Influence of Winkler and viscoelastic foundation on free vibration of functionally graded beam integrated with Terfenol-
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(2020) 42:591
TECHNICAL PAPER
Influence of Winkler and viscoelastic foundation on free vibration of functionally graded beam integrated with Terfenol‑D layer Mukund A. Patil1 · Ravikiran Kadoli1 Received: 13 May 2020 / Accepted: 6 October 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract Free vibration of functionally graded beam integrated with Terfenol-D layer on Winkler-two parameter and viscoelastic foundation are studied by means of differential quadrature method within the framework of classical beam theory. The material properties of functionally graded beam integrated Terfenol-D layer are estimated by using the rule of mixture. The applied kinematic boundary conditions are implemented using 𝛿-point and modified weighting coefficient approach. The solution of simply supported functionally graded material beam with Terfenol-D layer (FGMT) resting on the Winkler elastic foundation is obtained by using the technique of Navier. The numerical results obtained using differential quadrature method (DQM) and modified differential quadrature method (MDQM) are compared with exact results obtained from analytical formulation where excellent agreement is observed. The parametric study is carried out to encapsulate the influence of Winkler-two parameter and the viscoelastic foundation on the vibration characteristics of functionally graded beams integrated with Terfenol-D layer. Keywords Terfenol-D · Differential quadrature method (DQM) · Functionally graded material · Variable elastic foundation · Composite actuator
1 Introduction The applications of composite structures on Winkler and/ or viscoelastic foundations are mostly found in a wide class of engineering structures such as pile foundations, railway applications, strip footings, buttress foundations, stockpiling tanks, swimming pools, high-speed transportation or rocketsled technology, solid propellant rocket motors. Foundation is an important member to reduce the vibrations/oscillations of structural system. The Winkler elastic foundation is substantially used one-parameter foundation model, having boundlessly many closed-spaced linear springs and competent of normal load only. Technical Editor: Aurelio Araujo. * Mukund A. Patil [email protected] Ravikiran Kadoli [email protected] 1
Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, Mangalore, Karnataka 575025, India
Terfenol-D is smart materials with intrinsic properties such as large strain, high force, wide bandwidth and high energy density. With these distinctive properties, Terfenol-D can be used as an embedded actuator, used for the unwanted vibration suppression of flexible structures. The reduction in eddy current at higher operating frequencies, crystallographic orientation of particles, the preloading and potential use for structural health monitoring are the main advantages of composites containing Terfenol-D powder particles. Several studies have also carried out for the vibration behaviors of laminated and/or
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