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
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


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.


Asymmetric sandwich beam Temperature gradient Sinusoidal Pasternak foundation Dynamic stability 


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

Cross-sectional Area of ith layer


Beam width

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

Young’s modulus of ith elastic layer


Shear parameter


Foundation’s shear layer modulus


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


Length of beam




Shear layer thickness of foundation


Mass per unit length of beam


Ith layer’s density

\(\overline{\omega }\)

Nondimensional forcing frequency

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

Constant temperature gradient of ith layer




Nondimensional time


Lateral deflection of beam at ‘x


Number of functions


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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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