Free vibration of stepped beams: Higher mode frequencies and effects of steps on frequency

Jang, S. K.; Bert, Charles W.

doi:10.1016/0022-460x(89)90882-1

Cited by 52 publications

(15 citation statements)

References 3 publications

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“…In reference [5], the &&exact'' frequencies of a beam of circular cross-section with step change in diameter at the mid-point were compared with frequencies obtained by "nite element method and by a commercial code. Jang and Bert [6] published results of further combinations of boundary conditions. Manual symbolic expansion of the determinants would be laborious and has been done only for the simply supported case in references [1,2].…”

Section: Introductionmentioning

confidence: 97%

Natural Frequencies, Sensitivity and Mode Shape Details of an Euler–bernoulli Beam With One-Step Change in Cross-Section and With Ends on Classical Supports

Naguleswaran¹

2002

Journal of Sound and Vibration

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Section: Introductionmentioning

confidence: 97%

Natural Frequencies, Sensitivity and Mode Shape Details of an Euler–bernoulli Beam With One-Step Change in Cross-Section and With Ends on Classical Supports

Naguleswaran¹

2002

Journal of Sound and Vibration

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“…Farghaly considers various constraints at the end boundary in the analysis of the cantilever carrying a tip body [6]. The natural frequency of a stepped beam with two di!erent cross-sections is sought for various boundary conditions by Jang and Bert [7,8]. Subramanian and Balasubramanian describe the bene"cial e!ects of steps on the dynamic characteristics of beams [9].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Characteristics of Stepped Cantilever Beams Connected With a Rigid Body

Kwon

Park

2002

Journal of Sound and Vibration

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“…The exact methods include the derivation of the transcendental eigenvalue equations in order to evaluate the beam natural frequencies. In the case of relatively simple problems closed form solutions for the eigenvalue problem were obtained [4,5].…”

Section: Introductionmentioning

confidence: 99%

A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods

El-Sayed

Farghaly

2017

Shock and Vibration

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The exact solution for multistepped Timoshenko beam is derived using a set of fundamental solutions. This set of solutions is derived to normalize the solution at the origin of the coordinates. The start, end, and intermediate boundary conditions involve concentrated masses and linear and rotational elastic supports. The beam start, end, and intermediate equations are assembled using the present normalized transfer matrix (NTM). The advantage of this method is that it is quicker than the standard method because the size of the complete system coefficient matrix is 4 × 4. In addition, during the assembly of this matrix, there are no inverse matrix steps required. The validity of this method is tested by comparing the results of the current method with the literature. Then the validity of the exact stepped analysis is checked using experimental and FE(3D) methods. The experimental results for stepped beams with single step and two steps, for sixteen different test samples, are in excellent agreement with those of the threedimensional finite element FE(3D). The comparison between the NTM method and the finite element method results shows that the modal percentage deviation is increased when a beam step location coincides with a peak point in the mode shape. Meanwhile, the deviation decreases when a beam step location coincides with a straight portion in the mode shape.

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Free vibration of stepped beams: Higher mode frequencies and effects of steps on frequency

Cited by 52 publications

References 3 publications

Natural Frequencies, Sensitivity and Mode Shape Details of an Euler–bernoulli Beam With One-Step Change in Cross-Section and With Ends on Classical Supports

Natural Frequencies, Sensitivity and Mode Shape Details of an Euler–bernoulli Beam With One-Step Change in Cross-Section and With Ends on Classical Supports

Dynamic Characteristics of Stepped Cantilever Beams Connected With a Rigid Body

A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods

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