Natural frequencies of multispan curved beams

Culver, Charles G.; Oestel, D.J.

doi:10.1016/0022-460x(69)90216-8

Cited by 24 publications

(11 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[3,4]. The data and results are presented in Ta The results agree very well, which checks the correctness of the finite element formulation in the linear range.…”

Section: Linear Frequencies Of Simply Supportedsupporting

confidence: 62%

See 1 more Smart Citation

Nonlinear free vibration analysis of thin-walled curved beam with non-symmetric open cross section

Duan

Song

2008

J. Shanghai Jiaotong Univ. (Sci.

View full text Add to dashboard Cite

A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of flexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.

show abstract

“…[3,4]. The data and results are presented in Ta The results agree very well, which checks the correctness of the finite element formulation in the linear range.…”

Section: Linear Frequencies Of Simply Supportedsupporting

confidence: 62%

“…Culver et al [3,4] determined the free vibration frequencies of curved beams with re-spect to analytical solutions of the equations of motion. Chaudhuri et al [5,6] analyzed the free vibration of horizontally curved beams using finite element method (FEM).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration analysis of thin-walled curved beam with non-symmetric open cross section

Duan

Song

2008

J. Shanghai Jiaotong Univ. (Sci.

View full text Add to dashboard Cite

show abstract

“…Four important wave modes are conveyed in an elastic beam: a longitudinal wave, a torsional wave, and flexural waves in two directions. Previous studies are categorized into two groups: One group has studied the coupling between the longitudinal wave and one flexural wave [5,[9][10][11], and others have focused on the coupling between the torsion and the other type of flexural wave [12][13][14][15][16][17][18], mostly by civil engineers. However, research works on the coupling among four wave types are rather scanty so far [19,20].…”

Section: Kinetic Model Of the Curved Beammentioning

confidence: 99%

Effects of nearfield waves and phase information on the vibration analysis of curved beams

Jeong

2009

J Mech Sci Technol

View full text Add to dashboard Cite

At high frequencies, energy methods such as the statistical energy analysis and the power flow analysis have been popularly used to predict the averaged responses of vibro-acoustic subsystems. Usually, these energy methods ignore flexural nearfield components and phase information, mainly for simplicity. Such assumptions sometimes lead to an erroneous conclusion, in particular for complex structures and at medium frequencies around the Schroeder cutoff frequency. This paper deals with the effects of nearfield waves and phase information at medium to high frequencies by using the ray tracing method (RTM). A curved beam and a coupled beam system were chosen as test examples, which exhibit the typical mode conversion between various types of travelling waves. Propagation of longitudinal, flexural, and torsional waves was studied based on the Euler-Bernoulli beam theory. Analyses of the spatial distribution of vibrational energy quantities revealed that the conventional RTM could mimic the overall trend of the traveling wave solution. However, the results varied smoothly in space due to the neglect of wave interference. By considering the phase information, local fluctuations of vibration energy could be correctly described. It was confirmed that the flexural nearfield plays a significant role near boundaries and junctions. It was also shown that the accuracy of the analysis depends mainly on the modal overlap factor. Similar to other high frequency methods, the results become close to the traveling wave solutions as the modal overlap factor increases.

show abstract

“…Ojalvo [2] has presented an analysis of coupled twist-bending vibrations of incomplete circular rings by applying the classical Euler-Bernoulli beam theory. A twospan curved girder was modeled by Culver et al [3] for use in the bridge structures. However, there is a lack of analysis on the combination of circular arcs in literature.…”

Section: Introductionmentioning

confidence: 99%

Low frequency arc-based MEMS structures for vibration energy harvesting

Apo

Sanghadasa

Priya

2013

The 8th Annual IEEE International Conference on Nano/Micro Engineered and Molecular Systems

View full text Add to dashboard Cite

This study reports the novel arc-based cantilevers for reducing the natural frequency of MEMS cantilever beams without the addition of tip/point mass. The results show an increased potential for energy extraction from naturally occurring vibration sources. An analytical model was used to model the effective mechanical properties of multilayered MEMS cantilevers while the natural frequencies were obtained by applying a finite element code. Results were obtained for two geometries of arc-based cantilevers as well as their linear counterparts. These results demonstrate that arc-based cantilevers vibrate at frequencies significantly lower than their linear components (up to 40% reduction in natural frequency).

show abstract

Natural frequencies of multispan curved beams

Cited by 24 publications

References 8 publications

Nonlinear free vibration analysis of thin-walled curved beam with non-symmetric open cross section

Nonlinear free vibration analysis of thin-walled curved beam with non-symmetric open cross section

Effects of nearfield waves and phase information on the vibration analysis of curved beams

Low frequency arc-based MEMS structures for vibration energy harvesting

Contact Info

Product

Resources

About