Stiffness and Strength of Multilayer Beams

Abstract

This article describes an original method for calculating stiffness and strength of multilayer beams (MBs) when the beam is deformed within elasticity limits. It draws on previous studies by the same author, but for the first time fully describes the proposed method, both the theory and its practical application. This method is very useful for engineering calculations and scientific research. The equations obtained allow establishing the positions of neutral layers and of the geometric and stiffness centers when the cross section of the beam is not symmetric to both x- and y-axes. This study also presents the equations for establishing the stiffness for bending and shear, and for calculating normal and shear stresses at any point of the beam’s cross section. The efficiency and practical application of this new method are demonstrated by analyzing how MB stiffness and strength change depending on the influence of certain factors, such as mechanical properties of layers, number of layers, and their arrangement and dimensions.

Planar Timoshenko-like model for multilayer non-prismatic beams

“…Then, the same relations as described in Auricchio et al (2015) and Balduzzi et al (2016) are obtained. Considering a multilayer prismatic beam, both standard and advanced literature states that the horizontal stress has a discontinuous distribution within the cross-section, in case of different mechanical properties between the layers, whereas the shear stress has a continuous distribution (Bareisis 2006;Auricchio et al 2010;Bardella and Tonelli 2012). In contrary, the interlayer equilibrium (12) indicates a discontinuous crosssection distribution of axial as well as shear stresses.…”

“…It is worth mentioning that the so far introduced definition of shear stress distribution corresponds to the one provided by Bareisis (2006). In order to define the shear-stress…”

Lower Bounds on the Frequency Estimation Error in Magnetically Coupled MEMS Resonant Sensors

“…4. The inductance matrix relates the voltages and currents in the two coils (3) Using upper case letters to denote the Laplace transform of a variable, the Laplace transform of , assuming initial conditions for the currents are set to zero, is given by (4) Noting the positive sense for the resonator current, the impedance of the RC leg of the resonator gives the expression (5) Eliminating from (4) and (5) yields the transfer function from the Tx/Rx coil current to the MEMS coil current (6) Define the damping ratio and the undamped natural frequency by (7) The well-known quality factor is…”

“…Beyond the damping associated with intrinsic material properties, there is damping related to the coupling of the vibration to the device package and mounting, as well as air or gas damping for devices that are not vacuum sealed. In the case of multilayer beams, an equivalent torsional stiffness must be used (see [4] for related modeling methods). The transfer function (17) can then be written (20) Note, in contrast to (10), the numerator does not include a factor of .…”

Investigation of the flexural stiffness of asymmetric multilayer beams

“…The works [1-6] are devoted to the investigation of multilayer structural elements, mainly with one or two axes of symmetry. The influence of various factors on the regularities of the behavior of strength and stiffness in symmetric multilayer rods and beams is studied in [7,8]. In all cases, it is necessary to determine the location of the neutral layer.…”