• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.167-188
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• 2008

This study is concerned with the establishment of the characteristic equation of a combined system consisting of a cantilever beam with a tip mass and an in-span visco-elastic helical spring-mass, considering the mass of the helical spring. After obtaining the "exact" characteristic equation of the combined system, by making use of a boundary value problem formulation, the characteristic equation is established via a transfer matrix method, as well. Further, the characteristic equation of a reduced system is obtained as a special case. Then, the characteristic equations are numerically solved for various combinations of the physical parameters. Further, comparison of the results with the massless spring case and the case in which the spring mass is partially considered, reveals the fact that neglecting or considering the mass of the spring partially can cause considerable errors for some combinations of the physical parameters of the system.

• Journal of the Society of Naval Architects of Korea
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• v.40 no.1
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• pp.36-46
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• 2003

To investigate the affection of lumped mass and spring on the vibration power flow of cross-stiffened plate experiencing bending vibration, structural intensity analysis is done using the modal analysis based on assumed mode method. The numerical analysis is carried out varying the mass and spring constant and their attached positions. The results show that both the spring and the mass may cause to large variation of not only vibratory displacement but also vibratory power flow patterns in case of little change of natural frequencies, and the attachments near to excitation location can effectively reduce the magnitude of maximum structural intensity.

• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1105-1126
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• 2015

Many vibrating mechanical systems from the real life are modeled as combined dynamical systems consisting of beams to which spring-mass secondary systems are attached. In most of the publications on this topic, masses of the helical springs are neglected. In a paper (Cha et al. 2008) published recently, the eigencharacteristics of an arbitrary supported Bernoulli-Euler beam with multiple in-span helical spring-mass systems were determined via the solution of the established eigenvalue problem, where the springs were modeled as axially vibrating rods. In the present article, the authors used the assumed modes method in the usual sense and obtained the equations of motion from Lagrange Equations and arrived at a generalized eigenvalue problem after applying a Galerkin procedure. The aim of the present paper is simply to show that one can arrive at the corresponding generalized eigenvalue problem by following a quite different way, namely, by using the so-called "characteristic force" method. Further, parametric investigations are carried out for two representative types of supporting conditions of the bending beam.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2108-2117
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• 1996

The purpose of this paper is to investigate the influence of the exciter attached for the measurement of natural frequencies when extracting the frequency response functions of the test structure in experimental modal analysis. The procedure is first to model the attached exciter as an additional degree of freedom system and next to verify the suggested model by experimentally extracting the natural frequencies of the test structure with various values of exciter mass, stinger stiffness and attachment position of the exciter on the test structure. It is concluded that as additional degree of freedom system which includes the natural frequency of the exciter itself and axial stiffness of stinger should be considered to quantatively define the coupling effects of structure-exciter interaction on the measured natural frequencies. It is not the mass of the exciter itself but the coupling effect of the additional degree of freedom mass-spring system consisting of exciter body and armature coil that characterizes the natural frequency deviation. Therefore, when the natural frequency of this additional mass-spring system is outside of the test frequency range, the coupling effect of structure-exciter interaction can be minimized.

• Structural Engineering and Mechanics
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• v.57 no.6
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• pp.989-1014
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• 2016

This paper deals with the analysis of the natural frequencies, mode shapes of an axially loaded beam system carrying ends consisting of non-concentrated tip masses and three spring-two mass sub-systems. The influence of system design and sub-system parameters on the combined system characteristics is the major part of this investigation. The effect of material properties, rotary inertia and shear deformation of the beam system is included. The end masses are elastically supported against rotation and translation at an offset point from the point of attachment. Sub-systems are attached to center of gravity eccentric points out of the beam span. The boundary conditions of the ordinary differential equation governing the lateral deflections and slope due to bending of the beam system including developed shear force frequency dependent terms, due to the sub.system suspension, have been formulated. Exact formulae for the modal frequencies and the modal shapes have been derived. Based on these formulae, detailed parametric studies are carried out. The geometrical and mechanical parameters of the system under study have been presented in non-dimensional analysis. The applied mathematical model is presented to cover wide range of mechanical, naval and structural engineering applications.