU (1996) Interactive modelling of multibody systems with an object oriented data model. Mathematical Modelling of Systems2(1): 55–68.
11.
HeBRuiXTZhangH (2012) Transfer matrix method for natural vibration analysis of tree system. Mathematical Problems in Engineering2012(2): 397–415.
12.
HuangWHShaoCX (1996) Flexible Multibody System Dynamics. Beijing: Science Press.
13.
IIankoS (2005) Transcendental dynamic stability functions for beams carrying rigid bodies. Journal of Sound and Vibration279: 1195–1202.
14.
KaneTRLikinsPWLevinsonDA (1983) Spacecraft Dynamics. New York: McGraw-Hill Book Company.
15.
KreuzerEKustO (1996) Analysis of long torsional strings by proper orthogonal decomposition. Archive of Applied Mechanics67(1–2): 68–80.
16.
KuklaSPrzybylskiJTomskiL (1995) Longitudinal vibration of rods coupled by translational springs. Journal of Sound and Vibration185: 717–722.
17.
PascalM (1987) Dynamics analysis of a system of hinge-connected flexible bodies. Celestial Mechanics41(1–4): 253–274.
18.
PascalM (1991) Vibrations analysis of multibody systems. Dynamics and Stability of Systems6(3): 217–234.
19.
PestelECLeckieFA (1963) Matrix Method in Elastomechanics. New York: McGraw-Hill Book Company.
20.
PhilipDCAndrewBS (2011) Eigenvalue sensitivities of a linear structure carrying lumped attachments. AIAA Journal49(11): 2470–2481.
21.
RomeoGMiraldiERuscicaG, et al. (1992) A new test facility for measuring the coefficient of moisture expansion of advanced composite materials. Journal of Composites Technology and Research. 14: 225–230.
22.
RossitCALauraPAA (2001) Free vibrations of a cantilever beam with a spring-mass system attached to the free end. Ocean Engineering28: 933–939.
23.
RuiXTHeBLuYQ, et al. (2005) Discrete time transfer matrix method for multibody system dynamics. Multibody System Dynamics14(4): 317–344.
24.
RuiXWangGLuY, et al. (2008a) Transfer matrix method for linear multibody system. Multibody System Dynamics19(3): 179–207.
25.
RuiXTYunLLuY, et al. (2008b) Transfer Matrix Method of Multibody System and its Application. Beijing: Science Press.
26.
RuiXChenDYWangGP (2020) Numerical calculation of vortex-induced vibration of reinforced thermoplastic pipe. Chinese Journal of Theoretical and Applied Mechanics52(1): 1–11.
27.
SchiehlenW (1997) Multibody system dynamics: roots and perspectives. Multibody System Dynamics1: 149–188.
28.
ShabanaAA (1997) Flexible multibody dynamics: review of past and recent developments. Multibody System Dynamics1(2): 189–222.
29.
ShabanaAA (2010a) Computational Dynamics. New York: Wiley.
30.
ShabanaAA (2010b) Dynamics of Multibody Systems. New York: Cambridge University Press.
31.
UhrigR (1973) Elastostatik und Elastokinetik in Matrizenschreibweise das Verfrahren der Ubertragungsmatrizen. Berlin: Springer Verlag.
32.
WittenburgJ (2007) Dynamics of Multibody Systems: Dynamics of Systems of Rigid Bodies. Heidelberg, Berlin: Springer-Verlag.
33.
WittrickWHWilliamsFW (1971) A general algorithm for computing natural frequencies of elastic structures. The Quarterly Journal of Mechanics and Applied Mathematics24(3): 263–284.
