Point Force Research Articles

Shunted piezoelectric patch adaptive vibration absorber set to maximise electric power absorption: A comparison between parallel and series RL-shunts

This paper presents a comparative study on two types of shunted piezoelectric patch adaptive vibration absorbers, which can be bonded in batches on thin-walled structures to control the broad-band resonant response of low order flexural modes. The self-contained control units are formed by a thin piezoelectric patch connected either to a series or to a parallel resistive-inductive (RL) network. The two components of the shunt are adapted online in such a way as to maximise the time-averaged electric power absorbed by the shunt, which corresponds to minimising the time-averaged total flexural response of the hosting structure. The study considers a practical demonstrator formed by a thin rectangular plate with five piezoelectric patches connected to digital RL-shunts, which is excited in bending by a stationary white noise point force. The aim of the paper is to contrast the tuning and vibration control properties of the series and parallel RL shunts. More specifically, the online implementation of a recursive two-paths tuning strategy along R-constant and L-constant paths with an extremum seeking gradient search algorithm is analysed first for the two types of shunts. Then, the vibration control performance produced by the two types of shunts is investigated for the case where they are tuned to control the resonant response of the first flexural mode of the plate.

Transient in-plane analysis of cracked general orthotropic planes

An edge dislocation with a time-dependent Burgers vector in an orthotropic plane is analyzed. The stress field caused by a dynamic point force in the intact plane is determined. The displacement discontinuity of dislocation and direction of point load are at arbitrary angles with the Material Principal Axes (MPA), the general orthotropic plane. The density of dislocations is employed to construct integral equations for orthotropic planes weakened by several interacting cracks, making arbitrary angles with the MPA. The numerical solution of integral equations results in the density of dislocations on a crack surface. The results are employed to determine time-dependent Stress Intensity Factors (SIFs) at the tips of a crack and Crack Opening Displacement (COD). In the problem of general orthotropic planes containing cracks subjected to dynamic loads, crack orientations may cause their partial/total closing. Under the hypothesis of frictionless contact, we devise an iterative procedure to handle crack closing, as well. By contrast to cracks in the directions of MPA, expressions for the two modes of SIFs contain the density functions of both the climb and glide of the edge dislocation. Therefore, mode I SIF at an open tip of a crack may not be positive. Conversely, positive mode I SIF may occur at a closed crack tip. Numerical results of the SIFs and COD for several examples of orthotropic planes under dynamic point loads, while weakened by single and double parallel cracks, are presented. Moreover, in double cracks cases, the interaction between cracks is studied.

Acoustically enhanced porous media enables dramatic improvements in filtration performance

Indoor air pollution affects millions of people worldwide. Conventional air purification techniques struggle to balance between safety, power consumption, efficacy, and cost. Acoustics have previously been leveraged to improve air purification with fiber filters, but little is known about how the arrangement of the fibers influences the acoustic effects, particularly for non-agglomerative purification performance relevant to fine and ultrafine pollutants. Here, we explore performance enhancements to fiber filters by applying external standing acoustic waves. We investigate the effects of the porous media arrangement in ordered (aligned and staggered) and disordered fiber media by building a multiphysics model, incorporating thermos-viscous acoustics, laminar flow, and particle tracing. Particles are modeled as point forces to isolate acoustic radiation forces and streaming. Attractive acoustic radiation forces dominate in the porous domain, leading to increased particle/boundary interactions. We find that the average acoustic radiation forces scale linearly with the average scattered acoustic pressure by the fiber medium. The scattered pressure varies depending on the fiber arrangement, indicating that there is an optimal design to increase the performance of acoustic-induced effects. We show a dramatic increase in performance efficiency, up to two orders of magnitude (123 times) for a staggered domain. This work has important applications to further advance acoustically enhanced filtration as a compelling solution for micro/nanoparticle separation processes.

