Natural Vibration Modes Research Articles

Exploring seismic resilience in frame structures through advanced numerical modeling and dynamic nonlinear analysis of recycled aggregate concrete

This study developed an advanced three-dimensional spatial model to examine the behavior of Recycled Aggregate Concrete (RAC) frame structures using sophisticated nonlinear beam-column fiber elements. It thoroughly investigates the dynamic properties such as natural frequency, vibration modes, and stiffness of RAC structures and conducts a detailed nonlinear dynamic analysis focusing on acceleration, displacement, drift, and hysteresis curves. The seismic resilience of RAC structures, especially inter-story drift under various seismic intensities, was evaluated and compared with Natural Aggregate Concrete (NAC) structures by adjusting the concrete material model parameters in the finite element framework. The accuracy of the numerical model was validated against shaking table tests, showing that RAC and NAC structures comply with structural damage criteria across seismic phases from 0.066 g to 1.170 g. The findings suggest RAC structures are as seismically resilient as NAC ones, making them suitable for earthquake-prone areas.

Natural frequencies and modes of parametric vibrations of reservoir shell with shape imperfections

Development of software on the basis of the finite element method led to intensive creation of the numeral methods for the decision of static and dynamic problems of the thin shells. The finite element model of the thin shell has an infinite number of freedom degrees and natural frequencies, so solving the dynamics problem of the shell is difficult. If behavior of natural vibrations of the shell was researched, it is possible to talk about shell internal properties which take a great place at the forced vibrations including parametric one. It is important to take into account influence of the constant component of parametric load on natural frequencies and modes of the shell. Nowadays forming of an effective model of parametric vibrations of the shell with shape imperfections and choice of the most dangerous imperfections model remain relevant. Influence of real and modelled imperfections on natural frequencies and modes of reservoir shell parametric vibrations excited by axial load and on shell stability loss was investigated in this article. The finite element models of the shell was formed by software NASTRAN. The modelled shape imperfections as a lower buckling form of perfect shell under static pressure were presented. The real imperfections as the deviations of the shell wall from the vertical were obtained by theodolite surveying. The natural frequencies and modes of the imperfect shell taking into account the its previous stress state from action of the constant component of the parametric load were received by the Lanczos method. Investigations showed that the real imperfections of shell a little influenced on natural frequencies and modes of parametric vibrations. These decreased the critical loads on the first natural frequency on 0,58 % and increased on the second natural frequency shells on 0,79 %, but qualitatively changed the form of stability loss on these frequencies. Modelled imperfections had a greater but not considerable influence on natural frequencies and modes of the shell. But the modelled imperfections of the shell under constant component of parametric load considerably increased the critical load on the first and second natural frequency accordingly on 12,3 % and 5,26 % and changed the shell forms of stability loss. So the modelled imperfections of the shell in the form of the regular circular half-waves increased shell carrying capacity, but not decreased. This positive effect takes place at constructing of cylinder shells from the corrugated rolled sheets.

Changein the stress-strain state of elements of the «base – foundations – load-bearing structures» system dueto a possible progressive collapse

The calculation of a building for stability against progressive collapse using the LIRA SAPR-2019 software is considered. Two calculation approaches are compared: using a quasi-static formulation and direct integration of dynamic influences overtime. The first approach to calculating the local failure of an element used the force application principle defined for this element under normal operating conditions, but with the opposite sign (dynamism coefficient Kd=2, “pulldown” loading). These cond calculation approachis characterized by the dependence of the system response on the loading rate and the rate of removalof structures. To take into account damping, Rayleigh coefficients were determined by natural frequencies for two dominant modes of natural vibrations (No. 7, 10) based on the modal analysis of the system.The local failure time of the element was assigned as 0.1T (oscillation period) for natural vibration mode No.7, as the closest to the expected response of the system to the removal of the pylon. According to the calculation results, in the quasi-static formulation, a qualitative changein forces was recorded, where in stead of compression, tension appeared in the chain of pylons, which are located above the remote one, and in the dynamic formulation, a decrease of 70...90% in the magnitude of longitudinal forces in the pylons was recorded, that is, work was recorded on the principle of a hanging scheme. An increase in the load on the piles under the vertical load-bearing structures around the removed element is predicted under the scenario of a local failure of the structure; depending on the calculation method, the expected increase in the load on adjacent piles is 15...25%. Based on the results of the study, in order to increase the survivability and ensure the protection of building structures from progressive collapse, a decision was made to increase the reinforcement area by 30...35% for pylons in the entrance area to a dual-use structure, as well as in the radius of influence of a remote element, in order to absorb increasing forces by these elements when redistributing loads when removing an adjacent building element and assessing the load-bearing capacity of the remaining elements. It has been established that in this case, progressive collapse does not occur for this building.

