Abstract
In this paper, the vibratory properties and expression of natural modes of laminated composite beam with variable cross-section ratios of elastic modulus and density along the axis of the beam have been investigated via theoretical analysis. Based on the generalized Hamilton principle, the longitudinal and transverse vibration equations have been deduced by the means of variational method. Then, the natural frequencies of longitudinal and transverse vibration modes have been obtained using the method of power series, which agree well with finite element simulations. The first-order natural frequencies of longitudinal and transverse of composite beams are plotted as a function of the elastic modulus or densities difference of two components. With distinct material characteristics, the effect of shape factor on the first and second order lateral modes of composite beam is also revealed. In addition, the study shows that the boundary conditions impose a strong effect on the shape factor. The method presented in this paper is not only suitable for the laminated composite beam with variable cross-section, but will also be applicable to more general cases of composite beams of complex geometry and component in vibration mechanics. This controllable vibration performance achieved in this paper may shed some light on and stimulate new architectural design of composite engineering structures. © 2015, JVE INTERNATIONAL LTD.
| Original language | English |
|---|---|
| Pages (from-to) | 2491-2502 |
| Number of pages | 12 |
| Journal | Journal of Vibroengineering |
| Volume | 17 |
| Issue number | 5 |
| Early online date | 15 Aug 2015 |
| Publication status | Published - Aug 2015 |
| Externally published | Yes |
Funding
The work of X. C. is supported by the National Natural Science Foundation of China (11172231 and 11372241), AFOSR (FA9550-12-1-0159), and ARPA-E (DE-AR0000396). The work of B. L. is supported by the National Natural Science Foundation of China (11402188), the Fundamental Research Funds for the Central Universities (08143047) (2014gjhz16), and the Natural Science Foundation of Shaanxi (2015JQ1018).
Keywords
- Bernoulli-Euler composite beams
- Method of power series
- Natural frequencies
- Vibration mode