| Summary: | 碩士 === 中原大學 === 機械工程學系 === 87 === The investigation based on the theories of viscoelastic sandwich beam derived the equations of motion which was complex mode cause of the shear module in viscoelasticity is complex mode . During the vibration analysis , we choose the boundary condition as a simply support beam And the displacement field was effected by system frequency and loss factor . The material of the core damping layer of the sandwich beam is electrorheological ,whose shear module was effected by the
electric field .
In this study we discuss the vibrating behavior . Fixing the electric field we could see the influence of different thickness ration to the displacement and velocity fraction . By the way,fixing the thickness we had the influence of different electric field . Simultaneously , we also discuss the influence of loading frequency and harmonic vibration . We also findout the damping response of changing shear module of viscoelastic material by variour loading frequency . And,
the discussion and conculsion are listed in this paper .
Flexural vibration of viscoelastic sandwich beams has been in investigates since the 1960s . In a fundamental paper , Ross , Ungar , and Kerwin treated the problem by assumming a perfect interface , the same amount of transverse displacement in each layer,damping only from the shearing of the viscoelastic core , and simply supported end conditions . DiTaranto extended this analysis to include freely vibrating beams having unspecified end conditions . Based on DiTaranto’s work,sixth-order differential equations of motion were derived in terms of transverse displacement by Mead and Markus , and this theory was correlated with experimental data by Lu and Douglas . Yan and Dowell used the principle of virtual work to pbtain a set of five differential governing equations.A more accurate theory that includes the inertia effects of transverse , longitudinal ,and rotary motions was investigated by Rao and Nakra . In recent years , various vibration theories of undamped sandwich beams
have been developed by Vaswani et al .Ko , and Lu and Libove .
The effects of a viscoelastic adhesive layer on the dynamic response and structural damping of sandwich structures are studied by employing a developed sandwich beam theory . The two face layers are considered as ordinary beams (Euler beams) with both axial and bending resistance . The core material is considered to be viscoelastic . A developed high-order displacement field assumption is used in order to achieve a more accurate kinematics of the flexible viscoelastic core than would be possible under the classical assumptions for sandwich beams . Imperfect interface conditions between faces and core are defined as linear relations between longitudinal displacement discontinuites and the transverse shear stress at the adhesive layer . The viscoelastic properties of the adhesive layer and the core material are assumed in a complex modulus formula that is a function of frequency for a given temperature . The linear equations of motion that describe the vibration of the sandwich finite beam are derived based on the Hamilton principle . Consistent boundary conditions are given by prescribimg either the stress resultants or the corresponding time derivatives of the displacement components . The numerical results of a mechanical impedance example are verified with experimental data in the literature . The effects of storage modulus and loss factors of adhesive layers are investigated numerically for simply supported beams under harmonic excitation . It is shown that the viscoelastic adhesive layers have a definite influence on structural
damping of the sandwich beam .
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