Forced Response Research Articles

Specific changes in contractive functions and skeletal muscle architecture in humans in response to the use of two protocols of unmodulated neuro-muscular electrostimulation

The purpose of this study was to study the effect of unmodulated low-frequency superficial of neuromuscular electrical stimulation (NMES) of 30 and 60 min/day for 7 weeks on the force, velocity-strength properties of the triceps surae muscle (TS) and architecture (lengths and angles of fascicles) of human the medial gastrocnemius muscle (MG). Many studies have examined the effect of training intensity (percentage of maximal voluntary isometric contraction — MVC) during NMES on muscle force response. However, no study has examined the effect of the number of NMES sessions per day over 7 weeks on changes in the TS strength. Ten healthy volunteers (23.2 ± 3.2 years; age range 18–28 years) volunteered for the study and were randomly assigned to group 1 (30 min NMES) and group 2 (60 min NMES) 5 times a day. NMES for a 7-week period, a total of 35 NMES workouts Isometric triceps calf strength was recorded with a Biodex isokinetic dynamometer. The longitudinal ultrasonic images of the MG was measured in vivo using the B-mode Edge ultrasound system. After a 7-week training period, MVC and voluntary maximal “explosive” strength differed significantly between groups. Based on electrical stimulation parameters and healthy subjects in this study, electrical training caused an increase in foot extensor muscle strength and a gradient in voluntary explosive strength when used for 5 training per week for 30 min for 7 weeks.

Numerical Investigation of the Excitation Characteristics of Contaminated Nozzle Rings

The deposition of combustion residues in the nozzle ring (NR) of a turbocharger turbine stage changes the NR geometry significantly in a random manner. The resultant complex and highly asymmetric geometry induces low engine order (LEO) excitation, which may lead to resonance excitation of rotor blades and high cycle fatigue (HCF) failure. Therefore, a suitable prediction workflow is of great importance for the design and validation phases. The prediction of LEO excitation is, however, computationally expensive as high-fidelity, full annulus CFD models are required. Previous investigations showed that a steady-state computational model consisting of the volute, the NR, and a radial extension is suitable to reduce the computational costs massively and to qualitatively predict the level of LEO forced response. In the current paper, the aerodynamic excitation of 69 real contaminated NRs is analyzed using this simplified approach. The results obtained by the simplified simulation model are used to select 13 contaminated NR geometries, which are then simulated with a model of the entire turbine stage, including the rotor, in a transient time-marching manner to provide high-fidelity simulation results for the verification of the simplified approach. Furthermore, two contamination patterns are analyzed in a more detailed manner regarding their aerodynamic excitation. It is found that the simplified model can be used to identify and classify contamination patterns that lead to high blade vibration amplitudes. In cases where transient effects occurring in the rotor alter the harmonic pressure field significantly, the ability of the simplified approach to predict the LEO excitation is not sufficient.

A body hair-inspired multi-directional piezoelectric energy harvester with spatial internal resonance effect

To improve the ability of piezoelectric energy collection (PEH) devices to convert multi-directional energy sources, a body hair-inspired multi-directional broadband piezoelectric energy harvester with spatial internal resonance effect is proposed. It is constructed from a zigzag beam and a rigid pendulum. The motion of the pendulum in three orthogonal directions causes bending deformation of the fixed-end of the zigzag beam. Furthermore, the system can also achieve internal resonances in all three directions, broadening the system bandwidth. This paper presents the configuration and working principle inspired by this concept along with the dynamic equations of its electromechanical system. The resulting analytical and numerical solutions are given. The forced responses of the system at spatial internal resonance under different excitation levels were analyzed in the frequency domain. The prototype was fabricated and the experimental setup was built up to measure the output characteristics. Experimental results show that the proposed PEH device can achieve spatial multi-degree-of-freedom collection of vibration energy and provide stable and considerable voltage output levels under excitation in three orthogonal directions. Moreover, the working bandwidth of the system increases with the increase of external excitation level. The proposed PEH device exhibits high energy harvesting capability and potential application in complex excitation environments.

