Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory

Modal Analysis of Tapered Beam-Column Embedded in Winkler Elastic Foundation

“…It has been also successfully employed for different vibration problems of structural members such as plates and shells [20][21][22][23]. For more details of the mathematical background and application of the DSC method in solving problems in engineering, the readers may refer to some recently published reference [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In the context of distribution theory, a singular convolution can be defined by [11] …”

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

“…Civalek and Demir [21] employed nonlocal elasticity theory of Eringen to study bending analysis of Euler-Bernoulli microtubules and numerically showed that nonlocal continuum theory is superior to classical theory, especially for some boundary conditions. According to the MCST, bending, buckling, and vibration behavior of micro scale plate resting on the elastic foundation are investigated by Akgöz and Civalek [22]. Among all viscoelastic foundations, the effect of Kelvin-Voigt foundation on the vibration of nanostructures such as carbon nanotubes (CNTs), nanobeams and nanoplates has been further investigated by some researchers.…”

An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories

“…Also, different studies on the behavior of micro-beams and micro-plates were carried out by Akgöz and Civalek [25]. Based on the modified couple stress theory, an Navier solution for bending, buckling and vibration of micro-plates resting on a Winkler elastic foundation was presented in [26]. Hamilton's principle was utilized for obtaining the equation.…”