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.
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Abbreviations
- \(A_{i} (i = 1,2,3)\) :
-
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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Nayak, D.K., Pradhan, M., Jena, P.K., Dash, P. (2020). Dynamic Stability Analysis of an Asymmetric Sandwich Beam on a Sinusoidal Pasternak Foundation. In: Deepak, B., Parhi, D., Jena, P. (eds) Innovative Product Design and Intelligent Manufacturing Systems. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-2696-1_10
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DOI: https://doi.org/10.1007/978-981-15-2696-1_10
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