AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING

507 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, unknown): “In recent years, based on Finkelstein’s quantum sets [9, 10], fractal and fractional calculus have had quite a triumph in high energy physics, and all conceivable applications in science and technology as well, especially in as nanotechnology [11–15].”
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review (2012, methodology): “1 Basic idea of Parameter–Expansion Method In order to use the PEM, we rewrite the general form of Duffing equation in the following form[100]:”
THE VARIATIONAL ITERATION METHOD WHICH SHOULD BE FOLLOWED (2010, unknown): “[6,7]).”
The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators (2019, background): “If we choose w(t)=1, we have Ren–Hu’s modification.41 If we choose wðtÞ ¼ RðtÞ, we have ~R1 ¼ Z T=4 0 R21ðtÞdt (16) ~R2 ¼ Z T=4 0 R22ðtÞdt (17) For simplicity, we can use discrete weighted average ~R1 ¼ XN i¼1 Ax 2 1cosx1ti þ fðAcosx1tiÞ wðx2tiÞ XN i¼1 wðx2tiÞ (18) ~R2 ¼ XN i¼1 Ax 2 2cosx2ti þ fðAco”