Influence of Winkler and viscoelastic foundation on free vibration of functionally graded beam integrated with Terfenol-D layer

Patil, Mukund A.; Kadoli, Ravikiran

doi:10.1007/s40430-020-02677-9

Cited by 10 publications

(3 citation statements)

References 35 publications

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“…A large variety of types of structural elements is considered, including beams [187,194,195,206,213,228,232], plates [193,202,203,214,218,220,227], shells [204], composite beams [186,198,201,207,211,215,224,225], composite plates [155,185,191,199,200,210,212,222,223,226], composite shells [190,216,219,221], nanobeams [184,189,196], FG nanoplates [192,197,208,[229][230][231], and FG nanoshells/nanopanels [188,209,217].…”

Section: Structural Elements On Viscoelastic Foundationsmentioning

confidence: 99%

“…The possibility of applying a simpler foundation model, i.e., the Winkler model with a Kelvin-Voigt viscoelastic component, is also commonly investigated, as in [187,188,215,230,231] using the linear description, or in [213,218,224] with the non-linear elastic element. The fractional derivative within this model was considered in [193,214].…”

Section: Structural Elements On Viscoelastic Foundationsmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Lewandowski,

Litewka,

Łasecka-Plura

et al. 2023

Buildings

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The paper is devoted to a review of recent achievements in the field of dynamic analysis of structures and structural elements, such as beams and plates, with embedded viscoelastic (VE) dampers and/or layers. The general characteristics of VE materials, their rheological models, and methods of parameters identification are discussed. New formulations of dynamic problems for systems with VE elements are also reviewed. The methods of determination of dynamic characteristics, together with the methods of analysis of steady-state and transient vibrations of such systems, are also discussed. Both linear and geometrically non-linear vibrations are considered. The paper ends with a review of the methods of sensitivity and uncertainty analysis, and the methods of optimization, for structures with VE elements.

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Section: Structural Elements On Viscoelastic Foundationsmentioning

confidence: 99%

Section: Structural Elements On Viscoelastic Foundationsmentioning

confidence: 99%

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Lewandowski,

Litewka,

Łasecka-Plura

et al. 2023

Buildings

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“…e DQM is a numerical solution technique which is noticeably growing to be used in solving the boundary and initial value problems; it is considered a wellsuited alternative to the well-known conventional numerical methods such as the finite difference technique. Patil and Kadoli [20] utilized the DQM to study the influence of the Winkler foundation on the free vibration of a functionally graded beam.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Tapered Timoshenko and Euler–Bernoulli Beams on an Elastic Foundation with Moving Loads

Abbas

bakr

Nassar

et al. 2021

Journal of Mathematics

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This research studies the vibration analysis of Euler–Bernoulli and Timoshenko beams utilizing the differential quadrature method (DQM) which has wide applications in the field of basic vibration of different components, for example, pillars, plates, round and hollow shells, and tanks. The free vibration of uniform and nonuniform beams laying on elastic Pasternak foundation will be studied under three sets of boundary conditions, that is, mixing between being simply upheld and fixed while utilizing the DQM. The natural frequencies and deflection values were produced through the examination of both beam types. Results show great concurrence with solutions from previous research studies. The impact of the nonuniform cross-section area on the vibration was contemplated. A comparison between the results from both beams is obtained. The focus of this work is on studying the deflection difference between both beam theories at different beam dimensions as well as showing the shape of rotation of the cross section while applying a nodal point load equation to simulate the moving load. The results were discussed and a general contemplation about the theories was developed.

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Development of analytical and FEM solutions for static and dynamic analysis of smart piezoelectric laminated composite plates on elastic foundation

2023

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This paper proposes new analytical and finite element solutions for studying the effects of elastic foundations on the uncontrolled and controlled static and vibration responses of smart multi-layered laminated composite plates with integrated piezoelectric layers, acting as actuators and sensors. A non-polynomial higher-order plate theory with zigzag kinematics involving a trigonometric function and a local segmented zigzag function is adopted for the first time for modeling the deformation of a smart piezoelectric laminated composite plate supported on an elastic foundation. This model has only five independent primary variables like that of the first-order shear deformation theory, yet it considers the realistic parabolic behavior of the transverse shear stresses across the thickness of the laminated composites plates, and also maintains the continuity conditions of transverse shear stresses at the interfaces of the laminated plates. A two-parameter foundation model, namely Pasternak’s foundation, is used to model the deformation and shear interactions of the elastic foundation. The governing set of equations is derived by implementing Hamilton’s principle and variational calculus. Two different solution methods, namely, a generalized closed-form analytical solution of Navier-type, and a C0 isoparametric finite element (FE) formulation, are developed for solving the governing set of equations. The solutions in the time domain are obtained with Newmark’s average acceleration method. Comprehensive parametric studies are presented to investigate the influence of elastic foundation parameters, piezoelectric layers, loading, and boundary conditions on the static and dynamic responses of the smart composite plates with piezoelectric layers. The effects of the elastic foundations on the vibration control of the smart composite plates are also presented by coupling the piezoelectric actuator and sensor with a feedback controller. Several benchmark results are presented to show the influence of the various material and geometrical parameters on the controlled and uncontrolled responses of the smart plates, and also the significant effect of the elastic foundations on the static and dynamic responses of the smart structures. The results obtained are in very good agreement with the available literature, and it can be concluded that the proposed analytical solution and FE formulation can be efficiently used to model the static and dynamic electro-elastic behavior of smart laminated plates supported on elastic foundations.

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Influence of Winkler and viscoelastic foundation on free vibration of functionally graded beam integrated with Terfenol-D layer

Cited by 10 publications

References 35 publications

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

Analysis of Tapered Timoshenko and Euler–Bernoulli Beams on an Elastic Foundation with Moving Loads

Development of analytical and FEM solutions for static and dynamic analysis of smart piezoelectric laminated composite plates on elastic foundation

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