Vibration confinement in a general beam structure during harmonic excitations

Foda, Mosaad A.; Albassam, Bassam A.

doi:10.1016/j.jsv.2005.12.057

Cited by 23 publications

(20 citation statements)

References 43 publications

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“…As seen in Table 1, only the solutions given in (Shanz and Antes, 2002;Foda and Albassam, 2006;Lin, 2008;Majkut, 2009; Saeid, 2001) could be generalized in order to solve models of arbitrary numbers of beams and boundary conditions. If further features are to be considered, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…For this reason, many good publications Latin American Journal of Solids and Structures 11 (2014) dedicated to dynamic frame response calculation do not conform to the requirements of an exact solution and therefore are not considered here. Concerning the dynamic response of frames, Table 1 compares different solution methods found in the literature [Abu-Hilal (2003), Foda and Albassam (2006), Gürgöze and Erol (2001), Lin (2008), Loudini et. al.…”

Section: Introductionmentioning

confidence: 99%

“…(2006), Saeid (2011)] and/or Green functions [Abu-Hilal (2003), Tang (2008), Davar and Rahmani (2009)]. Gürgöze and Erol (2001) use a distinct method based on a receptance matrix but cannot be considered exact since series solution is employed.As seen in Table 1, only the solutions given in (Shanz and Antes, 2002;Foda and Albassam, 2006;Lin, 2008;Majkut, 2009; Saeid, 2001) could be generalized in order to solve models of arbitrary numbers of beams and boundary conditions. If further features are to be considered, e.g.…”

mentioning

confidence: 99%

“…If further features are to be considered, e.g. concentrated masses and springs, these solutions would be limited to the ones developed in (Foda and Albassam, 2006;Majkut, 2009). Even so, these references are dedicated to solve single and/or in-line beams.…”

mentioning

confidence: 99%

“…On the other hand, considering that a given beam like structure is linear, the proposed method can be extended to a more general excitation type, with more than one distinct excitation frequency. The first order governing equations of Section 2 are a coupled PDE system that might be manipulated in order to obtain uncoupled PDEs for the displacements (Howson and Williams, 1973;Foda and Albassam, 2006). However, this operation would produce fourth order PDEs that are less suitable for Laplace transform (Schanz and Antes, 2002).…”

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confidence: 99%

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General exact harmonic analysis of in-plane timoshenko beam structures

Dias

2014

Lat. Am. j. solids struct.

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The exact solution for the problem of damped, steady state response, of in-plane Timoshenko frames subjected to harmonically time varying external forces is here described. The solution is obtained by using the classical dynamic stiffness matrix (DSM), which is non-linear and transcendental in respect to the excitation frequency, and by performing the harmonic analysis using the Laplace transform. As an original contribution, the partial differential coupled governing equations, combining displacements and forces, are directly subjected to Laplace transforms, leading to the member DSM and to the equivalent load vector formulations. Additionally, the members may have rigid bodies attached at any of their ends where, optionally, internal forces can be released. The member matrices are then used to establish the global matrices that represent the dynamic equilibrium of the overall framed structure, preserving close similarity to the finite element method. Several application examples prove the certainty of the proposed method by comparing the model results with the ones available in the literature or with finite element analyses.Keywords exact harmonic analysis; Laplace transform; Timoshenko beam; dynamic stiffness matrix; rigid offsets; end release. General exact harmonic analysis of INTRODUCTIONMany modern structures are formed by beam elements. These skeleton like structures are subjected to static and dynamic loads. Their beam members can be of various sizes, including beams with small length to beam height ratio. For the analysis of these structures, it is important to use a more refined beam theory, where the assumption of the cross section to remain plane is not enforced. Besides, harmonic loads can be of high frequency, when then it is important to keep in the beam model the cooperation of the rotatory inertia to the overall structure response. This motivates the use of the Timoshenko beam theory to obtain the damped steady state response for general plane frames subjected to harmonically time varying external forces. The study reported here concerns with an exact harmonic analysis using the classical Dynamic Stiffness Matrix, DSM. The problem at hand is non-linear and transcendental with respect to the excitation frequency [Howson and Williams (1973)]. The approach used to solve it is by the use of the Laplace transform.Focusing on the calculation of natural frequencies, Howson and Williams (2003) present a formulation based on the classical DSM obtained by a set of decoupled fourth order partial differential equations (PDE) for the unknowns deflection and rotation of the beam cross section. Dias and Alves (2009) also derive the DSM via the same procedure but reaches an improved formulation, argued to be more suitable for the eigenproblem solution. It has been noticed [Schanz and Antes (2002)] that the dynamic analyses of beams can be performed by decoupling deflection and rotation. In the study described here, the original coupled PDEs, combining deflection, rotation, bending moment and shear f...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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General exact harmonic analysis of in-plane timoshenko beam structures

Dias

2014

Lat. Am. j. solids struct.

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Alleviating vibrations along a harmonically driven nonuniform Euler–Bernoulli beam by imposing nodes

Baltan‐Brunet,

Kopp,

Cha

2023

Int Journal of Mech Sys Dyn

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A passive approach is developed to quench excess vibration along a harmonically driven, arbitrarily supported, nonuniform Euler–Bernoulli beam with constant thickness (height) and varying width. Vibration suppression is achieved by attaching properly tuned vibration absorbers to enforce nodes, or points of zero vibration, along the beam. An efficient hybrid method is proposed whereby the finite element method is used to model the nonuniform beams, and a formulation based on the assumed modes method is used to determine the required attachment force supplied by each absorber to induce the desired nodes. Knowing the attachment forces needed to induce nodes, design plots are generated for the absorber parameters as a function of the tolerable vibration amplitude for each absorber mass. When the node locations are judiciously chosen, it is possible to dramatically suppress the vibration along a selected region of the beam. As such, sensitive instruments can be placed in this region and will remain nearly stationary. Numerical studies illustrate the application to several systems with various types of nonuniformity, boundary conditions, and attachment and node locations; these examples validate the proposed method to passively control excess vibration by inducing nodes on nonuniform beams subjected to harmonic excitations.

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