Nonlinear Dynamic Response Research Articles

Dynamic Analysis of a Double-Cable-Stayed Shallow Arch Model Under Multi-Frequency Excitation by IHB Method

To reveal the dynamic properties of cable-stayed bridges under complex external excitations, a double-cable-stayed shallow arch model induced by multi-frequency harmonic excitations is established. The cable and shallow arch exhibit primary or subharmonic resonances by sweeping excitations simultaneously and asynchronously. Galerkin method, one/two time scales Incremental Harmonic Balance (IHB) method, and Runge–Kutta (RK) method are applied to explore the nonlinear dynamic responses. Research results demonstrate that both the cables and shallow arch present soft and hard spring properties, despite the very weak hard spring of the shallow arch; one-way dynamic interaction among the cables and the shallow arch is discovered when sweeping excitations asynchronously.

A Ball-Contacting Dynamic Vibration Absorber with Adjustable Stiffness and Nonlinear Characteristics

Structural vibration has always been a major concern in the engineering field. A dynamic vibration absorber in the form of contacts with adjustable stiffness (CDVA) offers effective vibration suppression and can improve conventional dynamic vibration absorbers with high sensitivity to frequency deviation and difficulty in adjusting the frequency. In this research, first, based on the theoretical model of the contact between a rubber ball and an inner cone, the feasibility of changing the axial contact state to change the structure’s natural frequency was verified using an ANSYS simulation. A theoretical model of the static contact stiffness between the ball and the inner cone was constructed using Hertzian contact theory and Hooke’s law, and a theoretical model of the cubic nonlinear elastic restoring force was used to characterize the stiffness properties of the rubber ball during compressive rebound. The steady-state frequency response equations of the main vibration structure were derived using the averaging method in conjunction with the two-degree-of-freedom dynamics model, and the stability of the solutions to the frequency response equations was obtained in conjunction with the stability determination criterion. Then, the impact of the CDVA’s design parameters on the nonlinear dynamic response of the primary vibration structure was simulated and analyzed. The resulting findings can serve as guidance for designing dynamic vibration absorber parameters. Based on the principles of ball-inner cone contact, a dynamic vibration absorber structure was proposed. A design test was conducted to verify the correctness of the contact stiffness model, and an experimental study was carried out to investigate the law of change in the dynamic stiffness and damping of the principle structure of CDVA under dynamic excitation conditions. Finally, the vibration test platform of the solidly supported beam structure was constructed, and vibration suppression tests of the CDVA in different compression states were conducted to investigate the tunability and feasibility of CDVA vibration suppression. The results showed that the dynamic vibration absorber had good vibration absorption characteristics and could be used for single-mode vibration suppression of multimodal main structures.

Evidence of nonlinearity tailoring in static and dynamic responses of honeycomb and auxetic hourglass lattice metastructures

Nature’s morphology and optimal energetic solutions remain the key motivation for designing cellular-based lattice structures. Understanding the nonlinear dynamical behaviors that arise from different lattice topologies of such structures in the metastructure framework is crucial for their successful implementation in various novel designs and technologies related to vibration and shape control. This paper presents a study of the static and dynamic response of auxetic and honeycomb lattices with hourglass or dome-shaped metastructures. The potential tailoring of nonlinearity of such responses through various design parameters that play a vital role in shaping the dynamic properties of such structures is discussed here. The impact of cell design parameters on the resulting macroscopic behavior is assessed using both numerical simulations and experimental studies. The transition from softening to hardening nonlinear dynamic responses is reported with cell topologies ranging from the regular honeycomb to auxetic topologies that are widely used as fundamental cells of cellular materials design. The experimental study is based on the time responses measured to verify the numerical predictions. The experimental system consists of different 3D printed hourglass samples based on the auxetic and honeycomb lattices on which dynamic testing using a laser Doppler vibrometer is performed. The design strategies proposed in this paper can be integrated into a wide range of lattice-based materials for noise and vibration control applications and biomedical devices.