Modal and vibration response characteristics of rotating support platform

In order to improve the strength and stability of the rotating support platform, modal and stress characteristics were simulated and calculated based on finite element analysis method. In Hypemesh, the model of the rotating support platform was established. In Abaqus, boundary conditions and loads were defined, and the natural frequencies and vibration modes of the first four orders were obtained. Based on the structure and stress characteristics of the crossbeam, different damping technologies were compared and analyzed, and rubber damping scheme was selected and designed. Through time mileage analysis, the load response and damping effect of damping scheme were verified. The results show that the rubber damping scheme can reduce the maximum stress by more than 15 % without changing the natural frequency substantially.

Stiffness identification of reinforced concrete beams using rotation rate sensors

Monitoring flexural stiffness variations of cracked reinforced concrete (r/c) structures is one of the most challenging problems of the dynamics of these structures. In this article, the application of rotation rate sensors for structural health monitoring of reinforced concrete beams is proposed as an alternative SHM method to, e.g. those utilising more expensive and laborious fiber optics. This subject was investigated with progressively damaged 6 m long reinforced concrete beams. During each damage state, the cracks were located and described in detail. Experimental modal analyses were carried out. Translational and rotational vibration modes were acquired using translational accelerometers and rotation rate sensors. The stiffness distributions of the damaged reinforced concrete beams were identified from the modal properties using model-updating techniques. It is demonstrated that stiffness distributions calculated using rotational modes are more accurate than those obtained from the familiar translational natural modes of vibrations. Further improvement of stiffness identification of r/c beams from their vibrations was obtained by combining the directly measured rotational modes and their approximations from translational modes by the central difference method.

ОСОБЕННОСТИ РАСЧЕТА ДИНАМИЧЕСКИХ ПАРАМЕТРОВ СТЕНДА ПРИ ИСПЫТАНИЯХ РЕДУКТОРА МОТОР-КОЛЕСА КАРЬЕРНЫХ САМОСВАЛОВ БЕЛАЗ

When conducting accelerated tests of transmissions and reducers of mobile machines, it is required to study the dynamic properties of the bench together with the test object installed on it. This is necessary to identify possible resonances in the oscillatory system and to select appropriate test modes, which exclude the occurrence of unacceptable levels of loads that violate the correspondence between the type and nature of damage in operation and during testing. The paper proposes a methodical approach to the calculational determination of the dynamic parameters (natural frequencies and natural modes of torsional vibrations) of the bench with a mechanically open loop during accelerated life tests of the two-row planetary motor-wheel reducers of BELAZ mining dump trucks, based on the study of the developed multi-mass dynamic model with lumped parameters. The calculation features consist in taking into account the existence of symmetry plane of the bench mechanical system with two reducers installed on it, as well as the presence of symmetrical branches in the planetary rows, formed by the masses of satellites rotating around their axes and elastic constraints connecting them with the sun and crown gears. The approach proposed makes it possible to significantly simplify calculations and to reduce the computation time.

Structures incorporating damping devices: Are we correct in our design thinking?

The use of discrete damping devices in New Zealand buildings is increasing as designers seek to limit damage to both architectural and structural building elements in moderate earthquakes. The overall damping of the structure becomes a combination of inherent material damping, hysteretic damping from yielding of building elements at specific locations and damping from discrete devices. For over 60 years, engineers have used simplified analysis procedures (e.g., modal response spectrum analysis) to predict building response under seismic actions. The design of structures incorporating viscous dampers requires a paradigm shift in approach as the force each damper resists is a function of the relative velocity between its ends. Popular pseudo-static design methodologies promote the use of a viscous strut in the analysis model to represent them. However, it is incorrect to use elastic, mode-based analysis for a structure incorporating damping devices and relying on significant inelastic behaviour. This paper elucidates the complex mechanics of damper-structure interaction by reviewing some of the established classical, modal‑based, simplified analysis techniques used in seismic design. A series of numerical investigations demonstrate how these techniques are usually invalid for structures that incorporate viscous dampers because they violate the laws of physics. The reason why mode-based techniques are invalid is explored with reference to the imaginary components of the natural modes of vibration and the effect on them of significant inelasticity within the structure. The dynamic characteristics of viscous dampers challenge conventional design approaches such as displacement-based design. This paper establishes that nonlinear time-history analysis is the only meaningful way of predicting the dynamic response of a structure incorporating viscous dampers when significant inelastic behaviour of the structure is expected.

