Nonlinear Dynamic Analysis Of Structures Research Articles

Optimization of materially nonlinear trusses subjected to dynamic loads

The structural optimization of trusses has been extensively studied over the past few decades. However, investigations incorporating material nonlinearity are still relatively scarce. The objective of this study is to propose a formulation for optimizing spatial truss structures, considering the material nonlinearity of the structure under dynamic loading. To address this problem, the Particle Swarm Algorithm (PSO) integrated into the Ansys program will be utilized for nonlinear dynamic structural analysis. To validate the optimization approach, a problem from the literature, considering material nonlinearity, will be analyzed. Additionally, will be compared the results obtained from the structural optimization considering and neglecting the material nonlinearity. This comparison aims to assess the real impact of material nonlinearity on optimization results.

Nonlinear dynamic analysis of ancient timber structures with rotary friction dampers

Nonlinear dynamic analysis of ancient timber structures with rotary friction dampers

A novel iterative algorithm for nonlinear inelastic dynamic analysis of truss structures; MCB-Spline+Sp time integration method

The focus of this work is on the development of a novel algorithm for the nonlinear dynamic analysis of structures. In the sake of a general and easy-to-implement solution method, the tangential stiffness matrix is calculated by combining the Cauchy-Riemann equations derived from the differentiation of complex functions and using the nodal displacement perturbation vector. An implicit direct time integration method based on a cubic B-Spline is integrated with the incremental-iterative method using a quadrature rule based on the interpolation of spline functions, which is referred to as the MCB-Spline+Sp time integration method. A step-by-step algorithm for developing a computer code to implement this method is provided. The effectiveness of the proposed approach is evaluated through several nonlinear time history analyses, which demonstrate its accuracy and efficiency by observing less computational efforts and fast convergence rate. Moreover, a comparison is made between the developed method and well-established techniques such as the Newmark and Standard-Bathe time integration methods in combination with the iterative Newton-Raphson method.

A reduced-order finite element formulation for the geometrically nonlinear dynamic analysis of viscoelastic structures based on the fractional-order derivative constitutive relation

A reduced-order finite element formulation for the geometrically nonlinear dynamic analysis of viscoelastic structures based on the fractional-order derivative constitutive relation

Nonlinear Dynamic Analysis of High-Strength Concrete Bridges under Post-Fire Earthquakes Considering Hydrodynamic Effects

This study employed the linear interpolation method to ascertain the curve relationship between the elastic modulus and stress of high-strength concrete C60 with temperature, and the nonlinear dynamic analysis of high-strength concrete bridge structures subjected to post-fire earthquake action at varying water levels was subsequently evaluated. It was established that both the hydrodynamic effects and the temperature effects have a considerable impact on the structural dynamic response of bridges. The presence of water has been observed to increase the dynamic response of pier structures. At water levels of 0 m and 10 m, the temperature effect results in a reduction in the fundamental frequencies of acceleration and displacement responses by 73.68% and a decrease in the fundamental frequency of stress responses by 83.33%. At a water level of 20 m, the fundamental frequencies of the acceleration, displacement, and stress responses decrease by 53.49%. In consideration of the acceleration and displacement at the pier top and stress at the pier base at a water depth of 10 m, the superposition of temperature effects and hydrodynamic effects results in an increase of 59.06% in acceleration, 25.93% in displacement, and 49.53% in stress than combination effects, respectively. At a water depth of 20 m, the superposition of temperature and hydrodynamic effects results in an increase of 92.82%, 100%, and 127.85% in acceleration, displacement, and stress, respectively. The combined effects of hydrodynamic and temperature effects cannot be described merely as a linear superposition of the two single actions. The research findings provide a significant theoretical basis for understanding the impact of multiple disasters, such as fires and earthquakes, on bridge structures.

