On the Eigenfrequencies of a Two-Part Beam–mass System

Exact free vibration analysis for mechanical system composed of Timoshenko beams with intermediate eccentric rigid body on elastic supports: An experimental and analytical investigation

“…The center of mass of this rigid body is located at its middle. Naguleswaran [7], Banerjee and Sobey [8] and Ilanko [9] presented three comments on the discontinuity conditions between the beam and rigid mass discussed by Kopmaz and Telli [6]. In addition Kopmaz and Telli illustrated through their author's reply [10] some interesting points which were carried out and very useful corrections were reported.…”

“…Kopmaz and Telli [6] considered the transverse vibration of a system consisting of a rigid body carried by two uniform beams of different flexural rigidity, length and pinned at the beam ends. The center of mass of this rigid body is located at its middle.…”

“…Graphical results for the variation in the modal frequencies and their associated modal shapes were presented in [17]. Very recently, the exact free vibration of multi-step Timoshenko beam system with several attachments including two degree of polynomial roots c c 1,2 distance from k 6 and k 5 to points of attachment * * c c , 1 2 c 1 /L, c 2 /L respectively e distance between the mass center of gravity and the point of attachment * e ratio defined as e L / . In this work, a mathematical model consists of two elastic thick beam segments with intermediate extended eccentric rigid mass is proposed.…”

Complex Impact Response of a Beam and Rigid Body Structure to Harmonic Base Excitation

“…The latter expression incorporates the influence of the beams' end shears, which were not considered in [15]. In S (1) , terms representing the contact spring's restoring force and moment about the body's centroid are appended to Equations (8) and (9), which are not discussed here explicitly for brevity.…”

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

“…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.…”