Natural Variability Can Mask Forced Permafrost Response to Stratospheric Aerosol Injection in the ARISE‐SAI‐1.5 Simulations

AbstractStratospheric aerosol injection (SAI) has been proposed as a potential method for mitigating risks and impacts associated with anthropogenic climate change. One such risk is widespread permafrost thaw and associated carbon release. While permafrost has been shown to stabilize under different SAI scenarios, natural variability may mask this forced response and make it difficult to detect if and when SAI is stabilizing permafrost. Here we use the 10‐member ensemble from the ARISE‐SAI‐1.5 simulations to assess the spread in projected active layer depth and permafrost temperature across boreal permafrost soils and specifically in four peatland and Yedoma regions. The forced response in active layer depth and permafrost temperature quickly diverges between an SAI and non‐SAI world, but individual ensemble members overlap for several years following SAI deployment. We find that, due to projected permafrost variability, it may take more than a decade of SAI deployment to detect the effects of SAI on permafrost temperature and almost 30 years to detect its effects on active layer depth. Not only does natural variability make it more difficult to detect SAI's influence, it could also affect the likelihood of reaching a permafrost tipping point. In some realizations, SAI fails to prevent a local tipping point that is also reached in a non‐SAI world. Our results underscore the importance of accounting for natural variability in assessments of SAI's potential influence on the climate system.

The Effect of Hyperelasticity and Nonlinearity on the Dynamic Behaviors of Hyperelastic Functionally Graded Beams on Nonlinear Elastic Foundation

Hyperelastic functionally graded materials have a wide range of application prospects in soft robotics and biomedical fields. This paper investigates the nonlinear free and forced vibrations of a hyperelastic functionally graded beam (HFGB) based on higher-order shear deformation beam theory. The geometrical nonlinearity is considered by using the von-Kármán’s nonlinear theory. The three-material-parameter free energy function named as Ishihara model is employed to characterize the hyperelastic material. The power-law gradient form along the thickness direction is adopted. The HFGB is resting on the elastic foundation. The Winkler, Pasternak and nonlinear stiffness coefficients are considered. The time-harmonic external force is applied to the HFGB. The nonlinear governing equations for the vibration of the HFGB are derived by using Hamilton’s principle, and are subsequently transformed into ordinary differential equations via Galerkin’s method. The nonlinear free vibration and primary resonance of the HFGB are investigated analytically by employing the extended Hamiltonian method and multiple scales method, respectively. The results indicate that the power-law index, slenderness ratio, material properties, and elastic foundation parameters have significant influences on the nonlinear frequency of free vibration as well as the frequency–response and force–response curves of forced vibration. The phase plane method is employed to analyze the system’s stability states under various excitation amplitudes. The relative error between the results of the current computational model and the published literature is less than 0.1 percent.

The importance of print orientation in numerical modelling of 3D printed structures under impact loading

Anisotropy is commonly observed in 3D-printed polymer and composite parts, particularly when manufactured by fused filament fabrication (FFF). This anisotropy can lead to difficulty obtaining accurate material properties during mechanical characterisation. This study establishes a connection between the print parameters used in specimen characterisation and their influence on the accuracy of numerical models for 3D-printed cellular structures under impact. Material properties from only one of the characterisation variants studied, with a parallel infill, accurately represented the force response and physical damage of the experimental samples. In contrast, the default characterisation specimen with a ±45° infill underpredicted the peak force and overpredicted the impact duration, potentially leading to underestimating impact severity. This discrepancy could result in greater damage to a person or structure being protected. It is recommended that the parallel infill pattern be used when characterising materials for use in FFF cellular structures under impact loading to ensure more reliable simulations and improved design of impact-resistant structures.

