Shock Spectrum Research Articles

Probing particle acceleration in Abell 2256: From 16 MHz to gamma rays

Merging galaxy clusters often host spectacular diffuse radio synchrotron sources. These sources can be explained by a non-thermal pool of relativistic electrons that are accelerated by shocks and turbulence in the intracluster medium. The origin of the pool and details of the cosmic ray transport and acceleration mechanisms in clusters are still open questions. Due to the often extremely steep spectral indices of diffuse radio emission, it is best studied at low frequencies. However, the lowest frequency window available to ground-based telescopes (10−30 MHz) has remained largely unexplored as radio frequency interference and calibration problems related to the ionosphere become severe. Here, we present LOFAR observations from 16 to 168 MHz targeting the famous cluster Abell 2256. In the deepest-ever images at decametre wavelengths, we detected and resolved the radio halo, radio shock, and various steep spectrum sources. We measured standard single power-law behaviour for the radio halo and radio shock spectra, with spectral indices of α = −1.56 ± 0.02 from 24 to 1500 MHz and α = −1.00 ± 0.02 from 24 to 3000 MHz, respectively. Additionally, we found significant spectral index and curvature fluctuations across the radio halo, indicating an inhomogeneous emitting volume. In contrast to the straight power-law spectra of the large-scale diffuse sources, the various AGN-related sources showed extreme steepening towards higher frequencies and flattening towards low frequencies. We also discovered a new fossil plasma source with a steep spectrum between 23 and 144 MHz, with α = −1.9 ± 0.1. Finally, by comparing radio and gamma-ray observations, we ruled out purely hadronic models for the radio halo origin in Abell 2256, unless the magnetic field strength in the cluster is exceptionally high, which is unsupportable by energetic arguments and inconsistent with the knowledge of other cluster magnetic fields.

Current spectrum and outcomes of infarct-related cardiogenic shock: insights from the CULPRIT-SHOCK registry and randomized controlled trial.

We analysed consecutive patients with acute myocardial infarction complicated by cardiogenic shock (CS) who were enrolled into the CULPRIT-SHOCK randomized controlled trial (RCT) and those with exclusion criteria who were included into the accompanying registry. In total, 1075 patients with infarct-related CS were screened for CULPRIT-SHOCK in 83 specialized centres in Europe; 369 of them had exclusion criteria for the RCT and were enrolled into the registry. Patients were followed over 1 year. The mean age was 68 years and 260 (25%) were women. 13.5%, 30.9%, and 55.6% had one-vessel, two-vessel, and three-vessel coronary artery disease (CAD), respectively. Significant left main (LM) coronary artery stenosis was present in 8.0%. 54.2% of the patients had cardiac arrest before admission. Thrombolysis in myocardial infarction (TIMI) 3 patency of the infarct vessel after percutaneous coronary intervention was achieved in 83.6% of all patients. Mechanical circulatory support was applied in one-third of patients. Total mortality after 30 days and 1 year was 47.6% and 52.9%. Mortality after 1 year was highest in patients with LM coronary artery stenosis (63.5%), followed by three-vessel (56.6%), two-vessel (49.8%), and one-vessel CAD (38.6%), respectively. Mechanical complications were rare (21/1008; 2.1%) but associated with a high mortality of 66.7% after 1 year. In specialized centres in Europe, short- and long-term mortality of patients with infarct-related CS treated with an invasive strategy is still high and mainly depends on the extent of CAD. Therefore, there is still a need for improvement of care to improve the prognosis of infarct-related CS.

Numerical modeling of time dependent Diffusive Shock Acceleration

Motivated by cosmic ray (CR) re-acceleration at a potential Galactic Wind Termination Shock (GWTS), we present a numerical model for time-dependent Diffusive Shock Acceleration (DSA). We use the stochastic differential equation solver (DiffusionSDE) of the cosmic ray propagation framework CRPropa3.2 with two modifications: An importance sampling module is introduced to improve statistics at high energies in order to keep the simulation time short. An adaptive time step is implemented in the DiffusionSDE module. This ensures to efficiently meet constraints on the time and diffusion step, which is crucial to obtain the correct shock spectra. The time evolution of the spectrum at a one-dimensional planar shock is verified against the solution obtained by the grid-based solver VLUGR3 for both energy-independent and energy-dependent diffusion. We show that the injection of pre-accelerated particles can lead to a broken power law spectrum in momentum if the incoming spectrum of CRs is harder than the re-accelerated spectrum. If the injected spectrum is steeper, the shock spectrum dominates at all energies. We finally apply the developed model to the GWTS by considering a spherically symmetric shock, a spiral Galactic magnetic field, and anisotropic diffusion. The time-dependent spectrum at the shock is modeled as a basis for further studies.

