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Structural Engineering and Mechanics Volume 26, Number 1, May10 2007 , pages 1-14 DOI: https://doi.org/10.12989/sem.2007.26.1.001 |
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Free vibration analysis of a Timoshenko beam carrying multiple spring-mass systems with the effects of shear deformation and rotary inertia |
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Jee-Ray Wang,Tsung-Lung Liu and Der-Wei Chen
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| Abstract | ||
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Because of complexity, the literature regarding the free vibration analysis of a Timoshenko beam carrying ?multiple? spring-mass systems is rare, particular that regarding the ?exact? solutions. As to the ?exact? solutions by further considering the joint terms of shear deformation and rotary inertia in the differential equation of motion of a Timoshenko beam carrying multiple concentrated attachments, the information concerned is not found yet. This is the reason why this paper aims at studying the natural frequencies and mode shapes of a uniform Timoshenko beam carrying multiple intermediate spring-mass systems using an exact as well as a numerical assembly method. Since the shear deformation and rotary inertia terms are dependent on the slenderness ratio of the beam, the shear coefficient of the cross-section, the total number of attachments and the support conditions of the beam, the individual and/or combined effects of these factors on the result are investigated in details. Numerical results reveal that the effect of the shear deformation and rotary inertia joint terms on the lowest five natural frequencies of the combined vibrating system is somehow complicated. | ||
| Key Words | ||
| Timoshenko beam; shear deformation; rotary inertia; spring-mass systems; shear coefficient; natural frequency. | ||
| Address | ||
| Jee-Ray Wang: Institute of Mechatronoptic Systems, ChienKuo Technology University, Changhua City, Taiwan 500, Republic of China Tsung-Lung Liu and Der-Wei Chen: Department of Naval Architecture and Marine Engineering, Chung Cheng Institute of Technology, National Defense University, Dashi, Taoyuan, Taiwan 335, Republic of China | ||