Enhanced coastal upwelling indices for Moroccan Atlantic Coast, their force–response variability and sensitivity to extreme events between 1993 and 2021

The Eastern Boundary Upwelling Systems (EBUS) are highly productive ecosystems globally, contributing approximately 20% of the world’s fishery resources and bearing significant ecological and socioeconomic importance. These EBUSs are primarily influenced and sustained by seasonal equatorward wind patterns. Along the Atlantic coast of Morocco, there are two distinct and persistently occurring upwelling patterns: a robust one to the south of (26°N) and a weaker one to the north. In this study, we present a coastal upwelling (transport) index based on combined contributions from both Ekman and Geostrophic transports, complemented by a recently refined thermal upwelling index based on sea surface temperature (SST). The seasonality patterns of these indices align with earlier research findings, revealing a sequence of wind-to-chlorophyll-to-SST lag relationship at all latitudes (24°N, 27°N and 32°N) during the period from 1993 to 2021. Subsequently, the two indices and Chlorophyll-a signature and three potential basin-scale driving factors, the North Atlantic Oscillation (NAO), the Azores High and the East Atlantic Oscillation (EAO) are analyzed to explore the interannual variability of the upwelling system and connect them to those of the prevailing wind patterns. Our analysis reveals three prominent periodicity bands: one near-decadal cycle spanning 8–10 years and two interannual cycles of 4–5 years and 2–3 years. It appears that the interannual bands are influenced by variations in the amplitude of the Azores high center pressure and are associated with the EAO, while the near-decadal cycles may be linked to the NAO. Furthermore, our examination of extreme events suggests that high (low) upwelling years tend to coincide with low (high) EAO years.

Initial atmospheric conditions control transport of volcanic volatiles, forcing and impacts

Abstract. Volcanic eruptions impact the climate and environment. The volcanic forcing is determined by eruption source parameters, including the mass and composition of volcanic volatiles, eruption season, eruption latitude, and injection altitude. Moreover, initial atmospheric conditions of the climate system play an important role in shaping the volcanic forcing and response. However, our understanding of the combination of these factors, the distinctions between tropical and extratropical volcanic eruptions, and the co-injection of sulfur and halogens remains limited. Here, we perform ensemble simulations of volcanic eruptions at 15 and 64° N in January, injecting 17 Mt of SO2 together with HCl and HBr at 24 km altitude. Our findings reveal that initial atmospheric conditions control the transport of volcanic volatiles from the first month and modulate the subsequent latitudinal distribution of sulfate aerosols and halogens. This results in different volcanic forcing, surface temperature and ozone responses over the globe and Northern Hemisphere extratropics (NHET) among the model ensemble members with different initial atmospheric conditions. NH extratropical eruptions exhibit a larger NHET mean volcanic forcing, surface cooling and ozone depletion compared with tropical eruptions. However, tropical eruptions lead to more prolonged impacts compared with NH extratropical eruptions, both globally and in the NHET. The sensitivity of volcanic forcing to varying eruption source parameters and model dependency is discussed, emphasizing the need for future multi-model studies to consider the influence of initial conditions and eruption source parameters on volcanic forcing and subsequent impacts.

Robust design of turbine blades with friction contacts in the presence of multiple response levels

Dry friction damping is a widely used solution to mitigate vibrations of turbine blades. At design stage, the computation of the forced response of assemblies of bodies in contact (whose relative motion could result in dry friction damping) could give non-unique solutions due to the possibility of having different static equilibria. Infinite possible vibratory levels in a range are hence possible. A desirable condition for designers is to deal with systems whose response boundaries are not far from each other, i.e. with a low scatter in the response. For systems with multiple vibration levels, the notion of robustness (a robust system has a small response scatter, and viceversa), is particularly important.A robust design is hence needed for such assemblies. Once a design parameter is identified, two possible approaches are possible to accomplish this task.The so-called manual approach explores a certain number of values of the design parameter belonging to a certain interval, and chooses the most robust configuration among those calculated. This computation could result in a huge effort if the number of considered values of the design parameter is high.To overcome this issue, a second approach is here proposed. It is based on a Nested Optimization Algorithm (NOA), which consists in two levels of optimization in order to directly find the most robust configuration in the considered range for the design parameter.In this paper, NOA is applied to a particular test case consisting in a lumped-parameter system simulating three blades with two UPDs interposed among them. Such a system provides the necessary coupling between different contact interfaces necessary to obtain multiple response levels. In addition, it is useful to investigate the mutual interaction among different UPDs.Results of NOA are presented together with the results of the manual approach in order to give a validation of the double optimization. Dependence of the response scatter from the contact states of the interfaces is also investigated.