Dynamic Response Analysis of Reinforced Column Subjected To Shock Wave Loading

This study focuses on the dynamical response of reinforced concrete members subjected to shock-wave loading, which can cause catastrophic damage to structures. The effects of high strain rate loading and lateral confinement on the member’s behavior are considered in the analysis. The Moment-Curvature (M-ϕ) relations are assessed using stress block equilibrium at yield and ultimate state, and an analytical model is developed that integrates the high strain rate material behavior to predict the peak deflection of the structural member. The study evaluates the dynamic response of the member using a simplified model based on single degree of freedom (SDOF) idealization, and the response of the member in elastic and elastic-plastic phases is modelled using the bilinear resistance function. The governing equation of motion is explained using the Newmark-Beta algorithm, and the shock spectrum predicting the maximum deflection is developed by varying the load duration and magnitude. Additionally, a Finite Element (FE) model is developed to provide a more detailed understanding of the member’s behavior under shock loading. The results obtained from the FE model are compared with the analytical deflection for extreme combinations of load duration and magnitude. The study provides valuable insights into the behavior of reinforced concrete members under extreme loads, which can help structural designers in predicting and design structures that can withstand such loading conditions. The results can also be used in the development of building codes and standards to improve the safety and resilience of structures subjected to shock-wave loading.

Recognizing patients as candidates for temporary mechanical circulatory support along the spectrum of cardiogenic shock

Abstract A growing body of evidence indicates that the benefits of temporary mechanical circulatory support (tMCS) in patients with cardiogenic shock (CS) is dependent on its aetiology and timing of implantation. As such, appropriate diagnosis, screening, selection, and treatment is crucial to achieving good outcomes with tMCS. Here, the latest guidance on CS phenotypes and diagnostics for correctly identifying tMCS candidates is discussed. This includes comprehensive overviews of patient screening with attention given to differences in CS presentation between the sexes, and contraindications for mechanical circulatory support.

SCAI classification, the importance of its dynamic reclassification in the first 24 hours and the impact of risk modifiers in cardiogenic shock admissions

Abstract Introduction The Society for Cardiovascular Angiography and Interventions (SCAI) shock stage classification has been proposed as a simple, easily applied framework to stratify mortality risk across the spectrum of cardiogenic shock (CS) severity. This categorization has been recently refined (2022) to incorporate the continuum dynamic trajectory of the disease, as well as other risk modifiers. The aims of this study were: 1) to validate the SCAI classification at admission in a cohort of patients admitted to the cardiac intensive care unit (CICU) due to CS; 2) evaluate the prognostic impact of SCAI stage variation during the first 24h of admission; 3) evaluate the prognostic impact of other risk modifiers. Methods We retrospectively analyzed patients consecutively admitted to the CICU with established CS (SCAI C and above) from all causes, from January 2017 to November 2022. SCAI staging was assessed at diagnosis and after 24 hours. The primary outcome was 30-day mortality. Results A total of 208 patients (66±16 years, 67% male) were included. Overall, 53% had an acute myocardial infarction, 34% were admitted due to decompensation of chronic heart failure, and 29.1% had a cardiac arrest. The proportion of patients in SCAI stage C to E at the time of diagnosis was 69% (n=143), 25% (n=52), and 6% (n=13), respectively. 30-day mortality increased across SCAI categories (p<0.001 – figure 1.1). After the first 24 hours, 34 (%) of patients improved SCAI category, 113 (%) remained in the same class, and 45 (%) worsened, with a 30-day mortality of 18%, 34%, and 62%, respectively (p<0.001 – figure 1.2). Risk modifiers also carried prognostic significance (figure 1.3). 30-day mortality was significantly higher in patients with acute myocardial infarction vs. other etiologies (52% vs. 32%; p=0.002), acute CS vs. acute-on-chronic CS (47% vs. 33%; p=0.034), and cardiac arrest (56% vs. 37%; p=0.005). Conclusion Early changes in SCAI classification reflect the dynamic nature of CS patients while retaining significant prognostic discrimination. 24h SCAI re-staging together with risk modifiers may be valuable in readjusting therapeutic strategies aiming at shock reversal.

