Harmonic Force Excitation Research Articles

Optimal tracking vibration absorber for wideband vibration suppression

Simple pendulum vibration absorbers are sometimes not robust enough in the face of variations in their environmental conditions and dynamic loads. In this work, a tracking vibration absorber is presented so as to modify the design of ordinary pendulum vibration absorbers. This model takes advantage of a curved surface instead of a constant radius path of conventional pendulums to enhance their robustness. Furthermore, a compound objective function is introduced for the optimization process, enabling these gravitational dynamic vibration absorbers to make use of their potential flexibility to adapt to a wide range of harmonic excitation circumstances. The governing dynamic equations are solved analytically through the Harmonic Balance method, and the optimization is carried out numerically for both the simple and compound objective functions. The performance, nonlinear behavior, frequency characteristics, and other aspects of this model optimized for various structural parameters are assessed and compared over a wide range of harmonic excitation forces. This study demonstrates how this suggested model is able to perform more robustly under diverse circumstances for a simple dynamic system and an N-story shear structure as a Multi Degree of Freedom (MDOF) System.

NONLINEAR FIELD RESPONSE OF PILES UNDER HORIZONTAL HARMONIC EXCITATIONS

Harmonic excitation of pile foundation is a typical dynamic phenomenon occur during machine vibration. In many cases, it has been found that the horizontal excitations are the critical ones which governs the design for machine-based pile foundations. In order to comprehend the horizontal frequency-amplitude responses of pile foundation under various harmonic excitation forces, forced vibration tests on several sets of small-scale single and pile groups have been carried out. According to the test results, there are two resonant peaks within the operational frequency range shown by the dynamic frequency-amplitude responses, where the first peak is found to be more dominant as compared to the second peak. Additionally, as resonant frequencies are lowered and resonant amplitudes grow for an increase in excitation forces, the response curves demonstrate the nonlinear patterns of pile groups. The basic dynamic characteristics of all soil-pile setups are found to be similar to each other. As the group's pile count increases, the resonant frequency values increase while the resonant amplitude values decrease, increasing the dynamic stiffness of the soil-pile systems. The resonant amplitude for the first peak of 2х2, 2х3, and 3х3-pile groups are found to be approximately 13%, 36% and 79% lower, respectively, as contrasted with the single pile under the same dynamic load.

Stress-based topology optimization of continuum structures under harmonic force excitation

In this paper, a new optimization method for the maximum von Mises stress minimization design of continuum structures subjected to harmonic force excitation is proposed. By using an extended Bi-directional Evolutionary Structural Optimization (BESO) method, the intermediate density elements with high stress state are avoided. To reduce the computational cost, the global von Mises stress is approximately measured by using a global stress measure based on the p-norm. Both sensitivities and topological variables are filtered to overcome the highly nonlinear stress behavior and stabilize the optimization procedure. A series of comparisons have been conducted to validate the effectiveness and practicability of the method on two-dimensional and three-dimensional benchmark design problems. The influence of varying excitation frequencies, damping and boundary conditions on the optimized results and the mode shapes are considered. The optimized results indicate that the proposed approach has good convergence and can achieve a reasonable design that effectively reduces the stress concentration effect at the critical stress areas. Strength of engineering structure under harmonic load is improved.

A nonlinear time delay control influence in simulation aircraft tail contain a vertical cantilever beam

Nonlinear time delay saturation controller (NTDSC) is used to minimize the vibrations of a vertical cantilever beam simulated as an airplane tail within harmonic excitation force. In the case of primary and 1:2 internal resonance as a simultaneous resonance case, an analytic solution is obtained by employing the multiple time scale perturbation technique to solve the nonlinear differential equations and modeling the system with NTDSC. Time histories and Poincare portraits were created to demonstrate the system without and with controller. The time-history response, as well as the impacts of the parameters on the system and controller, were simulated numerically using the MATLAB program. A good match is found when the approximate solutions are compared to the numerical simulations via the Runge–Kutta method fourth-order (RK4). The stability investigation of the steady state solution in the studied simultaneous resonance case is reviewed and analyzed via the Routh-Huriwitz approach. The impact of controller parameters and time delays on system response curves are examined. Also, the operation’s safe zone is established from the outcomes of the effect via various values of time delays on the system after adding the control scheme. The numerical and analytical solutions at time-history were compared using the MATLAB program to confirm their comparability. The outcomes of this study were used to develop a theoretical foundation for the system’s design and construction. A comparison is made with recently released papers to appear the difference between this study and the others.

