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Dynamic Stability Analysis of an Asymmetric Sandwich Beam on a Sinusoidal Pasternak Foundation

  • Dipesh Kumar Nayak
  • Madhusmita Pradhan
  • Prabir Kumar Jena
  • Pusparaj Dash
Conference paper
  • 45 Downloads
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

The dynamic stability of an asymmetric sandwich beam with viscoelastic core resting on a sinusoidal varying Pasternak foundation subjected to parametric vibration is observed. The effects of different parameters such as temperature gradient of each elastic layer, the ratio of modulus of the shear layer of Pasternak foundation to Young’s modulus of the elastic layer, core loss factor, stiffness of Pasternak foundation and elastic foundation parameter on the dynamic stability are investigated. Hamilton’s principle, generalized Galerkin’s method and Hill’s equations are utilized, followed by Saito–Otomi conditions to obtain the results.

Keywords

Asymmetric sandwich beam Temperature gradient Sinusoidal Pasternak foundation Dynamic stability 

Nomenclature

\(A_{i} (i = 1,2,3)\)

Cross-sectional Area of ith layer

\(B\)

Beam width

\(E_{i} (i = 1,3)\)

Young’s modulus of ith elastic layer

\(g\)

Shear parameter

\(G_{s}\)

Foundation’s shear layer modulus

\(G_{2}^{*}\)

Complex shear modulus of core

\(h_{i} (i = 1,2,3)\)

Ith layer’s thickness at ‘x

\(I_{i} (i = 1,2,3)\)

Second moment of inertia about relevant axis

\(l\)

Length of beam

\(l_{h1}\)

\(l/h_{10}\)

\(d\)

Shear layer thickness of foundation

\(m\)

Mass per unit length of beam

\(\rho_{i}\)

Ith layer’s density

\(\overline{\omega }\)

Nondimensional forcing frequency

\(\delta_{i} (i = 1,3)\)

Constant temperature gradient of ith layer

\(t\)

Time

\(\overline{t}\)

Nondimensional time

\(w(x,t)\)

Lateral deflection of beam at ‘x

\(p\)

Number of functions

References

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Dipesh Kumar Nayak
    • 1
  • Madhusmita Pradhan
    • 1
  • Prabir Kumar Jena
    • 1
  • Pusparaj Dash
    • 1
  1. 1.Veer Surendra Sai University of TechnologyBurlaIndia

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