Abstract We show how spectral submanifold theory can be used to construct reduced-order models for harmonically excited mechanical systems with internal resonances. Efficient calculations of periodic and quasi-periodic responses the are discussed in this paper its companion, Part II, respectively. The dimension a model is determined by number modes involved resonance, independently full system....

The composites provide design flexibility because many of them can be moulded into complex shapes. The carbon fibre-reinforced epoxy composites exhibit excellent fatigue tolerance and high specific strength and stiffness which have led to numerous advanced applications ranging from the military and civil aircraft structures to the consumer products. However, the modelling of the beams undergoin...

In this study, nonlocal nonlinear instability and the vibration of a double carbon nanotube (CNT) system have been investigated. The Visco-Pasternak model is used to simulate the elastic medium between nanotubes, on which the effect of the spring, shear and damping of the elastic medium is considered. Both of the CNTs convey a viscose fluid and a uniform longitudinal magnetic field is applied t...

Nonlinear plate bending within Mindlin's strain gradient elasticity theory (SGT) is investigated by employing somewhat non-standard finite element methods. The main goal to compare the results provided geometrically nonlinear three-dimensional (3D) and Reissner–Mindlin theory, i.e., first-order shear deformation (FSDT), SGT. For 3D Green–Lagrange relations are adopted, while von Kármán strains ...

Abstract The size dependent static pull-in instability of functionally graded (FG) microbeams in micro-electromechanical systems (MEMS) is studied, considering the influence axial force. material properties are varied beam thickness by a power-law function, and they calculated rule mixture. To account for microsize effect, classical Euler-Bernoulli theory employed combination with modified coup...

Focused laser differential interferometry (FLDI) is used to make freestream density fluctuation measurements in the von Kármán Gas Dynamics Facility (VKF) Wind Tunnel D at Arnold Engineering Development Complex. A comparison made between pitot-probe and FLDI after converting both pressure spectra. modification of Stainback Wagner’s theory, incorporating recent numerical results from Chaudhry et...