Validation of the BALLAR score for predicting 30-day mortality in patients requiring Impella monotherapy

Abstract Background The BALLAR score was published in 2021 with the aim of allowing clinicians to calculate 30-day mortality quickly and easily for patients requiring left-sided Impella monotherapy. The points are assigned as follows: Base Excess (mmol/L): < -2: 2 points, ≥ -2: 0 points ALbumin (mmol/litre): <25: 6 points, 25 - 34.9: 3 points, >34.9: 0 points LActate (mmol/litre): <2: 0 points, 2 – 4.9: 1 Point, >4.9: 4 Points Renal function - Creatinine Clearance (ml/min): <30: 6 points, 30 - 59.9: 4 points, 60 - 89.9: 1 point, >89.9: 0 points The scoring system performed well on its initial training cohort but had not previously been validated. Purpose To validate the BALLAR score using a predominantly external validation cohort requiring left-sided Impella therapy only, for any indication. Methods The data required to calculate the BALLAR score was retrospectively acquired for 89 patients. 39 patients were from our own UK tertiary centre, 7 from our sister hospital, and 43 from centres across the United States from the Impella Quality (IQ) assurance program. Results For the entire validation cohort of 89 patients, the BALLAR score showed both excellent discrimination and calibration statistics. The area under the receiver-operator characteristic (ROC) curve was 0.91 (0.84–0.98) (Figure 1), the Brier score was 0.11 versus a Naïve classifier of 0.23, the calibration slope was 0.92 calibration with Spiegelhalter’s Z-statistic of 0.98 (p=0.323, Figure 2). For the external validation cohort of patients, the discrimination remained excellent with the area under the ROC curve of 0.88 (0.79-0.98). The Brier score remained better than a naïve classifier at 0.15, but the calibration slope was unsurprisingly worse at 0.73 with a Spiegelhalter’s Z statistic of 2.07 (p=0.04). The negative predictive value of a BALLAR score ≤5 was 94%, and the positive predictive value was 100% of a BALLAR score > 12, highlighting the rapid escalation of mortality risk in patients in the mid-zone of the shock spectrum. Conclusions The BALLAR score maintains high discriminatory ability when applied to a validation cohort of patients requiring left-sided Impella monotherapy for any indication. Further prospective work is underway, including app development, to assess the clinical utility of the BALLAR score as a means of categorising patient risk.Image 1Image 2

Damage boundary spectrum of pelvis-lumbar spine of seated human under vertical wide-band shock environment

The assessment methods of personnel damage under real shock environments are still an issue. In this paper, a damage boundary for vibration-impact injury in a wide range of frequency domain based on pseudo-velocity shock spectrum (PVSRS) is first proposed with numerical simulation. A high-fidelity three-dimensional finite element (FE) model of pelvis-lumbar spine (P-LS) that the vulnerable organs of seated human under vertical impact conditions, was developed and validated. The random and complex impact loads in real environments were simplified to a series of sinusoidal accelerations with a single frequency and within one period, next loading those equivalent loads on P-LS FE model in vertical direction for batch computing. The results indicated that there is a certain critical failure load that can cause initial damage to P-LS for a specific single frequency. The injury patterns of P-LS show significant frequency sensitivity. The P-LS damage boundary can be obtained from the envelope curve of critical failure loads in PVSRS, which is a V-shaped curve and the frequency corresponding to the trough (18 Hz) is the first natural frequency of the coupled P-LS structures. The asymptote lines of damage boundary are highly consistent with that of theoretical results. The damage boundaries after classifying and standardizing, which rationality in wideband is verified by underwater explosion test data, show more comprehensive and advanced potentials for engineering application.

Shock Raman spectra and structural transformation of powdered TKX-50 by the plate impact experiments combined with real-time Raman detection

As an energetic material of great interest, the work capacity of dihydroxylammonium 5,5′-bistetrazole-1,1′-diolate (TKX-50) has been questioned recently. Although some research groups have explored the reasons for the low working ability of TKX-50, the plane impact experiment on powdered TKX-50 is obviously closer to the practical application, and the conclusions based on this are more guiding. Hence, we performed shock Hugoniot measurements of powdered TKX-50 between 5.65 and 16.29 GPa. The plane impact experiments of powdered TKX-50 were carried out and the shocked Raman spectra were collected. By Raman spectroscopy analysis, a new peak of powdered TKX-50 was found between 19.47 GPa and 24.96 GPa, which may be caused by decomposition/phase transition and was related with the low work capacity.

