A hybrid algorithm for solving inverse boundary problems with respect to intermediate masses on a beam

The inverse problem of determining the weight of three intermediate masses on a uniform beam from the known three natural frequencies has been solved. The performed numerical analysis allows restoring the value of only the second mass in a unique way. The inverse problem of determining the weight of three intermediate masses is solved uniquely except in the case when the first and the third masses are located geometrically symmetric relative to the middle of the beam. The hybrid algorithm for the unique solving inverse problem of determining the weight of three intermediate masses has been developed. The first three natural frequencies of the beam are calculated numerically by using the Maple computer package. Analytical relations between the masses are found.

Vehicle-Bridge Interaction System with Non-Uniform Beams

Since the bridge is often treated as the uniform beam for simplicity in most numerical studies of vehicle-bridge interaction, this study proposes a non-uniform vehicle-bridge interaction system by incorporating a three-mass vehicle model in a non-uniform bridge for wider applications, in which non-uniform beam elements of constant width and varying depth are considered. For clarity, the inclined ratios of the entire bridge and one beam element are separately defined in order to describe the non-conformity in computation while both mass and stiffness matrices are re-formulated to comply with the finite element sign convention. As the natural frequencies of a non-uniform bridge cannot be accessed directly, the vehicle scanning method is first adopted to obtain the bridge frequencies. Then, the parametric study is conducted by considering vehicle damping, bridge damping, and pavement irregularity. In addition to the vehicle frequency, the numerical results show that the proposed vehicle-bridge interaction system is able to scan the first four bridge frequencies with desired accuracy subject to pavement irregularity. Concerning the pitching effect of the vehicle, it is shown that the locations for installing sensors are actually affected by both the geometry and the cross-sectional geometry of the bridge in the concern of achieving high resolution of frequency identification.

Free vibration analysis of a rotating double tapered beam with flexible root via differential quadrature method

Purpose This study aims to develop the governing differential equation and to analyze the free vibration of a rotating non-uniform beam having a flexible root and setting angle for variations in operating conditions and structural design parameters. Design/methodology/approach Hamiltonian principle is used to derive the flapwise bending motion of the structure, and the governing differential equations are solved numerically by using differential quadrature with satisfactory accuracy and computation time. Findings The results obtained by using the differential quadrature method (DQM) are compared to results of previous studies in the open literature to show the power of the used method. Important results affecting the dynamics characteristics of a rotating beam are tabulated and illustrated in concerned figures to show the effect of investigated design parameters and operating conditions. Originality/value The principal novelty of this paper arises from the application of the DQM to a rotating non-uniform beam with flexible root and deriving new governing differential equation including various parameters such as rotary inertia, setting angle, taper ratios, root flexibility, hub radius and rotational speed. Also, the application of the used numerical method is expressed clearly step by step with the algorithm scheme.

Basic morphometric parameters of antlers in Roe deer (Capreolus capreolus L.) from imperial hunts in the Białowieża Primeval Forest

Roe deer (Capreolus capreolus L.) is adaptable to various habitat conditions and is widespread across Europe. The Białowieża Primeval Forest is an area in the moderate zone of lowland Europe and it is habitat for different game species. For the purposes of this study, the morphometric parameters of roe deer antlers shot in the Białowieża Primeval Forest by the Russian Czar Nicholas II during his reign (1894-1917) were analysed. Length of left and right beams, circumference of the left and right coronets, circumference of the left and right, length of the first and second tine end of the left and right beams, and inside span were measured and analysed. The results showed that during the imperial roe deer hunts in the period 1894 to 1917 in Białowieża Primeval Forest, individuals of similar morphometric trophy characteristics were hunted. The trophies were, on average, characterized by a slightly longer left beam, uniform beam circumference, coronet circumference, and very similar tine ends lengths.