A hysteretic model of localized frictional contacts with instrumental stiffness

The steady-state dynamic response of a single-degree-of-freedom system comprising both a hysteretic element and a spring is considered. The Hertz–Cattaneo–Mindlin theoretical framework for modeling of local tangential contact with friction is applied in conjunction with the Masing model of hysteresis to describe the hysteretic behavior of the multiple localized frictional contact interface. The steady-state tangential displacement amplitude of a rigid body under harmonic tangential force excitation is approximately determined by means of the equivalent linearization technique, based on the harmonic balance principle. A special attention is paid to the evaluation of the frictional damping and the determination of the backbone curve of the Masing model from the dissipation-amplitude relation.

Dynamic characterization of tapered composite sandwich plate with honeycomb core: Numerical and experimental investigations

In the present study, the numerical and experimental investigations on the dynamic performance of tapered composite sandwich plates with various configurations of a honeycomb core material are presented. The tapered composite sandwich plates are considered with the tapered composite plates as face sheets and honeycomb structure with and without strip reinforcements as core materials. Various tapered composite face sheets are formulated by dropping the plies longitudinally at various locations. Further, the various honeycomb core materials are designed such that stiffeners are reinforced at various locations longitudinally and transversely within the honeycomb patterns to enhance the stiffness and damping properties. Higher order Shear Deformation Theory (HSDT) is used to derive the governing differential equations of motion of the various honeycomb tapered composite sandwich plate and solved numerically. Experimental tests are performed to identify the various mechanical properties of composite face sheets and core materials. Various composite sandwich plates are also fabricated to perform the modal analysis and identify the dynamic properties. The effectiveness of the developed numerical model is demonstrated by comparing the natural frequencies and loss factors identified through experimental tests on the prototype sandwich plates. Various parametric studies are also performed to investigate the effect of strip reinforcement in the honey comb patterns, ply drop off and taper angle of face sheets, aspect ratio of sandwich plates, ply orientation of face sheets and boundary conditions on the free vibration characteristics of the tapered composite sandwich plates. In addition, the transverse vibration responses of tapered composite sandwich plates under harmonic force excitation are examined at different types of the honeycomb core design and the performances are compared with those obtained without the addition of composite strips to demonstrate the effectiveness of strip reinforcement in optimizing the stiffness and damping characteristics of the structures.

An harmonic equivalent excitation method for random vibration response

Many loads on engineering structures had obvious randomness, such as earthquakes, wind, sea waves, uneven pavement, etc. The calculation and analysis of random vibration were complicated and inefficient, which has perplexed the development of engineering technology for a long time. To solve the above problems, this paper proposed a harmonic equivalent excitation method for structural random vibration analysis. The excitation force of multi-frequency action in continuous time interval was converted into harmonic excitation force with the same effect as superposition excitation in each discrete time interval by a harmonic equivalent method. The frequency and amplitude of harmonic excitation force in discrete-time intervals were calculated, which were then taken as the deterministic load input of the structure. The response of the structure was calculated by the conventional structural dynamic analysis method. Finally, the harmonic equivalent excitation method was used to analyze random pavement excitation and its application in the control of time-delay vibration reduction. The results show that the harmonic equivalent excitation method simplifies the calculation form of random vibration analysis without reducing the accuracy, and provides an effective method for analyzing random vibration in the engineering field.

Nonlinear free and forced vibration analysis of sandwich cylindrical panel with auxetic core and GPLRC facing sheets in hygrothermal environment

In this study, the free and forced vibration analysis of composite sandwich panel subjected to the harmonic force excitation in the hygrothermal environment is investigated. The sandwich panel is composed of three-phase composites with polymer/Graphene platelet/fiber skins at the top and bottom surfaces and double-V auxetic honeycombs core layer with a negative Poisson’s ratio. Governing equations of motion within the framework of higher-order shear deformation theory (HSDT) and von Kármán nonlinearity are obtained. Applying the generalized differential quadrature method (GDQM) and homotopy perturbation technique, respectively the linear and nonlinear equations of motion results in solving the vibration problem. In the numerical illustration, at first validation of the present formulation is carried out by comparing the numerical results with those available in the open literature. Then the effects of several parameters such as geometric parameters of double-V auxetic core, force excitation, GPL volume fraction, and different boundary conditions on the nonlinear frequencies–amplitude of sandwich panel is studied. Finally, the important findings of this research indicate that the ratio of core thickness, inclined angle, and thickness to inclined length have significant effects on nonlinear frequencies–amplitude response. Based on the results of this article designers can development of different parts of aircraft.