Analysis of seismically‐isolated two‐block systems using a multi–rocking‐body dynamic model

AbstractA novel multibody rocking model is developed to investigate the dynamic response of two stacked rigid blocks placed on a linear base isolation device. The model is used to investigate the dynamic response of a realistic statue‐pedestal system subject to pulse‐like ground motions. The analysis shows that, in general, base isolation increases the safety level of the rocking system. However, for large period pulses or small size blocks, the isolator can amplify the ground motion, resulting in a lower minimum overturning acceleration than for the nonisolated system. Further, the amplification or shock spectrum of a linear mass‐dashpot‐spring oscillator, was found to be the reciprocal of the minimum nondimensional overturning acceleration of the investigated rocking system. Novel rocking spectra are obtained by normalizing the frequency of the pulse by the frequency of the isolator. The analysis also demonstrates how the dynamic response of the two stacked blocks is equivalent to that of a single‐block configuration coincident with the whole system assumed monolithic or the upper block alone, whichever is more slender.

Damage characteristics of cabin in navigational state subjected to near-field underwater explosion

An arbitrary Lagrange-Euler (ALE) method is used to establish a numerical model for the fluid-structure interaction of near-field underwater explosion while cabins are under sailing conditions. First, the ALE method is used to calculate shock wave and bubble pulsation loads of free field underwater explosion. The results show that the values of shock wave peak, bubble fluctuation period, maximum radius of bubble are similar to empirical formula calculation, which verifies the accuracy of ALE method in calculating explosion loads. On this basis, from the aspects of local damage, longitudinal strength and impact environment of cabin structure, the dynamic response characteristics of cabin structure under the coupling of impact and bubble load at a certain speed and different explosion distance are analyzed and compared with that at static condition. The results show that compared with the static state, the local damage is weakened, the longitudinal strength is increased, the difference of longitudinal strength between navigation and static state is 7%–12%, the shock spectrum value of the compartment corresponding to the explosion source is reduced, and the shock spectrum value of the adjacent compartment is slightly increased; When the cabin is sailing, the increase of the explosion distance within the maximum radius of bubble pulsation increases the action area of bubble pulsation load, and the effect of bubble pulsation load is enhanced, but the coupling enhancement of explosion load is difficult to appear, so that the damage of cabin structure is reduced. The working condition of the cabin suffering from near-field underwater explosion damage under the navigational state analyzed in this paper is closer to the reality, and more truly reflects the process of underwater explosion shock wave and bubble load coupling applied to cabins, which lays a foundation for the fuze warhead coordination design and relevant parameter setting when the torpedo and other underwater weapons give full play to the damage efficiency.

Association Between Shock Etiology and 5-Year Outcomes After Venoarterial Extracorporeal Membrane Oxygenation

BackgroundOutcomes of patients requiring venoarterial extracorporeal membrane oxygenation (VA-ECMO) vary greatly by etiology, but large studies that incorporate the spectrum of shock supported with ECMO are rare. ObjectivesThe purpose of this study was to describe the etiology-related outcome of patients with shock supported with peripheral VA-ECMO. MethodsAll consecutive adults with peripheral VA-ECMO between January 2015 and August 2018 at Pitié-Salpêtrière Hospital (Paris, France) were included in this retrospective observational study. The indication for VA-ECMO was cardiogenic shock. Rates of hospital death and neurological, renal, and pulmonary complications were evaluated according to etiology. ResultsAmong 1,253 patients, hospital and 5-year survival rates were, respectively, 73.3% and 57.3% for primary graft failure, 58.6% and 54.0% for drug overdose, 53.2% and 45.3% for dilated cardiomyopathy, 51.6% and 50.0% for arrhythmic storm, 46.8% and 38.3% for massive pulmonary embolism, 44.4% and 42.4% for sepsis-induced cardiogenic shock, 37.9% and 32.9% for fulminant myocarditis, 37.3% and 31.5% for acute myocardial infarction, 34.6% and 33.3% for postcardiotomy excluding primary graft failure, 25.7% and 22.8% for other/unknown etiology, and 11.1% and 0.0% for refractory vasoplegia shock. Renal failure requiring hemodialysis developed in 50.0%, neurological complications in 16.0%, and hydrostatic pulmonary edema in 9.0%. ConclusionsAlthough the outcome differs depending on etiology, this difference is related more to the severity of the situation associated with the cause rather than the cause of the shock per se. Survival to 5 years varied by cause, which may reflect the natural course of the chronic disease and illustrates the need for long-term follow-up.