The Vibro-Acoustic Characteristics Analysis of the Coupled System between Composite Laminated Rotationally Stiffened Plate and Acoustic Cavities

In order to study vibro-acoustic characteristics between composite laminated rotationally stiffened plate and acoustic cavities in the coupled system, first-order shear deformation theory (FSDT) and modified Fourier series are used to construct a unified analysis model. The involved coupled systems primarily encompass three types: the coupled system between composite laminated rotationally stiffened plate and cylindrical-cylindrical cavities, spherical-cylindrical cavities, and conical-cylindrical cavities. First, the first-order shear deformation theory and the modified Fourier series are applied to construct the allowable displacement function of the composite laminated rotationally stiffened plate and the allowable sound pressure function of the acoustic cavities. Second, the energy functionals for the structural domain and the acoustic field domain are established, respectively. According to the continuity condition of the particle vibration velocity at the coupling boundary between the composite, laminated cylindrical shell and the enclosed cavity, the coupling potential energy between the stiffened plate and two acoustic cavities is introduced to obtain the energy functional of the coupled system. Third, the Rayleigh-Ritz method is utilized to solve the energy functional and, when combined with artificial virtual spring technology, the suggested theory may be used to study the vibro-acoustic characteristics of a coupled system with arbitrary elastic boundary conditions. Finally, based on validating the fast convergence and correctness of the model, this paper will analyze the impact of crucial parameters on vibro-acoustic characteristics. Furthermore, by incorporating internal point forces and point-sound source stimulation, a steady-state response analysis of the coupled system will be conducted. This research can give a theoretical foundation for the vibration and noise reduction of a vibro-acoustic coupling system.

Effects of grafted polymers on the lipid membrane fluidity

Since the membrane fluidity controls the cellular functions, it is important to identify the factors that determine the cell membrane viscosity. Cell membranes are composed of not only lipids and proteins but also polysaccharide chain-anchored molecules, such as glycolipids. To reveal the effects of grafted polymers on the membrane fluidity, in this study, we measured the membrane viscosity of polymer-grafted giant unilamellar vesicles (GUVs), which were prepared by introducing the poly (ethylene glycol) (PEG)-anchored lipids to the ternary GUVs composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), and cholesterol. The membrane viscosity was obtained from the velocity field on the GUV generated by applying a point force, based on the hydrodynamic model proposed by Henle and Levine. The velocity field was visualized by a motion of the circular liquid ordered (Lo) domains formed by a phase separation. With increasing PEG density, the membrane viscosity of PEG-grafted GUVs increased gradually in the mushroom region and significantly in the brush region. We propose a hydrodynamic model that includes the excluded volume effect of PEG chains to explain the increase in membrane viscosity in the mushroom region. This work provides a basic understanding of how grafted polymers affect the membrane fluidity.

Feasibility investigation of using waste laminated packaging as bitumen performance enhancer

Millions of tons of laminated packaging are extensively utilized in aseptic food packaging due to its advantages in transporting and storing liquid foods, leading to the annual generation of waste laminated packaging (WLP). To address this concern, this study processes WLP recycled from milk and fruit juice packages into particles. The properties of WLP-modified bitumen were characterized through conventional and rheological tests, and the results were compared with those of the base bitumen. The tests reveal that the addition of WLP increases the softening point and peak force while decreasing penetration and ductility. Additionally, higher WLP content results in a larger modification index, higher failure temperature, lower non-recoverable creep compliance, and lower stress sensitivity. Furthermore, the stabilizing effect of low-density polyethylene in WLP, combined with the complete cross-linking of cellulose fibers, contributes to enhancing the fatigue life of the bitumen.

Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations.

We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model. Vesicle shapes are determined by minimizing the elastic energy subject to constraints of constant area and volume. The results show that pressurized vesicles can adopt higher-energy spindle-like configurations that require the action of point forces at the poles. If the internal pressure is lower than the external one, multilobed shapes are predicted. We utilize our results to rationalize experimentally observed spindle shapes of giant vesicles in a uniform AC electric field.

A study on soil propagation mechanism of traffic-induced vibration based on numerical analysis and theoretical approach

In order to clarify soil propagation mechanism of traffic-induced vibration, soil surface responses excited by vertical and horizontal force focused on the frequency characteristics are examined based on numerical analyses, theory of surface wave, and field observations. Relationships between natural frequency of surface soil and frequency at which wave with large amplitude propagates at distant points are examined. In the case of two-layer soil, vertical displacement amplitude excited by vertical point force becomes the largest at twice the natural frequency at distant points. Horizontal displacement amplitude excited by horizontal point force becomes the largest at the natural frequency at distant points.