An Efficient Propagation Approach to Forcing Softwood Shoots from Epicormic Buds and Subsequent Rooting of Paulownia elongata S. Y. Hu.

The current research describes the multiplication of Paulownia elongata S. Y. Hu, a timber plant, through the forcing of softwood shoots from epicormic buds under glasshouse conditions in spring and fall seasons. Different growth media were used to compare their effect on the forcing potential of epicormic buds. For this, 25-30-cm-long and 1.2-2-cm-diameter stem segments taken from the lower juvenile portion of a mother plant were placed horizontally in flat trays containing media, i.e., sterilized well-moistened sand, peat moss, perlite, and vermiculite individually. Furthermore, 4-6-cm-long forced softwood shoots were detached and treated with various concentrations of IBA (indole-3-butyric acid) and NAA (α-naphthyl acetic acid) either individually or in combinations for subsequent rooting. The response of shoot forcing was better in spring as compared to fall in terms of shoot length (cm), and number of shoots or leaves; however, an earlier bud break was observed during fall after 30 days of the initial experiment. The use of peat moss and vermiculite proved to be equally suitable for early bud break in both seasons, whereas in terms of shoot and leaf number as well as the shoot length (cm), the best outcome was observed in sand. Best rooting was observed at 3 gL-1 IBA + 3 gL-1 NAA in terms of root number per shoot, root length (cm), and days to root initiation while using sand as the growth medium after 50 days of the rooting experiment. The successfully established plantlets were further shifted to soil at Botanical Garden, University of the Punjab, Lahore, Pakistan, exhibiting an 87.5% survival rate. On the basis of the results obtained, it may be concluded that reasonable softwood shoot forcing in P. elongata may further be exploited for its mass scale nursery propagation as well as use in future in vitro studies.

Correlation and response of astronomical forcing in lacustrine deposits of the middle jurassic, sichuan basin, southwest China

The astronomical cycle characteristics of Mesozoic lacustrine fine-grained sedimentary rocks play a crucial role in understanding the formation environment of such sediments. The fine-grained sedimentary rocks of the Middle Jurassic Lianggaoshan Formation in the Sichuan Basin, China, constitute a significant lacustrine deposit. Previous research has primarily focused on its reservoir characteristics, with limited understanding of the relationship between lithofacies changes and astronomical cycles. To fill this knowledge void, we provide a continuous lacustrine core record of approximately 260 m from the XY-4 well, spanning the Lianggaoshan Formation in the Eastern Sichuan Basin. Initially, we categorized it into eight lithofacies types and established a lithologic ranking sequence based on this classification. Through time-series analysis, we identified the 405 Kyr long eccentricity cyc lecycle, 125 Kyr short eccentricity cycle, obliquity, and precession cycle. We emphasize the significance of the 125 Kyr short eccentricity cycle as the primary controlling factor during the deposition of the Lianggaoshan Formation. Subsequently, based on the 405 Kyr long eccentricity cycle, we established an age model for astronomical tuning, creating an astronomical age scale. The calculated sedimentation interval for the Lianggaoshan Formation ranges from 170.00 Ma to 172.74 Ma, spanning a total duration of 2.74 Ma. Meanwhile, the sedimentation interval for the Lower Liang 2 Submember is determined to be from 171.54 Ma to 172.52 Ma, lasting 0.98 Ma. Further comparison of TOC content and mineral composition with the orbital cycles reveals that TOC content and clay mineral content exhibit in-phase variations with the 125 Kyr short eccentricity. This characteristic contradicts the features of Cenozoic continental basins but aligns consistently with the characteristics of the Middle Triassic in North China. In contrast, silica minerals and carbonate minerals display anti-phase variations with the 125 Kyr short eccentricity. Different lithofacies demonstrate distinct responses to orbital cycles. Lithofacies characterized by higher organic matter content generally develop during the half-period with the maximum eccentricity. In contrast, lithofacies with lower organic matter content tend to occur during the half-cycle associated with the minimum eccentricity. Finally, based on the integrated analysis of lithological characteristics and astronomical cycles, we established two sedimentary modes: “Seasonally Pronounced Type” corresponding to the maximum eccentricity and “Seasonally Obscure Type” corresponding to the minimum eccentricity.

