article · Journal of Sandwich Structures & Materials
A mathematical model evaluates the free vibration behaviour of miniature three-layered plates comprising an exponentially graded core and piezomagnetic face sheets. Resting on a Pasternak foundation, the rectangular structure is analysed using modified couple stress theory to account for small-scale physical effects that classical continuum theories overlook. Material properties across the core vary smoothly through its thickness according to an exponential distribution. Using Hamilton principle and first-order shear deformation theory, seven equations of motion are formulated and solved analytically via Navier approach. Numerical evaluations show how natural frequencies respond to variations in plate dimensions, thickness ratios, core material inhomogeneity, the material length scale parameter, and underlying foundation stiffness. This theoretical framework provides an analytical method to predict resonant frequencies in tiny composite laminated structures operating under complex boundary conditions.
Understanding how tiny composite plates vibrate is essential for engineers developing advanced micro- and nano-scale devices. Classical structural models fail at microscopic scales where material dimensions alter mechanical responses. By accounting for size-dependent effects and complex layered materials, this analytical model helps researchers predict dynamic stability and mechanical behaviour in small-scale smart structures without relying solely on costly physical testing.
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The present work is devoted to the free vibration analysis of elastic three-layered nano-/micro-plate with exponentially graded core and piezomagnetic face-sheets using the modified couple stress theory. To capture size-dependency for a nano-/micro-sized rectangular plate, the couple stress theory is used as a non-classical continuum theory. The rectangular elastic three-layered nano-/micro-plate is resting on Pasternak’s foundation. The present model contains one material length scale parameter and can capture the size effect. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on the modified couple stress theory and first-order shear deformation theory. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually the natural frequency is scrutinized for different side length ratio, thickness ratio, inhomogeneity parameter, material length scale, and parameters of foundation numerically.
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DOI: 10.1177/1099636217734279
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