Vibration behaviors of orthogonally stiffened cylindrical shell coupled with internal circular plates in wavenumber-frequency domain

In this paper, vibration characteristics of orthogonally stiffened cylindrical shell coupled with multiple internal circular plates are discussed using wavenumber analysis. The theoretical model and formulation for the orthogonally stiffened cylindrical shell coupled with internal circular plates are developed by employing a modified variational method. A unified variational modeling procedure is employed to ensure the continuity conditions between each substructure, including cylindrical shell, circular plate, longitudinal stringer, and circumferential ring. The displacement components of the cylindrical shell are described by Fourier series along the circumferential direction and orthogonal polynomials along meridional direction. Thus, the responses of the shell in wavenumber domain can be naturally obtained. Convergence studies for the theoretical model are conducted by finite element method to verify the reliability of the present method. The vibration behaviors of the coupled model under three typical external loads, including single point force, multiple uniformly spaced point forces, and line force, are studied based on the vibration fields in wavenumber domain. The results indicate that the circumferential modal coupling effect and modal contribution to the total vibrations are sensitive to the types of external excitations, which induces the different vibration behaviors.

Real-time sound field separation of multiple unsteady rotating loading sources

This paper proposes a sound field separation technique based on the time-domain equivalent method for real-time separating the pressure field belonging to every source from the unsteady rotating loading multi-source sound field. In the proposed method, the transfer relationship between the mixed time-dependent pressure and the equivalent unsteady rotating forces is first established. Then, all the equivalent unsteady rotating forces are solved via time-domain inversion procedure. Finally, the corresponding equivalent unsteady rotating forces distributed on one interested source are used to calculate the pressure field generated by that source alone. Numerical simulations with four unsteady point forces rotating at different speeds around two different axes examine the validity of the proposed method. Keywords: Multiple unsteady loading sources rotating at different speeds around different axes, Sound field separation, Time-domain equivalent method

Design of sinusoidal-shaped inlet duct for acoustic mode modulation noise reduction of cooling fan

The noise reduction method of installing a sinusoidal-shaped inlet duct on a cooling fan is analyzed theoretically and experimentally in terms of the acoustic mode modulation. Based on Lowson's point force model, the correlation between the free field noise and acoustic mode of the fan rotor and the unsteady forces on the rotor blade surface is established. The azimuthal acoustic mode is demonstrated to partially reflect the composition and intensity of the acoustic source. The theoretical variation in azimuthal acoustic mode indicates that it is possible to completely cancel each mode simultaneously when the phase differences of forces of each order in the secondary source are controlled. A sinusoidal-shaped inlet duct noise reduction structure controlled by a parameter equation is proposed, and the preferred parameter selection is given by the far-field noise measurements. The results of azimuthal mode decomposition exhibit a similar trend to the theoretical analysis. Compared with the straight duct, the chosen sinusoidal-shaped inlet duct achieved greater noise reduction at the blade passing frequency and its first harmonic. The average total sound pressure level in the far field was 6.0 dBA lower than that of the prototype fan, and 1.4 dBA lower than that of the straight duct model.

A deterministic energy method for predicting the response of coupled finite structures

The forced response of finite, thin rectangular plates coupled by a line joint can be predicted using well-established analytical methods. However, such methods become difficult to implement for thick panels coupled by complex joints. In these cases, the finite element (FE) method and conventional statistical energy analysis (SEA) are viable alternatives. However, the FE method can be time-consuming at mid/high frequencies while SEA involves various approximations and assumptions. This paper develops a deterministic energy method for predicting the forced response of coupled complex panels based on a hybrid finite element/wave finite element method (WFE), modelling the panels as coupled wave-bearing subsystems. Excitation of the structure by a time-harmonic point force is considered. The method involves meshing only a small segment of the panel and the joint using finite elements, and is able to model complex structures such as laminated panels and joints with low computational cost. An illustrative example of the method is presented - coupled thin, rectangular plates coupled by an "L" shaped joint.

On the topological gradient method for an inverse problem resolution

Abstract In this work, we consider the topological gradient method to deal with an inverse problem associated with three-dimensional Stokes equations. The problem consists in detecting unknown point forces acting on fluid from measurements on the boundary of the domain. We present an asymptotic expansion of the considered cost function using the topological sensitivity analysis method. A detection algorithm is then presented using the developed formula. Some numerical tests are presented to show the efficiency of the presented algorithm.