Effect of boundary conditions on the low‐velocity impact damage mechanism of fiber metal laminate

AbstractThe boundary condition is a very important factor when characterizing the impact performance of a material or a structure. However, its effect on fiber metal laminate (FML) has been rarely mentioned. In the present investigation, three levels of low‐velocity impact tests were conducted on the glass fiber reinforced aluminum laminate (Glare) under two different boundary conditions, one was that defined in ASTM D7136 and another one was self‐designed that has the same constraint area but different constraint degree. One basis of the experiments, finite element analyses were performed to gain a deeper understanding of the different damage mechanisms. With which another three boundary conditions were investigated for further considering the effect of constraint areas on both the impact and non‐impact sides, including that defined in another commonly used standard ASTM D5628 and two self‐designed cases. It was indicated that the boundary conditions influenced less the force and energy responses of Glare laminate, regardless of the impact damage levels, and hardly on the damage behavior as well when perforation was encountered. However, influences were obtained under lower and intermediate damage levels, and it was the constraint area on the rear side and constraint degree that played the dominant roles, respectively. The results achieved can provide suggestions for reasonably evaluating the low‐velocity impact performance of FML.Highlights Comparisons were made between the low‐velocity impact behavior of Glare laminates under five different boundary conditions. Boundary conditions influenced hardly on maximum impact force and energy absorbed ratio, but evidently on damage behavior. Constraint area and constraint degree governed damage mechanism under lower and intermediate impact energies, respectively. Influence of boundary conditions on damage behavior disappeared when the impact energy was enough to perforate Glare laminate.

Elevation-dependent warming: observations, models, and energetic mechanisms

Abstract. Observational data and numerical models suggest that, under climate change, elevated land surfaces warm faster than non-elevated ones. Proposed drivers of this “elevation-dependent warming” (EDW) include surface albedo and water vapour feedbacks, the temperature dependence of longwave emission, and aerosols. Yet the relative importance of each proposed mechanism both regionally and at large scales is unclear, highlighting an incomplete physical understanding of EDW. Here we expand on previous regional studies and use gridded observations, atmospheric reanalysis, and a range of climate model simulations to investigate EDW over the historical period across the tropics and subtropics (40° S to 40° N). Observations, reanalysis, and fully coupled models exhibit annual mean warming trends (1959–2014), binned by surface elevation, which are larger over elevated surfaces and broadly consistent across datasets. EDW varies by season, with stronger observed signals in local winter and autumn. Analysis of large ensembles of single-forcing simulations (1959–2005) suggests historical EDW is likely a forced response of the climate system rather than an artefact of internal variability and is primarily driven by increasing greenhouse gas concentrations. To gain quantitative insight into the mechanisms contributing to large-scale EDW, a forcing–feedback framework based on top-of-atmosphere energy balance is applied to the fully coupled models. This framework identifies the Planck and surface albedo feedbacks as being robust drivers of EDW (i.e. enhancing warming over elevated surfaces), with energy transport by the atmospheric circulation also playing an important role. In contrast, water vapour and cloud feedbacks along with weaker radiative forcing in elevated regions oppose EDW. Implications of the results for understanding future EDW are discussed.