Evaluation of the Natural Vibration Modes and Structural Strength of WTIV Legs based on Seabed Penetration Depth

Evaluation of the Natural Vibration Modes and Structural Strength of WTIV Legs based on Seabed Penetration Depth

Enhancement of Contact Acoustic Nonlinearity Effect in a Concrete Beam Using Ambient Vibrations

Abstract Contact acoustic nonlinearity (CAN) is generated when oscillating crack faces open and close while a wave passes through it. However, reliably assessing the nonlinear effect due to micro-scale defects is challenging, especially in concrete structures, due to their large size, high attenuation, and low signal-to-noise ratio. However, concrete facilities vibrate due to ambient excitations such as vehicle movement, wind, and water flow. These ambient vibrations can be utilized in amplifying CAN. For example, a vehicle can be moved at a particular velocity over a bridge to amplify a particular natural mode of vibration. This paper illustrates a method of enhancing contact acoustic nonlinearity with the help of ambient vibrations of the structure. A finite element model of a concrete beam with a thin crack is developed. The base of the beam was oscillated at 100 Hz. Meanwhile, a 200 kHz ultrasonic excitation was applied on the beam to monitor its propagation through the crack. The closing and opening of the crack generate the nonlinear behavior of the ultrasonic pulse. A considerable increment of nonlinearity was observed demonstrating the efficacy of the proposed method. The time windows for the nonlinear zone have been identified. A laboratory experiment has been performed to demonstrate the proposed method in reinforced concrete beams. This investigation demonstrates that CAN can be utilized in monitoring concrete structures when ambient vibrations are taken into account.

Free vibration of rotating bifunctional gradient CNTs-reinforced ceramic matrix composites pre-twisted blade in thermal environment

Considering the thermal environment’s effect, we built a dynamics model of rotating pre-twisted ceramic matrix composites blades with elastic boundary constraints based on shell and first-order shear deformation theories. The model considers the effect of temperature and simplifies the blade to a twisted cylindrical plate. Based on the Lagrange equation, the differential equation of the vibration of a rotating pre-twisted blade of CNTs-reinforced ceramic matrix composites in the thermal environment was derived by using the orthogonal polynomial as the acceptable function. The natural frequencies and vibration modes of a rotating pre-twisted blade take into account the effects of Coriolis and centrifugal forces. The accuracy of the model is verified by comparing with the literature and Ansys results. The effects of temperature, the volume fraction of functional gradient, pre-twisted angle, and rotational speed on the model were studied in detail. The results show that the addition of carbon nanotubes can greatly enhance the ceramic-based blade. And both temperature and pre-twisted angle significantly affect the carbon nanotube enhanced functional gradient blades.

Symmetric and asymmetric free vibrations of rotating eccentric annular plate

The symmetric and asymmetric free vibrations of rotating eccentric annular plate in uniform thermal environment are studied in present paper. The priority of research is clarifying the different combined effects of various factors on symmetric and asymmetric vibrations of eccentric annular plate. In order to conveniently obtain the natural frequency and vibration mode of eccentric annular plate with irregular physical domain, the transformed differential quadrature method is employed. Due to the rotational motion, the initial configuration caused by centrifugal force is calculated before vibration analyses. Then the traveling wave vibration arisen from the Coriolis force is investigated. By comparing the vibration characteristics of annular plate with/without eccentricity, the different impacts of interaction between the geometrical size, boundary conditions, temperature rise, rotational motion, and eccentricity on symmetric and asymmetric vibrations are discussed. Results show that eccentricity leads to the splitting phenomena only in asymmetric vibrations. And it does not affect the symmetry of vibration. Temperature rise results in that the fundamental vibration mode shape shifts from symmetric to asymmetric. However, eccentricity inhibits the change. Rotational motion causes the occurrence of traveling wave vibration in asymmetric vibration whereas not in symmetric vibration.

