IMPROVED ANALYSIS OF A PROPPED CANTILEVER UNDER LATERAL VIBRATION

Continuous systems are sometimes analysed as lumped masses connected by massless elements. This reduces the structure’s degree of freedom and therefore simplifies the analysis. However this over simplification introduces an error in the analysis and the results are therefore approximate. In this work sections of the vibrating beam were isolated and the equations of the forces causing vibration obtained using the Hamilton’s principle. These forces were applied to the nodes of an equivalent lumped mass beam and the stiffness modification needed for it to behave as a continuous beam obtained. The beam’s stiffness was modified using a set of stiffness modification factors to . It was observed that by applying these factors in the dynamic analysis of the beam using the Lagrange’s equation, we obtain the exact values of the fundamental frequency irrespective of the way the mass of the beam was lumped. From this work we observed that in order to obtain an accurate dynamic response from a lumped mass beam there is need to modify the stiffness composition of the system and no linear modification of the stiffness distribution of lumped mass beams can cause them to be dynamically equivalent to the continuous beams. This is so because the values of the modification factors obtained for each beam segment were not equal. The stiffness modification factors were obtained for elements at different sections of the beam

Eliminating the Influence of Axle Parameters in Influence Line Identification

Accurate and rapid acquisition of the strain influence line of continuous beam plays a positive role in promoting the wide application of structural health monitoring. The structural response obtained from the sensors is used to estimate the strain influence line. However, most estimation methods ignore the influence of axle parameters on the structural response, resulting in a large error in identifying the strain influence line. This paper presents a method for eliminating the influence of axle parameters of moving vehicles on strain responses to estimate the strain influence line of continuous beams based on the long-gauge strain sensing technology. By analysing the mechanical characteristics of the multi-span continuous beam, a theoretical strain influence line expression is first established to obtain the strain influence line of the continuous beam accurately. The structural response only caused by axle weight, obtained by eliminating the influence of axle parameters, is then estimated for calibrating the theoretical strain influence line. Finally, different lane tests are also considered to solve the influence of different transverse position relations on the proposed method between the monitoring unit and the lane. Finally, numerical simulations are adopted to illustrate the effectiveness of the proposed identification method by simulating the strain time histories induced by a multi-axle vehicle. A field test also demonstrates the validity and feasibility of this method.

Compact line source generator for feeding continuous transverse stub arrays

Based on a substrate integrated lens (SIL), a compact line source generator (LSG) for feeding continuous transverse stub (CTS) arrays with linear-polarized (LP) beam scanning and dual-polarized (DP) operations is presented in this paper. The SIL consists of metamaterial cells with different sizes being arranged as concentric annulus and is printed on the center surface of two substrate layers. The SIL can convert the cylindrical wave generated by the feed probe of SIW-horn to the planar wave for feeding the CTS array. This rotationally symmetric SIL can be used conveniently to design LSG for feeding CTS arrays with the continuous beam scanning and DP operations, which has been verified by the fabrications and measurements. By simply rotating the SIW-horn along the edge of SIL, the 10-element LP-CTS array obtains a measured beam scanning range of ±35° with the highest gain of 20.6 dBi. By setting two orthogonal SIW-horns at the edge of the proposed SIL, the nine-element DP-CTS array with orthogonal radiation stubs is excited. The DP array obtains the gain of 20.3 dBi at the center frequency with the isolation of 28 dB and the cross-polarization level <−25 dB.

Dimensionless wave numbers evolution of a three spans simply supported beam when the intermediate supports are moving along the whole beam

Continuous beams simply supported with several intermediate supports are very common in engineering achievements everywhere. The paper shows the evolution of the dimensionless wave number in 3D format, respectively of the eigenfrequencies for a continuous beam with three openings when the intermediate supports take any position inside the beam. The frequency equation for calculating the dimensionless wave number is presented and the modal function is given with an example for the case where the eigenfrequency has the maximum value at fist vibration mode.