Analytical solution for forced vibration response of rectangular thin plates attached by straight and curved acoustic black hole beams based on symplectic and impedance method

In recent years, due to the excellent vibration reduction performance of the acoustic black hole (ABH), its application in engineering has become increasingly widespread. This paper proposes an analytical method which combines the symplectic method with the impedance method, for solving the forced response of the rectangular thin plates attached by the straight and curved ABH beams. The ABH beams and plate are connected by a short bar. Firstly, the impedance method is used to obtain the dynamic stiffness of the coupling end of the ABH beam. Secondly, the symplectic method is used to obtain analytical waves of the plates. By utilizing the relationship between force and displacement at plate-beam junction, the dynamic stiffness of the plate at the coupling point can be obtained. Finally, based on wave propagation analysis, the forced vibration response of the hybrid system are obtained. The numerical examples compared the calculation results of this method with the finite element method. The results show that the proposed method can effectively predict the forced response of the hybrid system considered in this paper. Then, the influence of the relative position between the coupling point and the excitation point on the vibration reduction effect was analyzed. This method is analytical, with accurate results and high computational efficiency.

Piperine enhances contractile force in slow- and fast-twitch muscle.

Piperine has been shown to bind to myosin and shift the distribution of conformational states of myosin molecules from the super-relaxed state to the disordered relaxed state. However, little is known about the implications for muscle force production and potential underlying mechanisms. Muscle contractility experiments were performed using isolated muscles and single fibres from rats and mice. The dose-response effect of piperine on muscle force was assessed at several stimulation frequencies. The potentiation of muscle force was also tested in muscles fatigued by eccentric contractions. Potential mechanisms of force potentiation were assessed by measuring Ca2+ levels during stimulation in enzymatically dissociated muscle fibres, while myofibrillar Ca2+ sensitivity was assessed in chemically skinned muscle fibres. Piperine caused a dose-dependent increase in low-frequency force with no effect on high-frequency force in both slow- and fast-twitch muscle, with similar relative increases in twitch force, rate of force development and relaxation rate. The potentiating effect of piperine on low-frequency force was reversible, and piperine partially recovered low-frequency force in fatigued muscle. Piperine had no effect on myoplasmic free [Ca2+] levels in mouse muscle fibres, whereas piperine substantially augmented the force response to submaximal levels of [Ca2+] in rat MyHCII fibres and MyHCI fibres along with a minor increase in maximum Ca2+-activated force. Piperine enhances low-frequency force production in both fast- and slow-twitch muscle. The effects are reversible and can counteract muscle fatigue. The primary underlying mechanism appears to be an increase in Ca2+ sensitivity. KEY POINTS: Piperine is a plant alkaloid derived from black pepper. It is known to bind to skeletal muscle myosin and enhance resting ATP turnover but its effects on contractility are not well known. We showed for the first time a piperine-induced force potentiation that was pronounced during low-frequency electrical stimulation of isolated muscles. The effect of piperine was observed in both slow and fast muscle types, was reversible, and could counteract the force decrements observed after fatiguing muscle contractions. Piperine treatment caused an increase in myofibrillar Ca2+ sensitivity in chemically skinned muscle fibres, while we observed no effect on intracellular Ca2+ concentrations during electrical stimulation in enzymatically dissociated muscle fibres.

Steady but model dependent Arctic amplification of the forced temperature response in 21st century CMIP6 projections

We examine sources of uncertainty in projections of Arctic amplification (AA) using the CMIP6 multi-model (MM) ensemble and single model initial-condition large ensembles of historical and future scenario simulations. In the CMIP6 MM mean, the annual mean AA ratio is steady at approximately 2.5, both in time and across scenarios, resulting in negligibly small scenario uncertainty in the magnitude of AA. Deviations from the steady value can be found at the low and high emission scenarios due to different root causes, with the latter being mostly evident in the summer and autumn seasons. Best estimates of model uncertainty are at least an order of magnitude larger than scenario uncertainty in CMIP6. The large ensembles reveal that irreducible internal variability has a similar magnitude to model uncertainty for most of the 21st century, except in the lowest emission scenario at the end of the 21st century when it could be twice as large.