Nonlinear Rigid-Elastic Coupled Modeling and Oscillation Mechanism Analysis of Rotor-Body-Slung-Load System

In order to reveal the mechanism of Category II rotor-body-slung-load coupled oscillation (RBSLCO) with the frequency range of 2.5~8 Hz, a novel nonlinear rigid-elastic coupled model is presented for the helicopter and slung load system (HSLS) with explicit formulation. The slung load system model is coupled with the current rigid-elastic coupled helicopter model, considering fuselage hook point rigid-elastic coupled movements, cable stretching, and hook point force from the slung load system. The results show that carrying the heaviest load is the vital state for Category II RBSLCO. As slung load mass ratio increases, rotor-fuselage coupling becomes stronger and the oscillation frequency shifts slightly, causing a maximum of 15% reduction in stability margin. In addition, even when the load is lightweight, another form of Category II RBSLCO may appear involving fuselage bending and cable stretching. This Category II RBSLCO behaves like the vertical bouncing but is divided into a high-frequency anti-phase oscillation and a relatively low-frequency in-phase oscillation.

Integral nonlocal stress gradient elasticity of functionally graded porous Timoshenko nanobeam with symmetrical or anti‐symmetrical condition

AbstractUtilization of symmetrical or anti‐symmetrical condition could improve the calculation efficiency. In this paper, a mathematical formulation is proposed to deal with the symmetrical or anti‐symmetrical condition in an integral nonlocal stress gradient model (INSGM), which is transformed equivalently into differential form with constitutive boundary condition as well as constitutive symmetrical or anti‐symmetrical condition. Unlike general constitutive boundary conditions, an integral item is introduced to constitutive symmetrical and anti‐symmetrical conditions, and they are opposite to each other. Based on INSGM with symmetrical or anti‐symmetrical conditions, static bending of simply‐supported (SS) and clamped‐clamped (CC) functionally graded porous Timoshenko nanobeams is investigated for symmetrical loads, including uniformly distributed load (UDL) and middle point force, as well as anti‐symmetrical loads, including anti‐symmetrical UDL and middle point moment. The exact solutions are deduced and expressed in explicit form for different boundary and loading conditions. Calculation shows that, under UDL, bending deflections of half Timoshenko nanobeams based on current model agree well with those for whole Timoshenko nanobeams based on general INSGM for both SS and CC boundary conditions. Numerical study is performed to show the effectiveness of current model.

PHYSICAL AND MATHEMATICAL MODELING OF THE DISTRIBUTION OF LOAD FORCES ON THE FEMINAL COMPONENT OF AN ENDOPROSTHESIS OF THE HIP JOINT UNDER REAL CONDITIONS

Determination of the factors causing the development of aseptic instability of endoprosthesis components is one of the main tasks of modern traumatology and orthopedics. It is important from a scientific and medical point of view to carry out physical and mathematical modeling of the distribution of load forces and their moments on the femoral component of a hip endoprosthesis. The purpose of the study: to conduct a physical and mathematical modeling of the distribution of load forces on the femoral component of a hip endoprosthesis under real conditions of incomplete axially symmetrical contact of the femoral component of the endoprosthesis and the femur, when the surface of the lower end of the endoprosthesis is not in contact with the surface of the bone. In the work, mathematical modeling of the distribution of point load forces and their moments on the contact surface between the femoral endoprosthesis stem and the bone marrow canal of the femur in real conditions is carried out. For qualitative estimates of point distributions of the load force, based on the analysis of previous results, an estimated empirical formula was obtained for these distributions: g(λ,λ1)=Р(λ,λ1) / 140λ7/2, in which the pressure Р(λ,λ1) is taken in kilograms per square centimeter (kg/cm2), and the point force g(λ,λ1) is in kilograms (kg). It was determined that the best, from the point of view of minimizing the harmful mechanical impact of the prosthesis on the femur, is the situation when the length of the prosthesis stem is not less than half the length of the femur (λ≥0.5). In this case, the values of the point load forces do not exceed 0.1 kg, at least for the length of the area of real contact, which is not less than half the length of the prosthesis stem (λ1≥0.5λ). It has been proven that the use of a prosthesis stem that is less than a third of the length of the femur is not advisable. Since already at the length of the prosthesis stem, which is 30 % of the length of the femur (λ=0.3), point loads increase rapidly and can reach from 0.55 to 1.5 kg depending on the length of the contact area. Such point loads are undesirable for the femur in the area of contact with the prosthesis in terms of the integrity of the femur.