Harvesting energy from shock environments via functionally graded magneto-electro-elastic materials

Given the fact that the environmental kinetic energy may appear in the form of shock pulse excitation, this paper aims to investigate the response of a shock excited cantilever beam equipped with two symmetric functionally graded magneto-electro-elastic layers. To this end, employing a hybrid procedure including the Ritz method together with the geometric nonlinear Euler-Bernoulli beam theory, the coupled magneto-electro-mechanical reduced equations of motion are obtained. The model predictions are compared and successfully validated by those available in the literature. Having the vibration frequency of the system, which is obtained by the method of multiple time scales, the optimal duration maximizing the influence of shock pulse acceleration is predicted using the power shock spectrum introduced in this study for the first time. The results reveal that the harvested power maximizes when the system fundamental frequency becomes 1.36 times the equivalent shock frequency.

Clinical characteristics and laboratory parameters in differentiating dengue from other acute febrile illnesses

BackgroundDengue infection is one of the most common viral infections globally, with a broad spectrum of clinical manifestations, including hemorrhage and shock. Early diagnostic confirmation of dengue infection is essential, but some areas may not have the appropriate diagnostic tools while its clinical symptoms are similar to other diseases. We aim to determine some significant clinical characteristics and laboratory parameters in differentiating dengue from other causes of febrile.ResultsThis study included 527 dengue patients and 268 control patients. Multivariate analysis showed older age (OR = 12.11; 95% 5.42–26.63, p < 0.001), the absence of diarrhea (OR = 0.12; 95% CI 0.06–0.25, p < 0.001), leukopenia (OR = 13.35; 95% CI 4.99–38.71, p < 0.001), thrombocytopenia (OR = 7.12; 95% CI 2.37–21.38, p < 0.001), and normal ESR (OR = 3.03; 95% CI 1.54–5.96, p = 0.001) are significant parameters in differentiating dengue with excellence (AUC value of 0.96) and good fit of the model (p value = 0.8). The cut-off is two significant variables with a sensitivity of 91.4% and specificity of 87.5%.ConclusionsTwo or more clinical signs can help clinicians differentiate dengue from other acute febrile illnesses.

Barge Bow Force–Deformation Relationships for Bridge Impact-Resistant Design: Development and Assessment Using Shock Spectrum Approximation

Barge Bow Force–Deformation Relationships for Bridge Impact-Resistant Design: Development and Assessment Using Shock Spectrum Approximation

A unifying theory of jet screech

This paper describes the mechanism underpinning modal staging behaviour in screeching jets. An upstream-propagating subsonic guided-jet mode is shown to be active in all stages of screech. Axial variation of shock-cell spacing manifests in the spectral domain as a series of suboptimal peaks. It is demonstrated that the guided-jet mode may be energized by interactions of the Kelvin–Helmholtz wavepacket with not only the primary shock wavenumber peak, but also suboptimal peaks; interaction with suboptimals is shown to be responsible for closing the resonance loop in multiple stages of jet screech. A consideration of the full spectral representation of the shocks reconciles several of the classical models and results for jet screech that had heretofore been paradoxical. It is demonstrated that there are multiple standing waves present in the near field of screeching jets, corresponding to the superposition of the various waves active in these jets. Multimodal behaviour is explored for jets in a range of conditions, demonstrating that multiple peaks in the frequency spectra can be due to either changes in which peak of the shock spectra the Kelvin–Helmholtz wavepacket is interacting with, or a change in azimuthal mode, or both. The absence of modal staging in high-aspect-ratio non-axisymmetric jets is also explained in the context of the aforementioned mechanism. The paper closes with a new proposed theory for frequency selection in screeching jets, based on the observation that these triadic interactions appear to underpin selection of the guided-jet mode wavelength in all measured cases.

An analytical method for the dynamic response prediction and produced test modes generated by vibro-shock test benches

This article describes a methodology for the computational forecasting of dynamic characteristics and test modes, implemented by vibro-shock stands of explosive action. Vibro-shock stands are widely used in ground-based experimental testing of onboard equipment of spacecraft for non-stationary broadband impact arising from the operation of pyrotechnic separation means. The principle of operation of these stands is based on the excitation of an intense non-stationary broadband vibration mode using an explosive energy source in a system of elastic-inertial elements (resonator), affecting the test object. The presented analytical technique is used to predict the test modes implemented by the vibro-shock stand in the form of a shock spectrum and for pre-test calculations in order to adjust the characteristics of the stand, ensuring the implementation of the necessary test modes. The reliability of the calculation results performed according to this technique is confirmed by experimental data. Key words: dynamic stiffness, method of initial parameters, shock loading, pyrotechnic separation means, ground experimental development, vibro-shock strength, vibro-shock stands of explosive action.

