Free vibration of structures composed of rigid bodies and elastic beam segments

Obradović, Aleksandar; Šalinić, Slaviša; Trifkovic, Dragan; Zorić, Nemanja D.; Stokić, Zoran

doi:10.1016/j.jsv.2015.03.001

Cited by 22 publications

(22 citation statements)

References 21 publications

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“…It was therefore, much easier for these earlier investigators to realise an analytical model of a multibody system using such a simplistic approach. Of course, for the problems with attachments represented by two or more degrees of freedom together with the consideration of their physical dimensions, the analytical formulation will be much more complex, see for example the attachment of a two-degree-of-freedom systems [35][36][37] , mass-spring-mass-damper [38] and two-part beam-mass [39][40][41][42][43][44][45][46][47] . It should be recognised at this stage that one of the accurate and popular methods of modelling a multi-body system is the transfer matrix method [29,46,[48][49][50] , which is relatively simple to use and is seemingly efficient, particularly when analysing chain-like multi-body systems.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, there are some difficulties to apply these existing methods to complex multibody systems. For example, unlike the numerical method where the stiffness and mass matrices can be formulated separately [9] , almost all existing analytical methods [45][46][47][48][49][50]2,6,13,52,14,15,[22][23][24]26,27,[29][30][31]55,[32][33][34][35][37][38][39][40]42,44,61,62] apply the usual determinant method for non-trivial solution of the eigenvalue problem for which the determinant of the coefficient matrix vanishes. The determinant method needs the evaluation of the determinant numerically for one frequency at a time.…”

Section: Introductionmentioning

confidence: 99%

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An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

Xiang

Sun

Banerjee

et al. 2021

Mechanical Systems and Signal Processing

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An exact dynamic stiffness method is proposed for the free vibration analysis of multi-body systems consisting of flexible beams and rigid bodies. The theory is sufficiently general in that the rigid bodies can be of any shape or size, but importantly, the theory permits connections of the rigid bodies to any number beams at any arbitrary points and oriented at any arbitrary angles. For beam members, a range of theories including the Bernoulli-Euler and Timoshenko theories are applied. The assembly procedure for the beam and rigid body properties is simplified without resorting to matrix inversion. The difficulty generally encountered in computing the problematic J0 count when applying the Wittrick-Williams algorithm for modal analysis has been overcome. Applications of different beam theories for both axial and bending vibrations have enabled the examination of the role played by rigid-body parameters on the multibody system's dynamic behaviour. Some exact benchmark results are provided and compared with published results and with finite element solutions. This research provides an exact and highly efficient analysis tool for multibody system dynamics which is for the free vibration analysis, ideally suited for optimization and inverse problems such as modal parameter identification.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

Xiang

Sun

Banerjee

et al. 2021

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

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“…Coupled partial differential equations are also analytically solved in [4] in the case of planar multi-story frame structures. The authors of this paper managed to extend the analytical procedures presented in their papers [5,6] to solving the vibration problem of embedded rigid bodies to both the beams themselves and the ends of the structure. The procedure for obtaining analytical solutions for the governing equations of all sections of the structure depending on time is presented.…”

Section: Introductionmentioning

confidence: 99%

Free vibrations of planar serial frame structures in the case of axially functionally graded materials

Obradović

Šalinić

Tomović

2020

Theor appl mech (Belgr)

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This paper considers the problem of modal analysis and finding the closed-form solution to free vibrations of planar serial frame structures composed of Euler?Bernoulli beams of variable cross-sectional geometric characteristics in the case of axially functionally graded materials. Each of these beams is performing coupled axial and bending vibrations, where coupling occurs due to the boundary conditions at their joints. The numerical procedure for solving the system of partial differential equations, after the separation of variables, is reduced to solving the two-point boundary value problem of ordinary linear differential equations with nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer the boundary conditions and reduce the problem to the Cauchy initial value problem. Also, it is possible to analyze the influence of different parameters on the structure dynamic behavior. The method is applicable in the case of different boundary conditions at the right and left ends of such structures, as illustrated by an appropriate numerical example.

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“…Indeed, balancing counterweights considerably increase the robot mass, hence possibly inducing higher motor loads [24,29]. Moreover they may trigger vibration phenomena [30][31][32][33], thus being potentially detrimental for PKMs in terms of machining tolerances and cutting tool life [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Gravity compensation of a 6-UPS parallel kinematics machine tool through elastically balanced constant-force generators

Martini¹

2018

FME Transaction

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Free vibration of structures composed of rigid bodies and elastic beam segments

Cited by 22 publications

References 21 publications

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

Free vibrations of planar serial frame structures in the case of axially functionally graded materials

Gravity compensation of a 6-UPS parallel kinematics machine tool through elastically balanced constant-force generators

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