## What is/are Timoshenko Theory?

Timoshenko Theory - Shear deformation and rotary inertia are incorporated using the Timoshenko theory.^{[1]}The effect of the Timoshenko theory and the Euler-Bernoulli theory are investigated in this paper through numerical and analytical analyses.

^{[2]}In this experimental work a scanning laser Doppler vibrometer is used to measure mode shapes and natural frequencies of beam bending vibrations above the critical frequency predicted by Timoshenko theory.

^{[3]}A modified analytical model originated from Timoshenko theory on bi-material beam is proposed to predict the swelling-induced bending shape of the bi-hydrogel strips, with explicit relations of bending curvature and mid-span deflection versus mismatch strain.

^{[4]}The segments are compact so Timoshenko theory is employed.

^{[5]}This article deals with the modeling and simulation of the vibration behavior of piezoelectric micro‐cantilever (MC) based on the Timoshenko theory and using multi‐scale (MTS) method in the air environment.

^{[6]}The finite element formulation of dynamic equations of pipeline conveying fluid are presented based on Timoshenko theory by considering the fluid–structure interaction and the effect of shear deformation.

^{[7]}The Mori–Tanaka homogenisation method is used for the continuous variations of the material properties of the microsystem along the thickness; the Kelvin–Voigt scheme is employed for the internal damping; the shear deformation and rotary inertia are modelled for the viscoelastic microbeam via the Timoshenko theory; the modified couple stress theory is used for size influences.

^{[8]}Based on the Timoshenko beam theory, incorporating geometric imperfections, the Kelvin-Voigt method is used for internal viscosity, the rotary inertia is automatically generated due to the Timoshenko theory, and the Mari-Tanaka scheme is used for the mixture.

^{[9]}An exact dynamic stiffness matrix for a beam is developed by integrating the Rayleigh–Love theory for longitudinal vibration into the Timoshenko theory for bending vibration.

^{[10]}Based on the Timoshenko theory, governing equations of flexible beam are obtained by using the principle of virtual work with consideration of initial deviations and a von Kármán type of kinematic nonlinearity.

^{[11]}The shear/normal strain field components are formulated using the Timoshenko theory.

^{[12]}A novel theoretical model for a laminate cantilever beam consisting of numerous superelastic shape memory alloy (SMA) layers, based on the ZM model and Timoshenko theory is introduced.

^{[13]}It is shown that even for thin rings on elastic foundation, high order corrections, beyond the ones of the Timoshenko theory, need to be considered for an accurate estimation of the critical speeds of rotating rings.

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