Seismic hazard study for the duration of ground-motions triggered by intraslab earthquakes

This paper presents a probabilistic seismic hazard analysis for the duration of ground motions in Mexico City caused by intraslab earthquakes. The study implies establishing criteria to measure the duration of ground motions and developing predictive equations (GMPEs) for its estimation. Focus is placed on the relative significant duration, DSr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{Sr}$$\\end{document}, which is based on the accumulation of energy of ground motions. The study extends to the development of hazard curves that allow estimating the annual probability of exceedance of said parameter. The scope is limited to ground motions caused by intraslab earthquakes occurring in Mexico and that engineeringly affect its capital, Mexico City, which is in a geographical region where the effects of soil-dynamic amplification are manifested considerably. A strong-motion database that includes 1517 horizontal accelerograms, with peak ground acceleration, PGA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PGA$$\\end{document}, greater than or equal to 3 cm/s2, recorded during 21 earthquakes from 1994 to 2023 were used to develop the GMPEs. The quantitative description of the time, size, and spatial distribution of the seismic-activity occurrence was defined using a catalog of 46 earthquakes that occurred from 1900 to 2023. The earthquakes have moment magnitude, Mw\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{w}$$\\end{document}, greater than or equal to 6. With the tools developed, amplitude- and duration-based hazard-consistent accelerograms can be simulated and used in nonlinear dynamic analyses (NDAs) of structures. This study includes an application example where three sites in Mexico City are selected to compute inelastic response spectra. Hysteretic-energy demands up to 5 times higher are found after a comparison between the inelastic-response spectra from hazard-consistent accelerograms and those provided by current Mexican regulations.

Modification of wavelet-based downsampling method to reduce computational error in nonlinear dynamic analysis

One of the significant obstacles in conducting linear and non-linear time history analysis is its time-consuming nature. In this article, a new downsamlping method based on discrete wavelet transform (DWT) and smoothing is proposed to overcome this problem. In order to assess the precision of this approach, 50,000 linear and non-linear dynamic analyses of single degree of freedom (SDOF) systems and 300 nonlinear dynamic analyses of frame structures have been performed. One hundred Fema440 records were utilized to generate approximate waves up to the third level and the outcomes of this method were then contrasted with those of DWT. It has been demonstrated that the third-level approximate wave produced by DWT, previously considered dependable in other research, generates significant errors in results and the average error (absolute error percentage of the acceleration spectrum) of its third-level approximate wave is approximately 17.5%. On the other hand, the proposed method generated approximate waves with an average error of less than 4.5% across all behavior coefficients and periods and the error rate decreases as the period and behavior coefficient increase. Analysis of steel moment-resisting frames indicated that the lowest error in both methods is achieved for the base shear and across different engineering demand parameters, the average error rate for the proposed method was below 7.5%. Furthermore, caution must be exercised when employing the proposed method for structures with periods shorter than 0.5 s.

Nonlinear dynamic collapse analysis of space semi-rigid frames using finite particle method

Based on the finite particle method, this work presents a general numerical method to perform the nonlinear dynamic collapse analysis of space semi-rigid structures. A space connection element composed of two particles and six zero-length springs is proposed to simulate the space semi-rigid connection. Geometrical nonlinearity is addressed through fictitious motion, while material and connection behavior nonlinearities are captured by updating the element stiffness matrix and the connection stiffness matrix, respectively. Member and connection fracture models are convenient for simulating fracture behaviors during collapse processes. To verify the effectiveness of the proposed method, the numerical results are compared with those from previous studies, and energy conversion analyses are adopted. The analysis results indicate that only member fractures occur at beam ends in the rigid and linear semi-rigid frames, while only connection fractures occur at beam ends in the nonlinear semi-rigid frame.

