Stability analysis of an exponentially tapered, pre-twisted asymmetric sandwich beam on a variable Pasternak foundation with viscoelastic supports under temperature gradient

Nayak, Dipesh Kumar; Dubey, A.; Nayak, C. R.; Dash, P. R.

doi:10.1007/s40430-020-2210-0

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…However, large setting angles were found to have a negative impact on dynamic stability. Nayak et al [8] investigated a tapered beam of exponential variation, pre-twisted system on a Pasternak foundation supported viscoelastically and a temperature grade. Pradhan et al [9] examined the stability of an uneven sandwiched beam on a foundation of Pasternak type with a temperature grade.…”

Section: Introductionmentioning

confidence: 99%

“…Banerjee [15] presented the problem-solving approach by dynamic stiffness method for sandwich beam. Nayak et al [16] investigated a tapered beam of exponential variation, pre-twisted system on a Pasternak foundation supported viscoelastically and a temperature grade. A functionally graded, pre-twisted thick cantilever beam was the subject of an investigation by Mohanty et al [17] into its vibration and dynamic stability.…”

Section: Introductionmentioning

confidence: 99%

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Free Vibration Analysis of Timoshenko Sandwich Beam Tapered Along Thickness and Width Resting on Pasternak Foundation

Madhusmita Pradhan,

Nabakishor Dang,

Pusparaj Dash

et al. 2024

Int Res J Adv Engg Hub

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This study delves into the analysis of the free vibration characteristics of a Timoshenko sandwich beam tapered along both width and thickness, subjected to an axially pulsing load on a Pasternak foundation. Integral to this investigation are the comprehensive considerations of energy expressions encompassing bending, axial deformation, kinetic energy, and strain energy induced by transverse shear stress. Subsequently, the differential equations governing the system, along with the associated boundary conditions, are deduced utilizing Hamilton's principle, followed by their non-dimensionalization. Leveraging series solutions from prior research that satisfy these equations and boundary conditions, each coordinate of the system is addressed. In the quest for a deeper understanding, Galerkin’s energy principle is employed to derive matrix expressions for key parameters such as mass and stiffness. Utilizing these matrices, Eigenvalues are computed to ascertain the natural frequencies of the system. The findings are presented through a series of graphical representations, elucidating the influence of various system parameters.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Timoshenko Sandwich Beam Tapered Along Thickness and Width Resting on Pasternak Foundation

Madhusmita Pradhan,

Nabakishor Dang,

Pusparaj Dash

et al. 2024

Int Res J Adv Engg Hub

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“…Nayak et al [12] carried out a stability analysis of an exponentially tapered beam on a variable Pasternak foundation. Nayak et al [13] investigated the free and forced vibration of coupled beam systems resting on variable viscoelastic foundations. Coskun et al [14] analyzed the elastic stability of variable cross-section columns by means of some analytical approximation techniques.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Non-Uniform Functionally Graded Beams on Inhomogeneous Foundations Subjected to Moving Distributed Loads

Huang,

Liu,

Zhao

2023

Applied Sciences

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Inhomogeneous materials, variable foundations, non-uniform cross-sections, and non-uniformly distributed loads are common in engineering structures and typically complicate their mechanical analysis considerably. This paper presents an accurate and efficient numerical method for the dynamic analysis of non-uniform functionally graded beams resting on inhomogeneous viscoelastic foundations subjected to non-uniformly distributed moving load and investigates the effects of non-uniformities and inhomogeneities on material, foundation, and load. Based on the Timoshenko beam theory and a Chebyshev spectral method, a consistent discrete dynamic model is derived, which can deal with all axially varying properties. A series of numerical experiments are carried out to validate the convergence and accuracy of the proposed method. The results are compared with those obtained through finite element analysis or in the literature, and excellent agreement is observed. Then, the dynamic response of an axially functionally graded beam resting on an inhomogeneous viscoelastic foundation and subjected to a non-uniformly distributed moving load is investigated. The results show that the material gradient and the inhomogeneous foundation can alter the vibration amplitudes and critical speeds of the beam significantly. Compared with more realistic non-uniformly distributed moving load models, idealized concentrated and uniformly distributed moving load models produce apparent computation errors in vibration amplitudes.

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Parametric Stability Analysis of a Spring Attached, Pre-Twisted, Rotating Sandwich Beam with Tip Mass and Viscoelastic Support

Nayak

Dash

2021

Int. J. Str. Stab. Dyn.

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This paper inspects the influence of a spring attachment provided on the top elastic layer on the stability of a pre-twisted, rotating sandwich beam having viscoelastic supports at the root under the impact of a periodically varying axial load. The spring is deployed on the beam to achieve more strength to weight ratio without compromising the stability. The beam is exponentially tapered, and a tip mass is at the free end to represent the rotating members in various types of machinery as closely as possible. The ruling equations and inter-related boundary conditions are attained by applying Hamilton’s principle. To obtain the solution, a matrix equation was developed through the assumed-mode variational method. The resulting matrix equation was converted to a coupled Hill’s equation of parametric vibration through the modal matrix corresponding to the free vibration problem. Finally, static and dynamic stability graphs were obtained for several system parameters such as position and length of the attached spring on the top elastic layer, the mass of the spring attachment, stiffness of the spring attachment, angle of pre-twist, tip mass, taper parameter, temperature gradient parameter, setting angle, viscoelastic spring stiffness, etc. to analyze their impact on the system’s stability. Saito and Otomi conditions were used to obtain dynamic stability plots. Greater stability is achieved due to the spring attachment on the top of the top elastic layer.

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Stability analysis of an exponentially tapered, pre-twisted asymmetric sandwich beam on a variable Pasternak foundation with viscoelastic supports under temperature gradient

Cited by 3 publications

References 23 publications

Free Vibration Analysis of Timoshenko Sandwich Beam Tapered Along Thickness and Width Resting on Pasternak Foundation

Free Vibration Analysis of Timoshenko Sandwich Beam Tapered Along Thickness and Width Resting on Pasternak Foundation

Dynamic Analysis of Non-Uniform Functionally Graded Beams on Inhomogeneous Foundations Subjected to Moving Distributed Loads

Parametric Stability Analysis of a Spring Attached, Pre-Twisted, Rotating Sandwich Beam with Tip Mass and Viscoelastic Support

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