Epidemiology and causes of cardiogenic shock.

Cardiogenic shock is a complex clinical syndrome of end-organ hypoperfusion due to impaired cardiac performance. Although cardiogenic shock has traditionally been viewed as a monolithic disorder predominantly caused by severe left ventricular dysfunction complicating acute myocardial infarction (AMI), there is increasing recognition of the diverse causes of cardiogenic shock and wide spectrum of clinical severity. The purpose of this review is to describe the contemporary epidemiology of cardiogenic shock, including trends in clinical outcomes and recent efforts to refine risk assessment. The incidence of cardiogenic shock among patients with AMI has remained remarkably stable at 3-10%; however, the proportion of cardiogenic shock cases related to AMI has decreased over time to ∼30%, while the proportion of cardiogenic shock cases due to acute decompensated heart failure has steadily increased. Estimated in-hospital mortality from cardiogenic shock in contemporary registries is approximately 30-40%, suggesting modest improvement in cardiogenic shock outcomes over the last decade. There is a wide spectrum of clinical severity among patients presenting with cardiogenic shock, which is described by the Society for Cardiovascular Angiography and Interventions clinical staging criteria. Improved clinical characterization and risk assessment of patients with cardiogenic shock may facilitate more effective clinical investigations of this morbid clinical syndrome.

Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces

This study presents a semi-analytical solution of the non-linear dynamic response, shock spectrum, and dynamic buckling of an imperfect angle-ply laminated composite plate under various types of in-plane pulse forces. The laminated composite plate is modeled using a higher-order shear deformation theory and von-Kármán geometric nonlinearity. The non-linear governing partial differential equations (PDEs) of imperfect laminated composite plates are derived via Hamilton’s principle. Using Galerkin’s method, the non-linear PDEs are transformed into non-linear algebraic equations for the static stability problems and non-linear ordinary differential equations for the dynamic problem such as dynamic response, shock spectrum, and dynamic buckling. The buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the composite plate is evaluated using the post-buckling analysis based on the Tsai-Wu failure criterion. The dynamic response and shock spectrum of the composite plate are determined via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the Tsai-Wu failure criterion. Dynamic buckling is to be characterized by dynamic load factor (DLF), which is represented as the ratio of the dynamic failure load to the static failure load. Based on the pulse/shock duration time, the pulse forces are divided into three loading regimes known as impulsive, dynamic, and quasi-static. The study revealed that the DLF values are &gt; 1, &lt; 1, and [Formula: see text]1 respectively for the case of impulsive, dynamic, and quasi-static loading regimes of pulse force. The influences of various types of in-plane pulse forces, amplitude and time duration of pulse forces, and amplitude of initial geometric imperfections on the non-linear dynamic response, shock spectrum, and dynamic buckling behavior of the laminated composite plate are addressed in detail. The results will help in the appropriate design of the laminated composite plate against dynamic buckling.

Nonlinear Response and Buckling of Imperfect Plates Under In-Plane Pulse Forces: A Semi-analytical Investigation

This study presents a semi-analytical solution of the nonlinear dynamic response, shock spectrum, and dynamic buckling of a simply supported imperfect plate under various types of in-plane pulse forces. Here, the plate is modelled based on higher-order shear deformation theory (HSDT) considering the von-Karman geometric nonlinearity. The governing nonlinear partial differential equations (NLPDEs) of the imperfect plates are developed via Hamilton’s principle. Using Galerkin’s method, the NLPDEs are converted into sets of nonlinear algebraic equations (NLAEs) for static stability problems and nonlinear ordinary differential equations (NLODEs) for dynamic problems. The critical buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the plate is evaluated using nonlinear static stability analysis based on the yield stress failure criterion. The dynamic response and shock spectrum of the plates are plotted via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the yield stress failure criterion. Dynamic load factor (DLF) is the ratio of dynamic failure load to static failure load. Based on the pulse duration time, the pulse forces are divided into three categories known as impulsive, dynamic, and quasi-static. In the case of impulsive, dynamic, and quasi-static loading regimes, DLF > 1, DLF < 1, and DLF $$\approx$$ 1, respectively. The results obtained from the current works will help in the appropriate design of the imperfect plates against dynamic buckling.