Changes in the North Atlantic Oscillation over the 20th century

Abstract. The North Atlantic Oscillation explains a large fraction of the climate variability across the North Atlantic from the eastern seaboard of North America across the whole of Europe. Many studies have linked the North Atlantic Oscillation to climate extremes in this region, especially in winter, which has motivated considerable study of this pattern of variability. However, one overlooked feature of how the North Atlantic Oscillation has changed over time is the explained variance of the pattern. Here we show that there has been a considerable increase in the percentage of variability explained by the North Atlantic Oscillation (NAO) over the 20th century from 32 % in 1930 to 53 % by the end of the 20th century. Whether this change is due to natural variability, a forced response to climate change, or some combination remains unclear. However, we found no evidence for a forced response from an ensemble of 50 Coupled Model Intercomparison Project Phase 6 (CMIP6) models. These models did all show substantial internal variability in the strength of the North Atlantic Oscillation, but it was biased towards being too high compared to the reanalysis and with too little variation over time. Since there is a direct connection between the North Atlantic Oscillation and climate extremes over the region, this has direct consequences for both the long-term projection and near-term prediction of changes to climate extremes in the region.

Coupled modal characteristics of a bladed rotor bearing system under aerodynamic and rotor excitations: Modelling and numerical study

Bladed Rotor Bearing System is considered in the coupled vibration analysis among blades and the rotor system. The governing equations of motion are derived based on Lagrange’s equation, which accounts for the coupled vibrational modes. The model is discretised based on the Galerkin finite element method. A comparative analysis on the influence of uniform and pre-twisted blade configurations on the BRBS and on individual blades is carried out. Free vibration analysis for various blade geometry configurations is studied and results show that natural frequencies of the blades are reduced in the presence of pre-twist whereas the same is increased with double-taper. The Campbell diagram revealed the presence of frequency veering among the blades and rotor loci of natural frequencies for a specific blade configuration. The influence of aerodynamic and external excitations on the blades and the rotor, respectively, are considered in the forced response analysis, where the resulting effects of both the excitations on the individual blades and the BRBS for different blade configurations are studied.

Analytical solution of forced vibration of rectangular plates with part through surface crack based on wave propagation method

An analytical wave propagation framework is developed in this study for steady state forced vibration of plates with part through surface cracks for the first time. Rectangular thin plates with partial-width and full-width cracks are considered. The analytical waves are obtained by solving the dual equations of the plate established considering the line–spring model (LSM) of crack. The dual equations formed here are characterized by simultaneously solving kinematic variables and their dual dynamic variables. Both conventional and refined LSMs are considered. Two ways are proposed to generate the system equation in wave space based on the relationships of wave propagation, wave reflection and wave scattering. Compared with the traditional methods, most of them can only give exact analytical solutions under the condition of opposite-side simply supported boundaries, the developed analysis framework can treat arbitrary combinations of simple boundary condition of the cracked plate. Comparisons of results of the proposed method with those from the literature and finite element method (FEM) validate the effectiveness of the proposed method. A series of parametric studies for investigating the effects of length, position and depth of crack on the forced response of cracked plate are also presented. The proposed framework are effective for predicting the forced responses and natural frequencies of thin plates with part-through surface cracks.

Finite element analysis of locally strengthened stainless-steel tube under lateral impact loading

In this study, a Finite Element (FE) model of locally strengthened high-strength stainless-steel tube subjected to lateral impact loads is established using LS-DYNA to investigate its dynamic behaviours. The accuracy of the FE results is verified by comparing with the test results. The impact force, bending moment, stress and strain responses as well as the internal energy dissipation histories of the strengthened tube are analysed during the entire impact process. The results indicate that the impact resistance of the strengthened tube is obviously enhanced as compared to hollow stainless-steel tube. Furthermore, parametric studies are conducted to reveal the influence of axial compressive force, impact position, impact velocity and material strength on the impact behaviour of the strengthened tube. The results show that the application of axial compressive force reduced the impact force and increased the deformations of the strengthened tube. The impact resistance of the strengthened tube performed an increasing trend when moving the impact position towards the support and increasing the material strength. In addition, the increase of impact velocity significantly reduced the impact duration. Finally, design recommendations and process were proposed to facilitate the application of locally strengthened tube.