Nonlinear dynamic response of a temperature-dependent FGM spherical shell under various boundary conditions and thermal shocks: Examination of dynamic snap-through

In this study, a comprehensive exploration of the nonlinear dynamic snap-through phenomenon observed in shallow spherical shells composed of functionally graded materials (FGMs) is examined. The analysis encompasses the interplay of thermomechanical characteristics within metal and ceramic phases, taking into account their temperature-dependent behaviors. To address this problem, the transient heat conduction equation in a nonlinear form, accounting for the temperature dependence factor is derived. To solve this complexity, the Generalized Differential Quadrature (GDQ) method is employed, coupled with the Crank-Nicolson time integrating scheme, leveraging an iterative approach for precision. The formulation of nonlinear dynamic motion equations is based on Hamilton's principle and incorporates the utilization of nonlinear strain-displacement equations and uncoupled thermoelasticity. In the spatial domain, GDQ proves invaluable in solving these nonlinear, coupled equations. In the temporal domain, the Newmark procedure in conjunction with the Newton-Raphson iterative method are utilized to navigate through dynamic equations, yielding insights into shell's behavior over time. In the initial stages of the investigation, we validate our spherical shell formulation and methodologies by comparing shell's response with existing, simpler works. This step ensures the reliability and accuracy of our model. The primary objective is to assess the presence and characteristics of the thermal snap-through phenomenon within the shell under these diverse conditions.

Numerical simulation of the 2010 4-story reinforced concrete structure tested on the E-defense shake table

Due to advancements in computational tools, performing a full nonlinear response history analysis of structures at the system level using detailed numerical simulations of components has become less demanding, even on standard personal computers. However, the modelling approaches need to be calibrated and verified against experimental measurements to ensure the accuracy of the system-level predictions. In this study, an advanced numerical simulation method is used to predict the 3D nonlinear dynamic response of a four-story reinforced concrete building tested at E-Defense shake table. The structure is modelled in the finite element analysis programme DIANA, using a previously developed and validated approach to predict the failure modes of doubly reinforced walls with confined boundary regions. Curved shell elements are used to model the walls and slabs, and the reinforcement is modelled using embedded bar elements. The frame elements are modelled using beam elements with the effect of confinement on the concrete behaviour represented in the material constitutive model. The numerical versus experimental response comparison is conducted at both local and global levels. For local levels, the base shear versus top displacement curves, strain gradients as well as the crack pattern predicted by the numerical model are compared with the test measurements. The inter-story drift response history is considered as the metric for the global level assessment. The effects of different modelling parameters on the accuracy of predictions are also investigated.

Nonlinear dynamic analysis of opto-electro-thermo-elastic perovskite plates

AbstractPhotostrictive materials have attracted tremendous interest as the new generation of smart materials that can achieve a direct conversion from optical energy to mechanical energy. Understanding their nonlinear mechanical properties under light illumination is of paramount significance for their realistic optomechanical applications. This article proposes a novel opto-electro-thermo-elastic constitutive model that can consider the effects of photostriction, photothermal temperature, and electrostriction for metal halide perovskite crystals and investigates the nonlinear static and dynamic responses of the perovskite plates. The nonlinear governing equations are established based on the first-order shear deformation theory and von Kármán nonlinearity and are numerically solved by the differential quadrature method. A detailed parametric investigation is performed to analyze the effects of light and electricity on the nonlinear mechanical behaviors of perovskite plates. It is concluded that light illumination leads to the presence of optical stress and thermal stress in the perovskite plates, giving rise to increased static and dynamic deformations and stresses, as well as reduced postbuckling and free vibration characteristics. The research findings pave the way for the optomechanical applications of perovskite-based smart materials and structures.