Dynamic characteristics of segmental assembled HH120 wind turbine tower

The analysis of dynamic characteristics is crucial in the design of wind tower structures. The dynamic behavior of wind towers is primarily influenced by structural stiffness and mass distribution. In particular, the segment thickness of prefabricated concrete towers should be selected and optimized based on computed results of stress distribution in order to achieve the desired dynamic performance. The main objective of this research is to investigate the effects of design factors, such as segmental thickness and top mass of wind blades, hub, and nacelle, on the natural frequencies and vibration modes of the precast concrete towers. For the finite element analysis, a high-rise wind turbine tower with a hub height of 120 m (HH120 tower) is utilized. Finally, the theoretical model for the reduced degrees of freedom system is validated using the results from the finite element analysis.

The modal analysis of laminated composite cylinders under axial tension loading in ANSYS

Natural frequencies and vibration modes of laminated composite cylinders were calculated under axial tension loading by the finite element method using ANSYS Mechanical software package. Two types of axial tensile load were modelled: a suspended weight and a static axial load in the zone of weight attachment into the cylinder. The features of the modal analysis of a prestressed system depending on the type of applied tensile load were analyzed. The numerical results obtained were compared and the possible reasons for their discrepancy were explained.

Assessment of the structural integrity of glulam using modal analysis and finite element updating

The increasing adoption of glued laminated timber (Glulam) as an environmentally conscious material in construction has been driven by its excellent structural properties and lower carbon footprint compared to other conventional materials. However, its organic nature underscores the need to ensure the long-term integrity of these glulam structures. This paper proposes a novel approach to non-destructive testing (NDT) through the combined application of modal analysis and updated finite element modelling. These advanced techniques allow a more accurate and detailed assessment of the structural condition of glulam. Modal analysis identifies changes in natural frequencies and vibration modes caused by potential material degradation, providing valuable structural health information without compromising the integrity of the material. To achieve this objective, the paper proposes to compare the real values measured in the modal analysis with those obtained from the numerical model by formulating an objective function that measures the error between the two. The differences between the two models are reduced using techniques based on Particle Swarm Optimization (PSO). The work presents a specific formulation aimed at achieving greater efficiency in the search for defects in this material. The results of the proposed method are verified by laboratory tests. For this purpose, glulam samples with different defects were tested and their identification was verified by updating the finite element models, demonstrating the ability and accuracy of the method to identify areas where the structural stiffness has decreased due to deterioration.

An estimation of mechanical stresses in the stator of the NB-514 motor of an electric locomotive

The aim of the research is to determine the causes of cracks in stators of traction electric motors of the NB-514 series. The application of mathematical modeling using the finite element method, which allows one to evaluate the mechanical stresses arising in the stator under the influence of thermal and vibration loads, is considered. The results of thermal modeling are presented for uneven heating of the electric motor frame to temperatures typical for the hourly operation of a traction motor. The results of vibration modeling, including the study of natural vibration modes and frequencies, are also presented. Based on the results of the studies, it was concluded that the cause of the formation of cracks in the area of ventilation hatches is a complex of cyclically repeating temperature and vibration effects, creating points of mechanical stress with a large value in the area of crack formation. Vulnerabilities in the design of the electric motor frame have been identified. Options have been proposed for improving the design of the ventilation hatches of the frame, allowing reducing mechanical stresses with a constant area of the ventilation and inspection hatches.

Complex Modal Characteristic Analysis of a Tensegrity Robotic Fish's Body Waves.

A bionic robotic fish based on compliant structure can excite the natural modes of vibration, thereby mimicking the body waves of real fish to generate thrust and realize undulate propulsion. The fish body wave is a result of the fish body's mechanical characteristics interacting with the surrounding fluid. Thoroughly analyzing the complex modal characteristics in such robotic fish contributes to a better understanding of the locomotion behavior, consequently enhancing the swimming performance. Therefore, the complex orthogonal decomposition (COD) method is used in this article. The traveling index is used to quantitatively describe the difference between the real and imaginary modes of the fish body wave. It is defined as the reciprocal of the condition number between the real and imaginary components. After introducing the BCF (body and/or caudal fin) the fish's body wave curves and the COD method, the structural design and parameter configuration of the tensegrity robotic fish are introduced. The complex modal characteristics of the tensegrity robotic fish and real fish are analyzed. The results show that their traveling indexes are close, with two similar complex mode shapes. Subsequently, the relationship between the traveling index and swimming performance is expressed using indicators reflecting linear correlation (correlation coefficient (Rc) and p value). Based on this correlation, a preliminary optimization strategy for the traveling index is proposed, with the potential to improve the swimming performance of the robotic fish.

