Analytic and numeric analysis for deformation of non-prismatic beams resting on elastic foundations

Background The buckling load as well as the natural frequency under axial load for non-prismatic beam is a changeling problem. Determination of buckling load, natural frequency, and elastic deflection is very important in civil applications. The current paper used both perturbation method (PM), analytic method, and differential quadrature method (DQM), numerical method, to find buckling load and natural frequency with different end supports. The deflection of the beam resting on an elastic foundation under transverse distributed and axial loads is also obtained. Both PM and DQM are used for non-prismatic beams with rectangular and circular cross sections in the vibration analysis. The comparisons of results obtained from both PM and DQM showed perfect agreement with analytical solution for uniform beams with different end supports. The PM and DQM succeeded powerfully for investigating the buckling load as well as the natural frequency for non-prismatic beam. Results The percentage of relative error between DQM and PM doesn’t exceed than 5% if the gradient of rectangular section height and the gradient of circular section radius are less than 0.6. As the gradient of height and radius increase, the maximum deflection decreases and the location of maximum deflection displaced toward the smaller moment of inertia. Conclusions The PM has not been used for solving the problem of non-prismatic beams resting on elastic foundations subjected to transverse distributed and axial loads. The current research proved the good ability of PM as an analytical solution for a complicated problem and defined its range of accuracy as compared to DQM. Also, it introduced accurate empirical formulae to find both natural frequency and buckling load of non-prismatic beams. These empirical formulae represent a good achievement in vibration analysis of non-prismatic beams.

Vibration analysis of an axially functionally graded material non-prismatic beam under axial thermal variation in humid environment

The vibration analysis of an axially functionally graded material non-prismatic Timoshenko beam under axial thermal variation in humid environment is carried out using the harmonic differential quadrature method. In this modeling, the length and width of the beam remains constant whereas thickness of the beam is linearly varied along the axis of the beam. The material properties are temperature dependent and are assumed to be varied continuously along the axial direction according to power law distribution. Three types of temperature variations are considered in this study, that is, uniform temperature rise, linear temperature rise, and non-linear temperature rise. The temperature of the beam remains constant under uniform temperature rise condition and it is varied linearly and nonlinearly along the length of beam for rest of the conditions. The beam is subjected to uniform moisture concentration to impose humidity. Hamiltonian’s approach is used to derive the governing equations of motion. The resultant governing equations are then solved using the harmonic differential quadrature method to obtain the natural frequencies of the axially functionally graded material non-prismatic beam. The results obtained using the harmonic differential quadrature method are compared with results obtained for special cases. The effects of thermal variation, humidity, non-homogeneity parameter, and end conditions on natural frequencies of the non-prismatic beam are reported.

A Non-Prismatic Beam Element for the Optimization of Flexure Mechanisms

Flexure joints are rapidly gaining ground in precision engineering because of their predictable behavior. However the range of motion of flexure joints is limited due to loss of support stiffness in deformed configurations. Most of the common flexure joints consist of prismatic leaf springs. This paper presents a simple non-prismatic beam formulation that can be used for the efficient modelling of non-prismatic leaf springs. The resulting stiffness and stress computed by the non-prismatic beam element are compared to the results of a finite element analysis. The paper shows that the support stiffness of two typical flexure joints can be increased up to a factor of 1.9 by using non-prismatic instead of prismatic leaf springs.

Determination and monitoring of strength properties of aircraft composite structures by magnetic microwires

The submitted paper deals with the application of magnetic microwires as sensors. The aim is to summarize the engineering view of the given issue and to inform about necessary steps for practical application of such a new sensor in the aircraft industry. The paper talks about the formation of composite samples necessary for tensile strength tests, the aim of which is to obtain material properties of composite materials. The obtained material properties of fiberglass samples are processed into graphical and tabular form. Subsequently, the material properties are used in the strength calculations of the prismatic beam, in which magnetic microwires are applied in the experimental part of the work. There are described in the submitted article two application of magnetic microwires as a stress monitoring sensors.