Some Complicating Effects in the Vibration of Composite Beams

In the last 50-60 years, use of composite structures in engineering applications has increased. Due to this fact many studies have been conducted related with composite structures (such as: shells, plates and beams). Bending, buckling and free vibration analysis of composite structures has taken considerable attention. Beams are one of these structures that are used in mechanical, civil and aeronautical engineering applications (such: robot arms, helicopter rotors and mechanisms). Considering these applications free vibration problem of the composite beams are studied in the previous studies. Kapania & Raciti, 1989 investigated the nonlinear vibrations of un-symmetrically laminated composite beams. Chandashekhara et al., 1990 studied the free vibration of symmetric composite beams. Chandrashekhara & Bangera, 1993 investigated the free vibration of angle-ply composite beams by a higher-order shear deformation theory. They used the shear flexible finite element method. Krishnaswamy et al., 1992 solved the generally layered composite beam vibration problems. Chen et al., 2004 used the state-space based differential quadrature method to study the free vibration of generally laminated composite beams. Solution methods for composite beam vibration problems depend on the boundary conditions, some analytical (Chandrashekhara et al., 1990, Abramovich, 1992, Krishnaswamy et al., 1992, Abramovic & Livshits, 1994, Khdeir & Reddy, 1994, Eisenberger et al., 1995, Marur & Kant, 1996, Kant et al., 1998, Shi & Lam, 1999, Yildirim et al., 1999, Yildirim, 2000, Matsunaga, 2001, Kameswara et al., 2001, Banerjee, 2001, Chandrashekhara & Bangera, 1992, Ramtekkar et al., 2002, Murthy et al., 2005, Arya, 2003, Karama et al., 1998, Aydogdu, 2005, 2006) solution procedures have been used. Many factors can affect the vibrations of beams, in particular the attached springs and masses, axial loads and dampers. This type of complicating effects is considered in the vibration problem of isotropic beams. Gurgoze and his collogues studied vibration of isotropic beam with attached mass, spring and dumpers (Gurgoze, 1986, Gurgoze, 1996, Gurgoze & Erol, 2004). Vibration of Euler-Bernoulli beam carrying two particles and several particles investigated by Naguleswaran, 2001, 2002. Nonlinear vibrations of beam-mass system with different boundary conditions are investigated by Ozkaya & Pakdemirli, 1999, Ozkaya et. al., 1997. They used multiscale perturbation technique in their solutions.