A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation

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Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations (2017, result): “Tables 1 and 2 present respectively the comparisons of the non dimensional natural frequency and the mid-span deflection w(L/2) obtained from the present new beam theory with other beams theories results of Chen et al. (2004) and Ying et al.”
Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations (2008, background): “Meanwhile, the comparisons of natural frequency parameter k 1⁄4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qAlx2=EI 4 q of the same beam to those in [39,41] are also presented in Table 2.”
Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations (2010, methodology): “[39] proposed a mixed method, which combined the state space method and the differential quadrature method, for bending and free vibration of arbitrarily thick beams resting on Pasternak’s elastic foundations.”