Numerical Simulation of a Partly Filled Rectangular Tank with Fuel Oil

Sloshing refers to a certain kind of fluid movement that changes as it progresses. It possesses properties that are both nonlinear and exceedingly unpredictable, and these properties affect the tank wall. This effect may lead to structural wear, which in turn can cause the tank to fail. Benzene and gasoil liquids are used to test the effect of sloshing liquid and accompanying pressure on the wall tank caused by the baffles in partially full fluid tanks. To attain this, modeling of the interaction between fluid and structure is justified using the finite element analysis while the ANSYS Fluent is used to do the simulation. Specifically, the analysis enables us to anticipate the pressure that is being exerted on the shield, the influence of sloshing on the grounding point forces, and the size of the sloshing waves. The pressure distribution over time indicates a reduction of pressure on the tank wall as a result of utilising a vertical baffle if compared to the case of a tank wall without a baffle. The usage of vertical shields allows for around 20% of the greatest contact energy to be deflected, which is attributed to the potential of generating turbulence and vortices by the baffle.

The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory

The equations of a planar elastica under pressure can be rewritten in a useful form by parameterizing the variables in terms of the local orientation angle, θ , instead of the arc length. This ‘ θ -formulation’ lends itself to a particularly easy boundary layer analysis in the limit of weak bending stiffness. Within this parameterization, boundary layers are located at inflection points, where θ is extremum, and they connect regions of low and large curvature. A simple composite solution is derived without resorting to elliptic functions and integrals. This approximation can be used as an elementary building block to describe complex shapes. Applying this theory to the study of an elastic ring under uniform pressure and subject to a set of point forces, we discover a snapping instability. This instability is confirmed by numerical simulations. Finally, we carry out experiments and find good agreement of the theory with the experimental shape of the deformed elastica.

Analysis of linearized elasticity models with point sources in weighted Sobolev spaces: applications in tissue contraction

In order to model the contractive forces exerted by fibroblast cells in dermal tissue, we propose and analyze two modeling approaches under the assumption of linearized elasticity. The first approach introduces a collection of point forces on the boundary of the fibroblast whereas the second approach employs an isotropic stress point source in its center. We analyze the resulting partial differential equations in terms of weighted Sobolev spaces and identify the singular behavior of the respective solutions. Two finite element method approaches are proposed, one based on a direct application and another in which the singularity is subtracted and a correction field is computed. Finally, we confirm the validity of the modeling approach, demonstrate convergence of the numerical methods, and verify the analysis through the use of numerical experiments.

Non-negative intensity for a heavy fluid-loaded stiffened plate

Localisation of sound sources on vibrating structures is a critical part of the design in many engineering applications. In structures with stiffeners, so-called Bloch–Floquet waves are generated due to the interaction between the flexural waves in the host structure and the flexural/torsional waves of the stiffeners. It is known that the Bloch–Floquet waves have a significant contribution to the radiated sound. However, it is not understood which area of the vibrating stiffened structures contributes significantly to the radiation in the far-field. Non-negative intensity (NNI) is a powerful tool developed recently to locate the surface regions on structures that can contribute to the radiated sound power. Although NNI has been used for several distinct structures under different excitations, it has not been considered for analysing structures with stiffeners. In this work, NNI is evaluated for an infinite fluid-loaded stiffened plate subjected to a point force to localise the sources of sound and to shed light on the mechanism involved in the far-field radiation. An analytical model formulated in the wavenumber domain is presented to carry out fast calculations of the plate vibroacoustic responses and the NNI maps. A parametric study is then performed by comparing the vibroacoustic responses with the NNI maps to highlight the capability of NNI for sound source localisation. This is achieved by analysing the results for stiffened/unstiffened structures with excitation on/between the stiffeners, and at frequencies either in a passband or in a stopband. Moreover, the NNI maps are further explained and interpreted using identified Bloch–Floquet radiating bands.