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.

Delamination Prediction in Composite Beams with Built-In Piezoelectric Devices Using Modal Analysis and Neural Network

Abstract: The effect of prescribed delamination on natural frequencies of laminated composite beam specimens is examined both experimentally and theoretically. Delamination is of particular interest because it can cause catastrophic failure of the composite structure. One consequence of delamination in a composite structure is a change in its stiffness. This change in stiffness will degrade the modal frequencies of the composite structure. Modal testing of a perfect beam and beams with different delamination size is conducted using polyvinylidene fluoride film (PVDF) sensors and piezoceramic (PZT) patch with sine sweep actuation. Modal testing of beams is also conducted using PVDF sensors and instrumented hammer excitation. The results of piezoceramic patch excitation and instrumented hammer excitation are discussed. The experimental modal frequencies are compared with the results obtained using a simplified beam theory. Also, backpropagation neural network models are developed using the results from the beam theory and used to predict delamination size. The effect of learning rate and momentum rate on neural network performance are discussed. Modal frequencies can be easily and accurately obtained with PZT patch excitation and PVDF sensing. There is good agreement between modal frequencies from modal testing and those from the simplified beam theory. The neural network models developed successfully predict delamination size.

Thermo-electro-mechanical characteristics of functionally graded piezoelectric actuators

Abstract: This paper investigates the static bending, free vibration, and dynamic response of monomorph, bimorph, and multimorph actuators made of functionally graded piezoelectric materials (FGPMs) under a combined thermal-electro-mechanical load by using the Timoshenko beam theory. It is assumed that all of the material properties of the actuator, except for Poisson's ratio, are position dependent due to a continuous variation in material composition through the thickness direction. Theoretical formulations are derived by employing Hamilton's principle and include the effect of transverse shear deformation and axial and rotary inertias. The governing differential equations are then solved using the differential quadrature method to determine the important performance indices, such as deflection, reaction force, natural frequencies, and dynamic response of various FGPM actuators. A comprehensive parametric study is conducted to show the influence of shear deformation, temperature rise, material composition, slenderness ratio, end support, and total number of layers on the thermo-electro-mechanical characteristics. It is found that FGPM monomorph actuators exhibit the so-called 'non-intermediate' behavior under an applied electric field.

A Nonlocal Higher-Order Shear Deformation Beam Theory for Vibration Analysis of Size-Dependent Functionally Graded Nanobeams

Abstract: In this paper, free vibration characteristics of functionally graded (FG) nanobeams based on third-order shear deformation beam theory are investigated by presenting a Navier-type solution. Material properties of FG nanobeam are supposed to change continuously along the thickness according to the power-law form. The effect of small scale is considered based on nonlocal elasticity theory of Eringen. Through Hamilton’s principle and third-order shear deformation beam theory, the nonlocal governing equations are derived and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results for FG nanobeams as compared to some cases in the literature. The numerical investigations are presented to investigate the effect of the several parameters such as material distribution profile, small-scale effects, slenderness ratio and mode number on vibrational response of the FG nanobeams in detail. It is concluded that various factors such as nonlocal parameter and gradient index play notable roles in vibrational response of FG nanobeams.