Thermoelastic Vibrations of Nonlocal Nanobeams Resting on A ‎Pasternak Foundation Via Dpl Model

The present work introduces the thermoelastic vibrations of nonlocal nanobeams resting on a twoparameter foundation. the governing equations are formulated for linear winkler–pasternak foundation type based on the generalized dualphaselag heat conduction and nonlocal beams theories. the nanobeam is subjected to a temperature ramping function. the coupled equations of the problem are formulated and solved by laplace transform technique. the effects of the nonlocal parameter and different foundation parameters on the field variables are illustrated graphically and discussed. the results obtained are consistent with previous analytical and numerical results.