Free Vibration Analysis of a Cantilever Beam Carrying Any Number of Elastically Mounted Point Masses With the Analytical-and-Numerical-Combined Method

Wu, Jong‐Shyong; Chou, H. M.

doi:10.1006/jsvi.1997.1501

Cited by 68 publications

(28 citation statements)

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“…The dimensional and physical properties for the cantilever beam with spring-mass systems are the same as the configuration previously studied in ref. [15]. Then, the distribution functions U c (x) of the spring-mass system are set as δ(x − 3L/4) and δ(x − L) respectively, and the according parameters of the spring-mass systems are…”

Section: Locationmentioning

confidence: 99%

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The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

Xiao

Sheng

Liu

et al. 2013

Shock and Vibration

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Abstract. The flexible beams carrying attachments often appear in engineering structures, modal analysis of those structures is important and necessary in structural design. This manuscript develops a proposed analytical method as a general tool for solving the free vibration of varying cross-section beams carrying various types of attachments with different distributions and arbitrary boundary conditions. In current practice, the natural frequencies of beam carrying lumped and uniform sprung mass and resting on Pasternak soil are calculated and compared with those in references to verify the methodology firstly. Then, the natural frequencies of beam carrying non-uniform spring-mass systems and stepped beam on Pasternak soil are calculated by the proposed method to study free vibration of beam carrying attachments with non-uniform cross section or distribution. Finally, some important conclusions are derived from results, which reveal that distribution density of spring-mass system at peaks of the mode shape makes dominate effects on the change of the natural frequencies at that mode and the natural frequencies of the stepped beam resting on elastic foundation are more sensitive to the increase of soil parameters.

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Section: Locationmentioning

confidence: 99%

“…Other studies of the influences of variable attachments on slender beam vibrations are given in Refs. [5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

Xiao

Sheng

Liu

et al. 2013

Shock and Vibration

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show abstract

“…If each two-dof spring-mass system is replaced by the two equivalent masses, m (v) eq, i and m (v) eq, k , defined by Equations (22) and (23), then the equation of motion for a uniform beam carrying p two-dof spring-mass systems will take the form [6] …”

Section: Characteristic Equation Of the Loaded Beammentioning

confidence: 99%

“…For example, Ozguven and Candir [1] and Manikanahally and Crocker [2] have investigated the dynamic characteristics of the absorbers composed of one and multiple degrees of freedom (dof) spring-mass systems, respectively. Gürgöze [3,4], Wu and Chen [5], Wu and Chou [6], Larrondo et al [7], and Rossit and Laura [8] have researched the natural frequencies or/and mode shapes of beams carrying one or/and multiple single-dof spring-mass systems. Wu and Chen [9] and Wu et al [10] have used the analytical-and-numerical-combined method to study the free vibration characteristics of a uniform cantilever beam carrying multiple one-dof spring-mass systems with dampers.…”

Section: Introductionmentioning

confidence: 98%

Use of equivalent mass method for free vibration analyses of a beam carrying multiple two‐dof spring–mass systems with inertia effect of the helical springs considered

2005

Numerical Meth Engineering

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SUMMARYThis paper investigates the free vibration characteristics of a beam carrying multiple two-degree-offreedom (two-dof) spring-mass systems (i.e. the loaded beam). Unlike the existing literature to neglect the inertia effect of the helical springs of each spring-mass system, this paper takes the last inertia effect into consideration. To this end, a technique to replace each two-dof spring-mass system by a set of rigidly attached equivalent masses is presented, so that the free vibration characteristics of a loaded beam can be predicted from those of the same beam carrying multiple rigidly attached equivalent masses. In which, the equation of motion of the loaded beam is derived analytically by means of the expansion theorem (or the mode superposition method) incorporated with the natural frequencies and the mode shapes of the bare beam (i.e. the beam carrying nothing). In addition, the mass and stiffness matrices including the inertia effect of the helical springs of a two-dof spring-mass system, required by the conventional finite element method (FEM), are also derived. All the numerical results obtained from the presented equivalent mass method (EMM) are compared with those obtained from FEM and satisfactory agreement is achieved. Because the equivalent masses of each two-dof spring-mass system are dependent on the magnitudes of its lumped mass, spring constant and spring mass, the presented EMM provides an effective technique for evaluating the overall inertia effect of the two-dof spring-mass systems attached to the beam. Furthermore, if the total number of two-dof spring-mass systems attached to the beam is large, then the order of the overall property matrices for the equation of motion of the loaded beam in EMM is much less than that in FEM and the computer storage memory required by the former is also much less than that required by the latter.

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“…From Figure 1 one sees that the left end of the beam, * , coincides with the left end of the "rst beam segment ( "1), hence from equations (8), (9), (25a) and (25b) one obtains…”

Section: Introductionmentioning

confidence: 97%

Free Vibration Analysis of a Cantilever Beam Carrying Any Number of Elastically Mounted Point Masses With the Analytical-and-Numerical-Combined Method

Cited by 68 publications

References 0 publications

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

Use of equivalent mass method for free vibration analyses of a beam carrying multiple two‐dof spring–mass systems with inertia effect of the helical springs considered

The Exact Solutions for the Natural Frequencies and Mode Shapes of Non-Uniform Beams With Multiple Spring–mass Systems

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