Modelling rotational friction damping devices using the Non-Smooth Dynamics method

The dynamic response of frames equipped with an anti-seismic rotational friction damper is studied. The algorithm of the Non-Smooth Dynamics method (NSD), specifically designed for the numerical simulation of non-smooth dynamical systems, was programmed to efficiently deal with the non-smooth character of the friction law. An extensive campaign of numerical computations was carried out to study different frames, either submitted to a harmonic excitation force or to the ground acceleration history of the El Centro earthquake. Each friction damper has two prestressed bracing bars; the cases of axially rigid and axially compliant bracing bars were considered. Performance criteria enabled to conclude on the optimal range for the maximum moment at the frictional hinge of the damper. For the analyzed frames of one, three and five floors and for both rigid and deformable bracing bars, under the action of the El Centro earthquake, it was concluded that the optimal range for the frictional moment is wide and approximately independent of the number of floors. An important reduction of the relative displacements and absolute accelerations of the floors of the frames with friction dampers was observed with respect to the situation of absent frictional damping.

Optimal design of a novel high‐performance passive non‐traditional inerter‐based dynamic vibration absorber for enhancement vibration absorption

AbstractThis paper proposes a novel high‐performance passive non‐traditional inerter‐based dynamic vibration absorber (NIDVA), tuned by the H∞ optimization using the patternsearch solver in MATLAB with the starting points, the optimum parameters based on the extended fixed points theory (EFPT). Then, the control performance of the proposed NIDVA is compared with the classic DVA and the high‐performance passive non‐traditional inerter‐based dynamic vibration absorber (NIDVA‐C4). Based on the optimum parameters under harmonic force excitation, the relative dynamic performance index (%RDP) of the proposed NIDVA registered improvements of 31%–63% and 54%–72% with respect to the NIDVA‐C4 and classic DVA, respectively, considering the mass ratio range from 1% to 10%. Regarding the suppression bandwidth index (%SB) for the mass ratio of 5%, the NIDVA can enlarge the SB by 50% and 62% with respect to NIDVA‐C4 and classic DVA, respectively. For the white noise excitation, more than 38%–64% and 53%–69% improvement of random vibration reduction can be obtained from NIDVA with respect to NIDVA‐C4 and classic DVA, respectively. Accordingly, results of this study provide some technical information to design more effective vibration control device in engineering practices.

Energy harvesting performance of an inerter-based electromagnetic damper with application to stay cables

Energy harvested from vibrating cables can serve as a sustainable and green power source for low-power sensing systems and vibration control systems. However, the energy-harvesting performance of inerter-based dampers installed at stay cables has rarely been reported so far. This paper investigates the energy-harvesting performance of a novel inerter-based electromagnetic damper, termed tuned inertial mass electromagnetic damper (TIMED), which is capable of converting cable vibration energy into electric energy to be harvested. Based on energy balance principles, a power flow model is established for the TIMED, considering major and minor power terms, which account for different power losses occurring during the energy conversion stages. This model is capable of predicting the output power and energy-harvesting efficiency under harmonic displacement or harmonic force inputs. A series of MTS dynamic tests were performed in a TIMED prototype to validate the theoretical model. Under a harmonic force excitation of 1.6kN near the damper’s resonance, the TIMED achieved a maximum output power of 69.54 W. To evaluate the actual performance of the TIMED, we conducted a full-scale experiment on a 135 m-long stay cable with the TIMED prototype. Full-scale experimental results illustrate that the maximum average output power of the TIMED attached to the tested cable in the free vibration case is up to 13.6 W, which is 48.3% larger than the counterpart of an electromagnetic damper (EMD). In addition, an optimal design strategy is proposed and validated for the cable-TIMED system. Numerical results demonstrated that, in theory, the output power of the TIMED can be 81.7% larger than that of an EMD. The performance enhancement of the TIMED over conventional EMD attributes to its displacement and energy amplification near resonance. This study may help to put forward the development of self-powered dampers or self-powered sensing systems in the years to come.

