Analysis of Nonlinear Cyclically Symmetric Isolation Sistem of a Cargo in a Container under Plane Harmonic Vibrations

The problem of calculating the system of a cylindrical shaped load transverse damping installed in a coaxial container is considered. This system has several annular belts of insulation with a cyclically symmetric arrangement of shock absorbers along the circumferential direction. A simple dynamic model of one insulation belt formed by polyurethane tunnel-type shock absorbers is investigated. Such shock absorbers have a high energy absorption coefficient and can operate at very high drafts comparable to their height, which is important when the space between the cargo and the container wall is limited. Within the proposed model framework, a harmonic nonlinear analysis of cargo plane oscillations under kinematic excitation coming from the container is considered. A method for reducing a nonlinear cyclically symmetric system with discrete elastic elements, which allows limiting the analysis to the calculation of a vibration isolation system with one degree of freedom, is proposed. Using the harmonic linearization procedure, the amplitude-frequency characteristics of oscillations and plots of vibration isolation coefficients of cargo at different values of excitation amplitude have been obtained. The results are verified by comparing the analytical solution with the results of numerical integration for a non-reduced nonlinear system with two degrees of freedom. The obtained solution allows choosing the vibration isolation belt parameters, in particular the number of shock absorbers and their stiffness, depending on the conditions of kinematic excitation and permissible overload

The method of kinematic excitation reconstruction based on measured suspension dynamic responses – experimental verification

The paper presents the method of kinematic road excitation reconstruction based on measured suspension dynamic responses and its reconstruction with use of estimated displacements of unsprung mass as a preliminary approximation of kinematic excitation and tracking control system with a PID controller that allows for faithful reconstruction of unsprung mass accelerations and, in turn, kinematic excitations. The authors performed an experimental verification of the method with use of one axle car trailer and measurements of road profile and acquiring signals of suspension dynamics responses. The signal processing methodology and obtained results are presented for random and determined excitations. The necessary requirements to use the method effectively were defined and its limitations were listed.

Vehicle Response to Kinematic Excitation, Numerical Simulation Versus Experiment

The article is devoted to the numerical simulation and experimental verification of a vehicle’s response to kinematic excitation caused by driving along an asphalt road. The source of kinematic excitation was road unevenness, which was mapped by geodetic methods. Vertical unevenness was measured in 0.25 m increments in two longitudinal profiles of the road spaced two meters apart with precise leveling realized by geodetic digital levels. A space multi-body computational model of a Tatra 815 heavy truck was adopted. The model had 15 degrees of freedom. Nine degrees of freedom were tangible and six degrees of freedom were intangible. The equations of motion were derived in the form of second-order ordinary differential equations and were solved numerically by the Runge–Kutta method. A custom computer program in MATLAB was created for numerical simulation of vehicle movement (eps = 2−52). The program allowed simulation of quantities such as deflections, speeds, accelerations at characteristic points of the vehicle, and static or dynamic components of contact forces arising between the wheel and the road. The response of the vehicle (acceleration at characteristic points) at different speeds was experimentally tested. The experiment was numerically simulated and the results were mutually compared. The basic statistical characteristics of experimentally obtained and numerically simulated signals and their power spectral densities were compared.

REDUCTION VIBRATIONS OF THE PILE FOUNDATIONS FOR MACHINES UNDER DYNAMIC LOADS BY HIGH-PRESSURE GROUP INJECTION METHOD

The vibration parameters of the foundations under dynamic loads or kinematic excitation directly depend on the stiffness and damping parameters of the base, the mass of the oscillating system consisting foundation, the machine and the «attached mass of soil». In the process of using pile foundations static load is transferred to the piles, the contact of the grillage with the ground is broken, and micro-gaps are formed. Micro-gaps impede the joint work of the soil mass of the inter-pile space with the foundation. An effective way to reduce the vibration parameters of foundations is the method of high-pressure group injection. The essence of the method lies in injection of a mobile cement-sand mortar into the soil base under the sole of the grillage under pressure exceeding the structural strength of the soil simultaneously through several injectors. The injection mixture eliminates micro-gaps and hardens the soil, which leads to an increase in the rigidity of the base and the involvement of an additional volume of soil mass in joint work with the foundation. The inclusion of inter-pile soil in joint work significantly increases the mass of the oscillating system and, as a result, reduces the parameters of horizontal and vertical vibrations of the pile foundation under dynamic loading and in the case of kinematic excitation. Injectors are immersed under the sole of the grillage through specially provided openings - injection conductors. The discharge points are usually located between piles and around the perimeter of the grillage. The parameters of the injection work (the number of injection points and their placement in the plan, the height of the injection horizons, the required volume of injected solution, the injection sequence, etc.) are assigned depending on the construction of the pile foundation, the engineering and geological conditions of the site, the dynamic operating mode of the equipment, and others factors. Strengthening pile foundations for machines under dynamic loads or vibration-sensitive equipment by high-pressure group injection can significantly reduce the amplitude of horizontal and vertical vibrations of foundations.