Effects of edge-crack orientation and depth on non-linear dynamics of laminated nanocomposite single-variable-edge plates

This paper presents an investigation into the free vibration and nonlinear dynamic analyses of new complex edge contour plate structures, known as single-variable-edge (SVE) plates. Cracks emerge at the center of the plate’s surface, and the effects of edge crack orientation and depth on the dynamical characteristics of the laminated nanocomposite SVE plates have been considered in this study. The functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) material was utilized for the edge-cracked plate that rests on a Winker-Pasternak elastic foundation. The Halpin-Tsai micromechanical model is used to predict the material characteristics, which are presumptively temperature-dependent. The rule of mixtures is employed to determine Poisson's ratio, density mass, and thermal expansion. The governing equations are established based on the theory of elasticity, and Von Karman-Donnell geometric nonlinearity assumption. To confirm the reliability and accuracy of this approach, the acquired findings are validated with those produced using Finite Element Analysis (FEA). Furthermore, the geometrical and material parameters, fracture properties, and environmental (temperature and elastic foundation) factors are also investigated in the study. The research findings hold significant implications for applications in aerospace and aeronautical, civil, and mechanical engineering.

Procedure for evaluation of LNG CCS with reference vessel using nonlinear dynamic analysis

This paper presents a procedure for evaluating the structural safety of Liquefied Natural Gas (LNG) Cargo Containment System (CCS) against sloshing load by comparing the results of linear and nonlinear dynamic structural strength analysis with those of verified reference vessels. This comparative procedure indirectly considers (1) limitation of implementing real physical phenomena in model experiments including the Froude scaling method, density ratio, etc., (2) assumptions in statistical analysis for calculating design loads, and (3) complicated effects not implemented in nonlinear dynamic analysis such as phase transition between liquid and gas, hull deflection, and the detailed geometry of the CCS, among others. The uncertainties in sloshing model experiments and statistical analysis can be addressed by introducing the pressure correction factors, which make the linear design loads of the reference vessel satisfy the CCS’s capacity. Finally, the structural nonlinearity, which was not accounted for in the nonlinear dynamic analysis, can be taken into consideration through a comparison of the usage factors from nonlinear dynamic analysis. To apply the proposed structural assessment procedure, the GTT NO96 series were selected and applied to two failure modes. In the application of this procedure, the Triangular Impulse Response Function (TIRF) method was adopted, to efficiently calculate numerous linear dynamic structural strength analyses required for Dynamic Amplification Factor (DAF). Through this application applying larger sloshing loads to the reinforced NO96 CCS of the target vessel compared to the reference vessel, the feasibility of this procedure was shown.

Damage and Failure of Aeroengine Blades Under Small UAV Impacts

Unmanned aerial vehicles (UAVs) may collide with vulnerable parts of other aircrafts, such as engine blades, causing accidents. The research on small UAV impact is limited. Besides, UAV impact with propeller and rotor blades is poorly understood. In this paper, a finite element (FE) model of a UAV with a weight of 4.78 kg, turbofan blades, propeller blades, and helicopter tail rotor blades was developed. The FE modelling was carried out by commercial software named LS‐DYNA R13.1.0, which is one of the most advanced simulation tools for nonlinear dynamic structural analysis, mainly solving numerical simulations of collision and penetration problems. First, the UAV FE model was validated by comparing the simulation results against the experiments. Next, simulations were conducted to investigate the damage of the three blades under UAV impact with different heading angles. The damage type and effect of UAV’s heading angle were analyzed and identified. The simulation results indicated that the turbofan blades experienced the more severe damage, compared with the propeller blades and tail rotor blades. The head orientation of the UAV has a significant effect on the impact force of the three aircraft engine blades. In addition, certain parts of the UAV (e.g., battery) can produce significant damage to the blades. The research findings are helpful for the safety assessment of the UAV impact damages to different aircraft engines.

