Dynamic response with respect to base movement of spring frame supported cantilever simple beam with concentrated mass
✍ Scribed by Jin Chen; F. Kosel
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 566 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0045-7949
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✦ Synopsis
In
this paper, the principle of relative motion is used to investigate the dynamic response of a spring-frame-supported cantilever simple beam with concentrated mass. Both free vibration and forced vibration caused by the base movement are studied. The cantilever simple beam is discretized into a simple beam and a cantilever beam. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each beam. The general analytical solution of the whole beam in terms of inixial parameters is obtained. In the case of free vibration, the frequency equation can be obtained in an analytical form, and in the case of base movement, a final solution can also be obtained analytically by using the dynamic response of the supporting spring frame as its vibrating source. From our analysis one can see that the accuracy of the solution of the spring-mass of two degrees of freedom is quite satisfactory for engineering purposes in the case of considering only the movement of the point where the concentrated mass P stands.