Impact of High Energy Mining-Induced Seismic Shocks from Different Mining Activity Regions on a Multiple-Support Road Viaduct

In this paper, the dynamic responses of a large-scale multiple-support road viaduct to mining-induced seismic events registered in two regions of mining activity were compared. The regions differ in geological structure, which results in discrepancies in the dominant frequency content. Spatial variation of ground motion causing the kinematic excitation non-uniformity was accounted for in the dynamic analyses of this large-scale structure. Non-uniform mining-induced kinematic excitation models were proposed, with respect to the specificity of mining origin quakes. The dynamic performance of the viaduct was determined using three different methods of calculation: the time history analysis, the response spectrum analysis, and the multiple support response spectrum analysis. Both the uniform and non-uniform kinematic excitation models were adopted for the dynamic performance assessment. The research revealed that the dynamic response of some members of the structure, determined using the non-uniform excitation model, was significantly greater than that obtained for the uniform one. Hence, in the dynamic analysis of multiple-support structures under mining-induced events, the effect of spatial variation of ground motion should be considered. The study pointed out that the commonly used response spectrum analysis may lead to the underestimation of the dynamic response of large-scale multiple-support structures. Instead, the multiple support response spectrum method, which takes into account the non-uniformity of ground motion, is recommended as a conservative approximation. This method provides a safe upper estimation of the full-dynamic analysis results of large-scale structures under mining-induced tremors. Finally, the research indicated that the dynamic performance of a structure strongly depends on the frequency range attributed to a specific mining region. The dynamic performance of identical engineering structures under tremors of similar maximal amplitudes may differ significantly due to discrepancies in frequency contents of shocks occurring in various mining regions.

Comparison of Results Obtained by Two Methods of Surface Mapping

Considering that the unevenness of the road surface is the primary source of the kinematic excitation of the vehicle, it is necessary to map the unevenness, and then to describe it mathematically. The data sets thus obtained represent an important input for numerical simulations of the motion of vehicles on the road. This paper deals with the analysis and comparison of results from two methods of mapping the surface of the road - exact levelling and spatial scanning. The obtained results are evaluated qualitatively and quantitatively by methods of mathematical statistics and probability theory.

Seismic Assessment of Footbridges under Spatial Variation of Earthquake Ground Motion (SVEGM): Experimental Testing and Finite Element Analyses

In this paper, the seismic assessments of two footbridges, i.e., a single-span steel frame footbridge and a three-span cable-stayed structure, to the spatial variation of earthquake ground motion (SVEGM) are presented. A model of nonuniform kinematic excitation was used for the dynamic analyses of the footbridges. The influence of SVEGM on the dynamic performance of structures was assessed on both experimental and numerical ways. The comprehensive tests were planned and carried out on both structures. The investigation was divided into two parts: in situ experiment and numerical analyses. The first experimental part served for the validation of both the finite element (FE) modal models of structures and the theoretical model of nonuniform excitation as well as the appropriateness of the FE procedures used for dynamic analyses. First, the modal properties were validated. The differences between the numerical and the experimental natural frequencies, obtained using the operational modal analysis, were less than 10%. The comparison of the experimental and numerical mode shapes also proved a good agreement since the modal assurance criterion values were satisfactory for both structures. Secondly, nonuniform kinematic excitation was experimentally imposed using vibroseis tests. The apparent wave velocities, evaluated from the cross-correlation functions of the acceleration-time histories registered at two consecutive structures supports, equaled 203 and 214 m/s for both structures, respectively. Also, the coherence functions proved the similarity of the signals, especially for the frequency range 5 to 15 Hz. Then, artificial kinematic excitation was generated on the basis of the adopted model of nonuniform excitation. The obtained power spectral density functions of acceleration-time histories registered at all supports as well as the cross-spectral density functions between registered and artificial acceleration-time histories confirmed the strong similarity of the measured and artificial signals. Finally, the experimental and numerical assessments of the footbridges performance under the known dynamic excitation generated by the vibroseis were carried out. The FE models and procedures were positively validated by linking full-scale tests and numerical calculations. In the numerical part of the research, seismic analyses of the footbridges were conducted. The dynamic responses of structures to a representative seismic shock were calculated. Both the uniform and nonuniform models of excitation were applied to demonstrate and quantify the influence of SVEGM on the seismic assessment of footbridges. It occurred that SVEGM may generate non-conservative results in comparison with classic uniform seismic excitation. For the stiff steel frame footbridge the maximum dynamic response was obtained for the model of nonuniform excitation with the lowest wave velocity. Especially zones located closely to stiff frame nodes were significantly more disturbed. For the flexible cable-stayed footbridge, in case of nonuniform excitation, the dynamic response was enhanced only at the points located in the extreme spans and in the midspan closely to the pillars.

Statistical characteristics of sources of vehicle kinematic excitation

The longitudinal and transverse road profiles represent the functions of a random variable from a mathematical point of view. It is appropriate to use methods of probability theory and mathematical statistics for their description. The unevenness of the runway surface is the main source of the vehicle's kinematic excitation. This paper describes the statistical properties of the mapped road profiles. It shows a way of categorizing road surface quality based on the power spectral density of unevenness. The interrelationships between the individual points of the profile and the profiles with one another are evaluated by correlation functions.