Timoshenko beam theory

About: Timoshenko beam theory is a research topic. Over the lifetime, 9426 publications have been published within this topic receiving 200570 citations.

Refined Structural Model for Thin- and Thick-Walled Composite Rotor Blades

Abstract: A refined structural model based on a mixed force and displacement method is proposed for the analysis of composite rotor blades with elastic couplings. The present formulation allows the modeling of either open-section or closed-section blades of arbitrary section shape, stacking sequence, and end restraint effects. The theory accounts for the effect of elastic couplings, shell wall thickness, section warping, warping restraint, and transverse shear deformations. A semicomplementary energy functional is used to derive, in a variationally consistent manner, the beam force-displacement relations. Bending and torsion related warpings and shear correction factors are obtained in closed form as part of the analysis. The resulting first-order shear deformation theory (Timoshenko) describes the beam kinematics in terms of the axial, flap and lag bending, flap and lag shear, twist, and torsion-warping deformations. The theory is validated against experimental data and other finite element results for graphite-epoxy composite beams of various cross sections such as I sections, box sections, and two-cell airfoils. Good correlation is achieved for all of the test examples. The influence of wall thickness and transverse shear on the static beam response is also investigated. Wall thickness effects are shown to become significant when the thickness-to-depth ratio of the beam reaches around 20%. The slenderness ratio has a significant effect on the transverse shear behavior of the beam, especially for beams with low slenderness ratios. It is also shown that the layup angle has a nonnegligible effect on the transverse shear behavior of the beam.

Modeling and Characterization of a Piezoelectric Energy Harvester Under Combined Aerodynamic and Base Excitations

Abstract: This paper develops and validates an aero-electromechanical model which captures the nonlinear response behavior of a piezoelectric cantilever-type energy harvester under combined galloping and base excitations. The harvester consists of a thin piezoelectric cantilever beam clamped at one end and rigidly attached to a bluff body at the other end. In addition to the vibratory base excitations, the beam is also subjected to aerodynamic forces resulting from the separation of the incoming airflow on both sides of the bluff body which gives rise to limit-cycle oscillations when the airflow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitations is derived using the energy approach and by adopting the nonlinear Euler–Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The resulting partial differential equations of motion are discretized and a reduced-order model is obtained. The mathematical model is validated by conducting a series of experiments at different wind speeds and base excitation amplitudes for excitation frequencies around the primary resonance of the harvester. Results from the model and experiment are presented to characterize the response behavior under the combined loading.