Free Vibration of Multi-Span Timoshenko Beams Using Static Timoshenko Beam Functions

Zhou, Ding

doi:10.1006/jsvi.2000.3266

Cited by 24 publications

(19 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is undeniable that the explicit expression of (46) is hard to get even for case 2 with only 2 fixed-hinge BCs. On the one hand, although the det step performed in (21) can obtain the characteristic equations with variables 1 and 2 , to solve the frequency is almost impossible with two unknown parameters. On the other hand, the derivations of (46) about 1 and 2 have introduced a set of implicit characteristic equations, which are considered to be super complicated.…”

Section: Bcs' Optimization Based On Casementioning

confidence: 99%

“…Further, [20] analyzed the multispan beams carrying multiple spring-mass systems with axial force based on Timoshenko theory. The free vibration of a multispan Timoshenko beam was studied by Rayleigh-Ritz method in [21], where the trial functions were composed of a series sine or cosine functions plus a set of polynomial functions. Furthermore, by using the transfer matrix method, [22] calculated the eigensolutions of a multispan beam with arbitrary numbers of flexible constraints and compared with the result of the Euler-Bernoulli beam.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Analysis of Timoshenko Beam with Arbitrary Constraints and a Further Optimization Based on Least Energy Principle

Zhang

Zhu

Zhe

et al. 2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Based on Timoshenko's beam theory, this paper adopts segmented strategy in establishing the governing equations of a multibeam system subjected to various boundary conditions, in which free, clamped, hinged, and elastic constraints are considered. Meanwhile, Galerkin method is incorporated as a competitive alternative, in which a new set of unified, efficient, and reliable trial functions are proposed. A further optimization in regard to boundary distributions under forces is implemented and established on the least absorbed energy principle. High agreement is observed between the analytical results and the FEM results, verifying the correctness of the derivations. Complete comparisons between the analytical and the numerical results indicate the Galerkin method is beneficial when slender ratio is larger than 30, in which the continuity of the deformation is proved to be a crucial influencing factor. A modified numerical strategy about optimal boundary is employed and the remarks imply the algorithm can be availably used to reduce the energy absorption of the whole system.

show abstract

Section: Bcs' Optimization Based On Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Timoshenko Beam with Arbitrary Constraints and a Further Optimization Based on Least Energy Principle

Zhang

Zhu

Zhe

et al. 2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Naguleswaran obtained the natural frequency values of the beams on up to five resilient supports including ends and carrying several particles by using BET obtained a fourth-order determinant equated to zero [24,25]. Zhou studied the free vibration of multi-span Timoshenko beams by using Rayleigh-Ritz method [26]. He developed the static Timoshenko beam functions which are composed of a set of transverse deflection functions and a set of rotational angle functions as the trial functions.…”

Section: Introductionmentioning

confidence: 99%

Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

Yeşilce

2011

Shock and Vibration

View full text Add to dashboard Cite

Abstract. The structural elements supporting motors or engines are frequently seen in technological applications. The operation of machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko single-span beams carrying a number of spring-mass system and multi-span beams carrying multiple spring-mass systems are plenty, but the free vibration analysis of Reddy-Bickford multi-span beams carrying multiple spring-mass systems has not been investigated by any of the studies in open literature so far. This paper aims at determining the exact solutions for the natural frequencies and mode shapes of Reddy-Bickford beams. The model allows analyzing the influence of the shear effect and spring-mass systems on the dynamic behavior of the beams by using Reddy-Bickford Beam Theory (RBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1-4 span beams are studied. The natural frequencies of Reddy-Bickford single-span and multi-span beams calculated by using the numerical assembly technique and the secant method are compared with the natural frequencies of single-span and multi-span beams calculated by using Timoshenko Beam Theory (TBT); the mode shapes are presented in graphs.

show abstract

“…The free vibration analysis of curved single-span beams based on the Timoshenko beam theory has been studied by using various methods such as the transfer matrix method [1][2][3], the dynamic stiffness method [4,5], the differential quadrature method [6], and the finite element method [7][8][9]. The research on the free vibration of straight multi-span beams based on the Timoshenko theory also has been carried out by the Rayleigh-Ritz method [10] and the transfer matrix method [11].…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of circularly curved multi-span Timoshenko beams by the pseudospectral method

Lee

2007

J Mech Sci Technol

View full text Add to dashboard Cite

The pseudospectral method is applied to the free vibration analysis of circularly curved multi-span Timoshenko beams. Each section of the beam has its own basis functions, and the continuity conditionsat the intermediate supports as well as the boundary condition are treated as the constraints of the basis functions so that the number of degrees of freedom matches the number of the pseudospectralexpansion coefficients. The computed natural frequencies are compared with those of existing literature, where it is shown that they are in good agreement.Numerical examples are provided for pinned-pinned,clamped-clamped and free-pinned boundary conditions for different numbers of sections and for differentthickness-to-lengthratios.

show abstract

Free Vibration of Multi-Span Timoshenko Beams Using Static Timoshenko Beam Functions

Cited by 24 publications

References 9 publications

Dynamic Analysis of Timoshenko Beam with Arbitrary Constraints and a Further Optimization Based on Least Energy Principle

Dynamic Analysis of Timoshenko Beam with Arbitrary Constraints and a Further Optimization Based on Least Energy Principle

Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

Free vibration analysis of circularly curved multi-span Timoshenko beams by the pseudospectral method

Contact Info

Product

Resources

About