Modal Analysis of 15 MW Semi-Submersible Floating Wind Turbine: Investigation on the Main Influences in Natural Vibration

One of the sources of sustainable energy with great, still untapped potential is wind power. One way to harness such potential is to develop technology for offshore use, more specifically at high depths with floating turbines. It is always critical that their structural designs guarantee that their natural frequencies of vibration do not match the frequencies of the most important oscillatory loads to which they will be subjected. This avoids resonance and its excessive undesired oscillatory responses. Based on that, a 3D finite element model of a 15 MW semi-submersible floating offshore wind turbine was developed in the commercial software ANSYS Mechanical ® to study its dynamic behavior and contribute to the in-depth analysis of structural modeling of FOWTs. A tower and floating platform were individually modeled and coupled together. The natural frequencies and modes of vibration of the coupled system and of its components were obtained by modal analysis, not only to verify the resonance, but also to investigate the determinant factors affecting such behaviors, which are not extensively discussed in literature. It was found that there is strong coupling between the components and that the tower affects the system as a result of its stiffness, and the floater as a result of its rotational inertia. The platform’s inertia comes mainly from the ballast and the effects of added mass, which was considered to be a literal increase in mass and was modeled in two manners: first, it was approximately calculated and distributed along the submerged flexible platform members and then as a nodal inertial element with the floater being considered as a rigid body. The second approach allowed an iterative analysis for non-zero frequencies of vibration, which showed that a first approximation with an infinite period is sufficiently accurate. Furthermore, the effects of the mooring lines was studied based on a linear model, which showed that they do not affect the boundary conditions at the bottom of the tower in a significant way.

Natural Frequencies and Modes of Longitudinal and Torsional Vibrations in Bars with Variable Cross Section

Natural Frequencies and Modes of Longitudinal and Torsional Vibrations in Bars with Variable Cross Section

CHARACTERISTICS OF THE INERTIAL PROPERTIES OF THE DISPERSED MATERIAL

It is noted that in the strength calculations of structural elements of aircraft, among other things, the modes of forced and natural vibrations are taken into account. In this regard, the dynamic properties of the transported cargo are taken into account, which are significantly different for solid and dispersed materials. Considered is a dispersed material located on a platform that performs harmonic oscillations. The main problem in establishing the dynamic properties of a dispersed material is the impossibility of calculating the average coefficient of dynamic friction, since its value is influenced by the interaction of dispersed particles with each other in the entire mass of the material, and not only with the surface of the platform. The description of the dynamic status of a dispersed material in the form of a composition of its unstable and stable statuses provides the key to solving this and similar problems.

Symmetry-breaking response of a flexible splitter plate attached to a circular cylinder in uniform flow

Static and dynamic fluid–structure interaction of a flexible plate behind a stationary cylinder in uniform flow is explored for a body-to-fluid mass ratio of 10. Steady flow-structure computations for Re = 150, based on the diameter of cylinder and free-stream speed, reveal four regimes with respect to increasing flexibility of the plate. The plate does not undergo any lateral deflection in regime 1 beyond which it undergoes a symmetry-breaking bifurcation causing it to spontaneously deflect laterally. The curvature is of the same sign along the entire length of plate in regime 2 while it changes sign along the plate in regime 3. The lateral deflection, however, is still maximum at the plate tip. The location of maximum deflection moves away from the plate tip in regime 4. The evolution of flow structures including the strength of various standing vortices, with flexibility, is studied. The role of reattachment of flow on the surface of the plate and the modification of the pressure distribution is explored. The critical Re, beyond which the splitter plate spontaneously achieves a deflected shape, decreases with increase in flexibility. It is estimated to be Re = 122.33 for the limiting case of an infinitely flexible plate. Computations for dynamic fluid–structure interaction reveal several regimes of lock-in with different natural vibration modes of the plate and related hysteresis. No lateral bias in the time-averaged deflection is found during lock-in; it occurs in the desynchronization regime that precedes the lock-in regime with second mode. For the mass ratio considered, the bias in the static and dynamic simulations start at the same flexibility.