Topology optimization of laminated composite structures under harmonic force excitations

In this paper, a topology optimization approach for the design of laminated composite structures under harmonic force excitations is proposed. A novel method is developed to calculate the harmonic response for composite laminates, which consists of two steps: firstly, based on the strain energy approach, the damping matrix model of composite laminates is established with the proportional damping assumption; then, the displacement response is calculated by the mode acceleration method The design objective of topology optimization is to minimize the displacement amplitude at the concerning point with an excitation frequency or a frequency band. An extended polynomial interpolation scheme is introduced to penalize the stiffness, damped stiffness and mass of elements. The analytical sensitivities of the objective and constraint functions to the density variables are derived in detail, and the globally convergent method of moving asymptotes is used to solve the optimization problem. Numerical examples are performed to demonstrate the effectiveness and feasibility of the proposed topology optimization method in improving the dynamic performance of laminated composite structures. The influence rules of excitation frequency and layer sequence on topologic shape are also discussed.

Dynamic Characteristics of a Superconducting Magnetic Bearing Under μm Displacements

The dynamic properties of a ring-shaped superconducting magnetic bearing used in textile machines were studied for a micrometer displacement range. Therefore, a new measurement setup was designed that allows to excite the freely levitating magnet ring in a defined direction with small excitation amplitudes. Here, we focus on radial and axial excitations with amplitudes between 2 μm and 30 μm. The data were analyzed by a fast Fourier transformation approach. The resultant excitation response was fitted by the transfer function of a spring-mass-damper system under harmonic force excitation, which gives the stiffness and damping coefficient for the particular excitation direction. The analysis shows a minor stiffness increase with decreasing excitation amplitudes in radial as well as in axial direction. At the same time, no clear trend was found for the damping coefficient. In contrast to other bearing designs, the studied ring-shaped bearing exhibits a ratio of 3 between the axial and radial stiffness.

A Comparison Between the Linear and Nonlinear Dynamic Vibration Absorber for a Timoshenko Beam

Dynamic vibration absorbers (DVAs) play an important role in the energy dissipation of a vibrating system. Undesirable vibrations of structures can be reduced by using the absorbers. This paper investigates the effect of an attached energy sink on the energy dissipation of a simply supported beam subjected to harmonic excitation. The aim is to design an optimal linear energy sink (LES) and a nonlinear energy sink (NES) and then compare them with each other. Each absorber includes a spring, a mass, and a damper. For each absorber, the optimum mass, stiffness, and damping coefficients are obtained in order to minimize the beam’s maximum amplitude at the resonant frequencies. The optimization problem is minimizing the maximum amplitude of the beam subjected to an arbitrary harmonic force excitation. For consideration of the effects of rotary inertia and shear deformation, the Timoshenko beam theory is used. The mathematical model of beam with DVA is verified by using the ANSYS WORKBENCH software. Finally, by considering the uncertainty on the DVA parameters it was observed that the LES is more robust than the NES.

Innovative negative-stiffness inerter-based mechanical networks

This paper presents the optimal design for novel negative-stiffness non-traditional inerter-based dynamic vibration absorbers called NS-NIDVAs. The underlying idea of negative-stiffness inerter-based mechanical networks (NS-IMNs) was inspired by the negative-stiffness technology concept. Firstly, the non-dimensional mathematical models for NS-NIDVAs are established considering the harmonic force excitation case, and then the dimensionless frequency response functions of the primary structure are computed for optimization purposes. Therefore, a dynamic stability analysis was conducted in order to determine the allowable boundary on negative stiffness variable. Moreover, the Extended Fixed Points Technique (EFPT) has been proposed as an optimal calibration procedure taking in account the undamped system case. In order to ensure a trade-off among the invariant points of the primary structure's FRFs, a constraint equation was added to the EFPT's optimality approach. It was proved that the allowable negative stiffness solution computed by the constraint equation is in accordance with that provided by the Routh- Hurwitz stability criterion. The short optimal explicit functions revealed that the NS-NIDVA-C4 has a similar optimal tuning magnitude as the NS-NIDVA-C6 and C3, with the devices providing the same dynamic performance. In view of this dynamic characteristic, the H∞ performance measure is computed for both NS-NIDVAs devices considering a practical application mass ratio range. When the NS-NIDVA-C4’s performance is compared to the other passive high-performance devices, an improvement of more than 50% in DMF reduction is obtained. Additionally, the NS-NIDVA-C4 can broaden the effective operating bandwidth from 46% to 82% when compared to the classic DVA. Therefore, it has been proved that NS-NIDVA-C4 has the versatility of yielding high-performance with a small physical mass of the DVA, which is the significant finding of this work.

