For structures were dealt with free and forced vibrations

              For many years, the idea of smart materials, structures was an attractive issue as well as many challenges for the researchers and engineers. A smart structure is an active or semi-active(hybrid) multifunction system which have capability of responding to external excitation in a controlled and prescribed fashion. There are various types of smart materials available such as piezoelectric materials, shape memory alloys,  self-healing material ERFuid ,MRFluid, Elastomers etc with a very wide range of applications in various industries ranging from aerospace, automotive, marine, civil engineering to medical equipments also.

            The dynamic behaviours of structures like beams, plates and shells are very  effective operations in many parts of the system such as in  automobiles, machineries and civil structures etc. using appropriate control method. The early works on the adaptive sandwich structures were dealt with free and forced vibrations in sandwich structures such as a beam with viscoelastic material as a core one. Mead and Markus1 worked on the forced vibrations study of damped type sandwich beam considering for different boundary conditions.

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                        Howson and Zare2 studied the flexural motion of a three layer sandwich beam have unequal face plates by using dynamic member stiffness method. Lin and Chin3 found the dynamic behaviour and instability of a rotating laminated beam considering a  constrained layer type of damping treatment under the  axial periodic type of load by using finite element approach and found the instability regions for the simple aswellas more complex form of resonant frequencies under the parametric type of excitation.

                        Recently the concept of functional systems based on the smart fluids like ERFluid/MRFluid 89 shows similar properties like that of the viscoelastic core type materials and its applications were introduced by the Carlson et.al30 31 Weiss et.al32 Don17-18contain ER/MR Fluid a core material. The controllable rheological properties works on semi-active means and these fluid comprise micron sized particles sensitive to the electric/magnetic field. The micro particles tend to form a columnar like structure which tends to increase in viscosity and converting its state to solid gel form and whenever the external excitation is removed, the solid state gel returns to the original liquid form and the characteristics of the fluid are restored.

Consequently the rheological properties of these fluids changes in mechanical properties such as damping and stiffness of the structure simultaneously. Don and Coulter5 worked on the dynamic behaviour of the ERFluid based adaptive structures using the very popular vibration theories namely the Ross,Kerwin Unagar(RKU), Mead and Markus(MM) models found the most effective ability of two theories for the ERFuid based structural modelling.Rahn  and Joshi6derived the dynamic models for the ER structures on the basis of viscoelastic sandwich beam. The instability of all modes ensured by using Lyapunov theory, the response of the ERFluid filled cantilever beam stability condition shown as well.Yalcintas and coulter7found the transverse vibrations of simply supported three layered ERFluid sandwich beam under sinusoidal actuation, the results between experimental and optimum electric field is required in order  to reduce the vibration of the beam under the excitation frequency.

                        The ER/MR adaptive beam consists of three layered structures comprising two elastic layers and core is made up of ER/MR material. Whenever under the actuation of external electric/magnetic field is applied, the mechanical properties of these  materials changes the dynamic characteristics of the laminated beam in significant way because of due to the shear deflection of the beam when ever MR/ER core material undergoes a shear strain.

                        The ER fluid material applications in structural problems worked by Yalcintas and Coutler19,20.In the year 1995 they had worked on the vibration problems in sandwich structures like ERFluid Beam Plate like structures and the effects of thickness and loss factors generated in the structure under vibration behaviour has been discussed. Then Lee21 has worked on the transverse free vibrations problems of sandwich beam and also investigated on the sandwich beam for transverse free vibration condition and has developed an iterative method to analyse the rheological properties of ERFluid in its nonlinear behaviour. In the year 2003 almost no research work done  on vibration study ERFuid sandwich plate.Taiwanese,Yeh and Chen Wang worked on  structural stability of ERFluid sandwich beam and investigated the dynamic behaviour of sandwich plate annular plate etc using ERFluid as core layer 22-27.

                        Hasheminejad and Maleki 28 used a classical thin plate theory and apply equation of motion under  the forced vibration condition  under various external transverse  excitation frequency ranges from 0 to 300Hz with an application of electric field strength of 0-3.5kV/mm.Mohammadi and Sedaghati 29 worked on nonlinear vibration study  ERFluid sandwich structures under different boundary conditions and found the nonlinear damping effect in  sandwich shell structure for the small and also for large displacements, ER core materials thickness ratio as well as strength of electric field.

                        The adaptive structures incorporating MR materials have been analyzed by many researchers in recent years. Yalcintas and Dai 11 discussed about vibration suppression capabilities of MR materials-based adaptive structures. They considered homogeneous three-layered adaptive beams with MR materials sandwiched between two elastic layers. To calculate the complex shear modulus of the MR fluid, they performed a free oscillation experiment and compared with theoretically investigations. The primary studies on dynamic characteristics of MR/ER sandwich structures were conducted on the multi-layer sandwich beam, which was due to its relatively simple mechanical model (Lara-Prieto et al., 2010)33.Furthermore, the experimental studies on MR/ER sandwich beam structures have been mostly conducted on the cantilever sandwich beams Berg et al., 1996;34 Chen et al., 1994;35 Don and Coulter, 1995; 5Gandhi et al., 1989;36Phani and Venkatraman, 2003,37 2005; Sun et al.10 presented the dynamic behaviour of an adaptive beam based on MR materials under pre-yield conditions and the relation between complex shear modulus of MR fluid within pre-yielding regime and magnetic field is studied. Also, a structural dynamic modeling approach was presented and vibration characteristics of MR adaptive structures were predicted for different magnetic field levels by them.Yeh and Shih 11 worked on dynamic response of simply supported adaptive beam subjected to the axial harmonic load and found natural frequency, loss factor, dynamic instability, buckling load etc.Rajamohan et al., 201038, 2010b39 20c;40 Wei etal.,201141 although some studies on clamped–clamped (Haiqing and King, 199742) and simply supported structures by Lee and Cheng, 1998;43.Rajamohan et al.12 developed the governing equation of a multi-layer beam structure employing MR fluid in the pre-yield regime by using the finite element and the Ritz methods. The validation of finite element results good agreement with those of Ritz and experimental methods. The properties of a multi-layered beam with MR fluid as a sandwich layer between the two layers of the continuous elastic structure were studied by Rajamohan et al. 12. They analyzed the forced vibration responses of the MR sandwich beam subjected to harmonic force excitation and observed that the natural frequencies could be increased by increasing the magnetic field while the magnitudes of the peak deflections could be considerably decreased


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