Computational evaluation of flight performance of flapping-wing nano air vehicles using hierarchical coupling of nonlinear dynamic and fluid-structure interaction analyses

This study endeavours to introduce an inventive hierarchical coupling methodology for evaluating the flight capabilities of polymer micromachined flapping-wing nano air vehicles (FWNAVs) using advanced computational tools. Furthermore, our objective is to provide a practical demonstration of FWNAVs in both tethered and airborne scenarios. These dual objectives represent the distinctive and pioneering aspects of this research. Such FWNAVs, which are insect-inspired robots, have a 2.5-dimensional structure. An FWNAV comprises a micro piezoelectric drive system and a pair of micro thin flexible wings. The drive system includes a micro transmission and a piezoelectric bimorph actuator. The flight performance of the designed FWNAV is evaluated using a hierarchical coupling approach, where the whole system is decomposed into a micro wing and a micro piezoelectric drive system. The coupling between these parts is modelled as one-way coupling and that between the micro wings and the surrounding air is modelled as strong coupling. In the one-way coupling analysis, nonlinear structural dynamic analysis is conducted for the micro piezoelectric drive system, where the dynamic response is transmitted to the micro wings via the Dirichlet boundary condition. In the strong coupling analysis, strongly coupled fluid-structure interaction analysis is conducted for the micro wings and the surrounding air to consider their strong coupling. The optimisation of flight performance is conducted using fluid-structure interaction analysis to achieve sufficient lift force to support the weight of an FWNAV. The design of a tethered and flyable FWNAV with a size of 10 mm or smaller is demonstrated. This FWNAV can be easily fabricated using polymer micromachining.

Reliability of Response-Controlled Stepped Sine Testing for Experimental Detection of Nonlinear Structure

Nonlinear structural dynamic analysis is required for mechanical structures experiencing nonlinearity through large force-vibration response ranges. Nonlinearities can be caused by large vibration displacements, material properties, or joints. Experimental modal analysis for nonlinear detection is achieved using conventional force-controlled stepped sine testing. However, this approach often encounters premature jumps in frequency response curves before reaching actual resonance peaks. In recent years, response-controlled stepped sine testing (RCT) has been introduced to precisely quantify resonant peaks. This approach, however, has only been limitedly utilised to detect and analyse nonlinearity in jointed structures and structures experiencing large displacement. In this paper, the reliability of the RCT approach is assessed for detecting nonlinearity from different sources. The experimental setup involves placing two magnets on opposite sides of a plate's free end to induce localised nonlinearity through magnet attraction. A low force magnitude of random excitation is employed to identify the frequency range of the first vibration mode using an electromagnetic shaker. Subsequently, RCT is performed within this range to measure the nonlinear forced response. Frequency response functions are measured at ten different controlled displacement amplitudes at the driving point. The analysis observed a symmetry curve of response in the measured FRFs. The results indicate that nonlinear hardening is detected at structures with localised magnet attraction. In conclusion, the reliability of applying the RCT approach for detecting nonlinearity from magnet attraction is achieved due to the absence of a jump issue in FRFs.

Nonlinear dynamic analysis and vibration suppression on the composite laminated plates with general boundary conditions in supersonic airflow

This paper performs the nonlinear dynamic analysis and vibration reduction of the panel structures subjected to supersonic airflow. The negative capacitance piezoelectric shunt damping circuit (PSDC) which contains bonded piezoelectric element and external negative capacitance is adopted. Based on the modified Ritz approach and energy approach, the formulations of the nonlinear panel structure with attached piezoelectric element are derived. A unified mathematical model for the nonlinear dynamic analysis of composite panels subjected to general edge boundaries in supersonic airflow is formulated. Furthermore, the Newmark approach and Newton iteration approach are utilized to calculate time domain responses of panel structures under aerodynamic pressure. Several numerical cases are further performed to verify the present formulations. Finally, impacts of several factors on the flutter characteristics of panel structures are investigated and the comparisons concerning the vibration responses of panels having and without PSDC are performed to verify vibration reduction properties of the present method. The numerical results show that the vibration and flutter of panels in supersonic airflow can be sufficiently suppressed by the present simple vibration reduction strategy.