A Novel Test Rig for the Basic Nonlinear Characterization of Bolted Joints

The paper aims at performing a comprehensive experimental study on the peculiar properties of a bolted joint, and investigates the damping induced at different interfaces (between flanges, bolt head/nut and flange, threads) during vibrations. A novel, simplified, single-bolt system joining a two-beam structure is designed and tested. Experimental results under different boundary conditions are presented, and the influence of the harmonic excitation force, as well as the bolt tension, is investigated. The test results show how the contact interface between the clamped flanges plays an important role in terms of frictional damping provided to the system during vibration, while the contact interfaces between the head/nut and flange, and secondarily between the threads, affect the system response at a less, but not negligible, extent. The test setup and test procedure can provide a database to validate single bolt contact models to be included in a more complex structure.

Mitigation of vibration of ship structure via local structural modifications

ABSTRACT This article presents a methodology for the reduction of ship structure vibration through local structural stiffness modifications. To identify the locations in the ship structure where the modifications should be made, three design criteria are considered: structural intensity, von Mises stress, and displacement. Two simple cases of cantilever beam and simplified ship were first tested under a harmonic excitation force at a frequency near resonance. The methodology was subsequently applied to a containership model subjected to propeller excitation forces. It is found that the von Mises stress is the most effective criterion in identifying the critical regions for structural modification. By increasing the thickness of plates in small localised regions, the global vibration level in the ship structure can be reduced by 50% when the excitation is near the resonant frequencies. The improvement varies with the structural damping present, and also on the model of mass distribution in the ship.

Frequency response of a cantilevered rectangular sheet under harmonic forced excitation in three-dimensional uniform flow

Flexible thin manufactures (sheets) are used in numerous engineering applications. In their manufacturing processes, the sheets are subjected to a fluid flow, and external disturbances can induce vibrations. The vibrations cause severe damage to the sheets. Therefore, an in-depth understanding of the vibration characteristics and excitation mechanism of a sheet in a fluid flow is essential. In this study, the vibration characteristics and excitation mechanism of a sheet under a harmonic forced excitation are investigated by both theoretical calculations and experiments. In the experiments, a harmonic displacement excitation is inputted at the leading edge of a sheet in a wind-tunnel by an exciter using the slider–crank mechanism. In the theoretical analysis, the sheet is modeled as a cantilevered beam, and the fluid force acting on the sheet surface is calculated using three-dimensional theory. The frequency response of the sheet in a uniform flow is investigated with changing the flow velocities and forcing frequencies inputted to the sheet. Finally, the work done by the fluid force acting on the sheet under the harmonic excitation is determined, and the excitation mechanism is discussed.It is found that the flow velocity considerably affects the sheet response. As the flow velocity increases, the amplitude of the second peak of the response becomes larger than that of the first peak. Moreover, the vibration mode of the second peak of the response transforms into a traveling-wave-type mode due to the modal coupling caused by the fluid force.

Active Approaches to Vibration Absorption through Antiresonance Assignment: A Comparative Study

Vibration absorption is a core research topic in structural dynamics and the mechanics of machines, and antiresonance assignment is an effective solution to such a problem in the presence of harmonic excitation forces. Due to recent developments in the theory of feedback control systems, the use of active control approaches to antiresonance assignment has been recently gaining more attention in the literature. Therefore, several methods exploiting state feedback or output feedback have been proposed in recent years. These techniques that just rely on servo-controlled actuators are becoming an interesting alternative to active approaches that emulate the well-known Tuned Mass Damper in an active (or semi-active) framework. This paper reviews and compares the most important approaches, with a greater focus on the methods exploiting the concept of control theory without adding new degrees of freedom in the system. The theoretical results, with the underlying theory, are discussed to highlight the key features of each assignment techniques. Several numerical examples where different techniques are applied and compared, also providing some analysis usually neglected in the literature, enrich the paper and demonstrate the key concepts.

Damping based on electromagnetic induction: A comparison of different minimal models

AbstractDamping of structural vibrations is a crucial part of modern engineering. Using electromagnetic interactions for this purpose is a modern and promising approach. To gain better understanding of phenomena involved in this technique investigations on minimal models of a B‐field modulation dampers are shown. Therefore two different setups are compared. One uses a permanent magnet as the source for the magnetic field, one uses a coil, respectively an electro‐magnet as the source. The contribution focuses on differences that occur, due to the different designs. Therefore the static behavior is analyzed as well as the system response on a harmonic force excitation.