Highly accurate closed-form solutions for free vibration and eigenbuckling of rectangular nanoplates

摘要: Abstract This work presents the highly accurate closed-form solutions for free vibration and eigenbuckling of isotropic rectangular nanoplates with arbitrary homogeneous boundary conditions based on Eringen’s nonlocal theory classical thin plate theory. The iterative separation-of-variable (iSOV) method Rayleigh quotient, which is most solution among all methods, used to obtain solutions, including exact well-known Navier Levy types solutions. different scale plates are achieved first time, presented in excellent explicit forms. present coincide well analytical numerical literature, verifying accuracy method. influences parameters, lengths frequencies critical buckling loads studied, effects explained physical sense. can be taken as benchmarks validation a guide parametric design structure, basis constructing new methods.