Linearly Implicit Algorithm with Embedded Newton Iteration of Velocity and its Application in Nonlinear Dynamic Analysis of Structures

With the application of energy dissipation and damping techniques such as viscous dampers and viscoelastic dampers in seismic engineering, dynamic equilibrium equations of overall structures involve nonlinear damping force. Therefore, numerical integration methods with explicit velocity expressions are more favorable. Based on the average acceleration method, a novel linearly implicit algorithm with explicit expression of velocity is proposed in which once Newton iteration is embedded. The stability of the proposed algorithm in solving equations of motion containing nonlinear restoring force and nonlinear damping force is analyzed using the root locus method. The nonlinear stability of the proposed algorithm is also examined using a single-degree-of-freedom shear-type structure. The dynamic response analysis of a three-storey shear structure model equipped with viscous dampers, a three-storey shear structure equipped with metal dampers, and an eight-storey planar frame structure, are carried to investigate the accuracy and stability of the proposed method with respect to the Chang method and the CR method. The results show that the proposed algorithm exhibits higher accuracy and finer stability for nonlinear dynamic problems.

Optimal Acceleration and Energy-Based Record Selection Using Artificial Intelligence Approaches and NP

ABSTRACT The new trend toward modern earthquake-resistant design of buildings based on nonlinear dynamic analysis accounting for peak and energy demands requires efficient ground motion record selection procedures. For this reason, in the present work, two record selection strategies based on acceleration and input energy spectrum considering the spectral shape via Np are presented. Furthermore, both record selection strategies are optimized by means of four artificial intelligence (AI) techniques: Genetic Algorithms (GA), Harmony Search (HS), Particle Swarm Optimization (PSO) and Vibrating Particle System (VPS). In particular, the effectiveness of each AI approach toward the best set of ground motion records for nonlinear dynamic analysis is compared. For this aim, spectral acceleration and input energy design spectra were considered, as well as 1024 seismic records obtained from the Pacific Earthquake Engineering Research Center. For all the AI or meta-heuristic approaches, the fitness function used is focused on minimizing the difference between the average spectrum of eleven ground motion records and the design spectrum using the well-known parameter Np, which represents the spectral shape in a range of periods. In addition, a penalization is included for those spectra with very large or low demands. Thus, 24 sets of eleven seismic records that can be used for nonlinear dynamic analysis of structures with a fundamental period of vibration of 0.6, 1.2 and 1.8 seconds were obtained and purposes. The results demonstrate the ability of the two records selection strategies analyzed and the four meta-heuristic procedures, achieving results quickly and simply regardless of the type of demands, intensities and periods considered. Finally, it is concluded that the VPS algorithm is better in comparison with GA, HS, and PSO since it obtains superior results in almost all the selected cases.

Seismic fragility analysis of containment structure subjected to near fault ground motions

This study presents seismic fragility analysis of the containment structure subjected to near fault ground motion. Prior to perform seismic fragility analysis, 20 near fault ground motion records with pulse characteristics are selected PEER database. Nonlinear dynamic analysis of the containment structure is performed automatically using Matlab scripts and Batch files. To quantify the global damage behavior of the containment structure subjected to near fault ground motion, energy-based global damage index is proposed. The evolution of global damage behavior and tensile damage of the containment structure are analyzed in depth. Goodness of fit for two widely used fragility fitting methods is compared. To quantify the uncertainty in fragility function parameters, Bootstrap resampling procedure and analytical statistical inference method are adopted to estimate the confidence interval of the fragility function parameters. Results indicated that the bottom of containment structure suffered from severe tensile damage and it is most vulnerable location of the containment structure. With the increase of peak ground motion intensity level, tensile damage increases rapidly and extends to higher elevations of the containment structure. The relative error for fragility function parameter x˜m is not more than 4%, and the error of fragility function parameter β˜R is more than 12%. In general, analytical statistical method provides good estimation for the confidence interval of fragility function parameter x˜m, while overestimate the confidence interval of fragility function parameter β˜R.

