Linear and Nonlinear Structural Mechanics

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The implicit corotational method and its use in the derivation of nonlinear structural models for beams and plates (2012, methodology): “More refined models can be obtained, by the same procedure, using more sophisticated theories, such as the thinwalled beam theory of Vlasov, the so-called generalized beam theories [Goncalves et al. 2009], and the anisotropic theories for plates [Nayfeh and Pai 2004].”
Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass (2012, neutral): “Hence (Ali and Padhi, 2009; Nayfeh and Pai, 2004)”
Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters (2012, methodology): “Because the axial strain of a differential element is given by [26] e= √( 1 + u′2)+ v′2 − 1 (1)”
Nonlinear Dynamics of Spring Softening and Hardening in Folded-MEMS Comb Drive Resonators (2011, methodology): “[24] and Nayfeh and Pai [25] solve the nonlinear equation of motion for a fixed-free cantilever beam using the method of multiple scales and observe hardening in the first mode and softening in higher modes.”
Natural frequencies of nonlinear vibration of axially moving beams (2011, background): “Therefore, for small but finite stretching problems, one can only consider the transverse motion [27].”