In this study, the effect of finite strain on bending of the geometrically nonlinear of micro laminated composite Euler-Bernoulli beam based on Modified Couple Stress Theory (MCST) is studied in thermal environment. The Green-Lagrange strain tensor according to finite strain assumption and the principle of minimum potential energy is applied to obtain governing equation of motion and boundary c...

A variational theory is presented for beam loading in microwave cavities. The beam-field interaction formulated as a dynamical whose stationarity according to Hamilton's principle will naturally lead steady-state solutions that indicate how cavity's resonant frequency, $Q$, and optimal coupling coefficient detune result of the loading. driven cavity Lagrangian derived from first principles, inc...

The ionization of residual gas by an electron beam in an accelerator generates ions that can resonantly couple to the beam through a wave propagating in the beam-ion system. The original theory of the Fast Ion Instability [1, 2] was developed assuming both a constant external focusing and the beam size. The theory predicts an instability in which an initial perturbation grows as ∼ exp(α√t). In ...

An analytic theory of cumulative multibunch beam breakup in linear colliders is developed. Included is a linear variation of transverse focusing across the bunch train as might be applied, e.g., by chirping the radiofrequency power sources or by using radiofrequency quadrupole magnets. The focusing variation saturates the exponential growth of the beam breakup and establishes an algebraic decay...

This paper presents the equations for the implementation of rotational quaternions in the geometrically exact three-dimensional beam theory. A new finite-element formulation is proposed in which the rotational quaternions are used for parametrization of rotations along the length of the beam. The formulation also satisfies the consistency condition that the equilibrium and the constitutive inte...