Impact of ground-motion duration on nonlinear structural performance: Part I: spectrally equivalent records and inelastic single-degree-of-freedom systems

In current seismic performance-based assessment approaches, nonlinear dynamic analysis of structures generally relies on ground motions selected based on their pseudo-spectral accelerations, with little or no consideration for ground-motion duration. Part I of this study, presented in this article, attempts to comprehensively quantify the impact of ground-motion duration on the nonlinear structural performance of case-study inelastic single-degree-of-freedom systems for shallow-crustal seismicity conditions. The effect of duration is decoupled from that of ground-motion amplitude and spectral shape by assembling sets of spectrally equivalent long- and short-duration records. Such sets are employed in incremental dynamic analyses of a wide range of computational models incorporating in-cycle and cyclic strength and stiffness deterioration. The structural response is quantified in terms of peak- and cumulative-based engineering demand parameters. Formal hypothesis testing is used to assess the statistical significance of duration’s impact on the median structural capacity of the considered structural systems. Furthermore, the derivation of duration-dependent fragility and vulnerability relationships demonstrates that ground-motion duration effectively impacts the nonlinear structural performance of various systems, and it should be accounted for in current practice. The fragility median values for highly deteriorating structural systems under long-duration ground motions are found to be up to 21% or 34.0% smaller than the short-duration counterpart if a peak- or cumulative-based engineering demand parameter is adopted, respectively.

Nonlinear vibration and stability analysis of a flexible beam-ring structure with one-to-one internal resonance

The nonlinear dynamic characteristics of a flexible beam-ring structure under fundamental harmonic excitation are systematically investigated. The nonlinear partial differential governing equations of motion for the beam-ring structure are derived by using Hamilton's principle and discretized into two coupled ordinary differential equations including quadratic and cubic nonlinearities by Galerkin's technique. The potential internal resonance relationship of the beam-ring structure is recognized through analyzing the mode shapes and linear frequencies. The method of multiple scales is utilized to approximately analyze the dynamic system and yield a set of autonomous equations under the case of 1:1 internal resonance and a primary resonance. The amplitude-frequency characteristics and the stability of the steady-state responses are studied numerically. The frequency-response curves show that some parameters of the amplitude-frequency equations have significant contributions to the nonlinear responses near resonance of the beam-ring structure. Finally, the bifurcation diagram is obtained and the Poincare map, power spectra and the largest Lyapunov exponent are used to identify the nonlinear dynamic behaviors of the beam-ring structure. From the numerical simulations, it is found that there exist typical nonlinear phenomena such as multi-value solutions, jumps, bifurcations, multiple periodic and chaotic motions in the beam-ring system. This work also proposes a reference for nonlinear modeling and dynamic analysis of similar complex structures.

A Cartesian spatial discretization method for nonlinear dynamic modeling and vibration analysis of tensegrity structures

For vibration analysis of a tensegrity structure, the development of a dynamic model is a key step. A common issue in the traditional dynamic modeling methods for vibration analysis of tensegrity structures is that structural members are oversimplified. Member internal displacements, including those in longitudinal directions for bar and cable members and those in transverse directions for cable members, were neglected. This oversimplification would inevitably prevent the dynamic model of a tensegrity structure so developed from revealing accurate responses, especially for those in the high-frequency domain. To resolve this issue, a new method called the Cartesian spatial discretization method is developed for nonlinear dynamic modeling and vibration analysis of tensegrity structures. This method can successfully incorporate member internal displacements in dynamic modeling of a tensegrity structure by defining positions of structural members as a summation of internal terms and boundary-induced terms in a global Cartesian coordinate system. The proposed method is applied to vibration analysis of a planar Snelson’s X tensegrity structure, a three-dimensional tensegrity tower, and an irregular tensegrity grid in simulation, and compared with the Lagrangian method based on generalized coordinates, the commercial finite element analysis software ANSYS and the finite element analysis method in literatures, respectively. Results show that the proposed method is accurate in predicting dynamic responses of tensegrity structures, especially for vibration analysis in the high-frequency domain. It is also demonstrated that the proposed method is applicable to both simple and complex tensegrity structures, and computationally efficient as it converges in a super-linear rate by using only a small number of internal terms of member displacements.