Transient Response of Sandwich Plates with Corrugated Core Under Mechanical-Thermal Loads

The nonlinear dynamic responses of the corrugated sandwich plate under mechanical-thermal loads are studied and analyzed. Based on hyperbolic parabola shear deformation plate theory (HPSDT), the partial differential equation of the sandwich plate with the corrugated core is established. Using the Galerkin truncation method, the nonlinear motion equation is derived. By the solution, the response of the corrugation plate with simply supported four edges at different temperatures is obtained and validated. Then the transient responses of the corrugated sandwich plate under different impact loads are analyzed, and the effects of the base materials, the corrugation types and the structural parameters of the corrugated plate on the transient responses are discussed in detail. The research provides a reference for improving the impact resistance of the sandwich plate in practical application.

Exact Sensitivity of Nonlinear Dynamic Response with Modal and Rayleigh Damping Formulated with the Tangent Stiffness

Exact Sensitivity of Nonlinear Dynamic Response with Modal and Rayleigh Damping Formulated with the Tangent Stiffness

Large Deformation Dynamic Characteristics of Cracked Laminated Panel and Improvement of Stiffness Using Shape Memory Alloy Fiber

Abstract This study explores the investigation of the nonlinear dynamic responses or time-dependent deflection analysis of a laminated composite shell panel integrated with a shape memory alloy (SMA), considering both undamaged and damaged set-ups. The primary focus of this research is to examine the impact of SMA incorporation on the structural behavior of the parent configuration, aimed at enhancing its structural stiffness. To ensure the validity of the proposed model, sensitivity analyses and numerical validations are presented. The mathematical framework employed in this study employs the higher-order shear deformation theory (HSDT), which offers enhanced accuracy in capturing the intricate behaviors of these shell panels. The dynamic responses are obtained using the Newmark average acceleration method. Numerical simulations are carried out using a dedicated MATLAB code developed in-house, allowing amplified correctness in outcomes and widespread analysis. The study thoroughly assesses a range of geometric parameters and those relevant to SMA for both intact and impaired shell panels. The outcomes of the investigation reveal affirmative findings, underscoring notable improvements in structural strength and enhanced nonlinear dynamic responses through the introduction of SMA reinforcement into the composite shell panel.

Dynamic responses and damage mechanisms of low-rise reinforced concrete frame structures subjected to rockfall impacts

ABSTRACT Combined with the validations of the nonlinear material models, this study addresses the nonlinear dynamic response, damage mechanisms and failure modes of reinforced concrete frame structures under rockfall impacts, utilizing explicit dynamic analysis software for detailed model of structures. The findings indicate that the peak impact force is primarily influenced by the impact velocity and subsequently by the impact mass, while the impact location exerts the least influence; A linear relationship is observed between the maximum impact force and rockfall diameter, whereas a nonlinear association exists with rockfall velocity; Predominant failure modes include global and local failures, with damage and failure predominantly concentrated on the impacted columns and their surrounding components; Notably, similar damage levels were observed for corner and edge middle columns of structures under rockfall impacts; The column base, mid-column and column top primarily exhibit flexural-shear failure, flexural failure and flexural-shear failure, respectively; Given the higher rate of plastic energy absorption during mid-column impacts compared to column base and top impacts, a rockfall striking mid-column results in higher dynamic response and greater structural damage. This study can provide useful reference in design and restoration of low-rise reinforced concrete frame structures located in areas prone to frequent geological disasters.

Nonlinear dynamical characteristics of carbon nanotube-reinforced composite beams with piezoelectric actuators and elastically restrained ends under thermo-electro-mechanical loads

Nonlinear free vibration and dynamical responses of carbon nanotube (CNT) reinforced composite beams with surface-bonded piezoelectric layers and tangentially restrained ends under thermo-electro-mechanical loads are investigated in this paper. The properties of constitutive materials are assumed to be temperature-dependent and effective properties of nanocomposite are estimated using an extended rule of mixture. Unlike previous studies, the present work considers the effects of tangentially elastic constraints of two ends on the nonlinear dynamic characteristics of hybrid beams. Motion equation is established within the framework of Euler-Bernoulli beam theory taking into account von Kármán nonlinearity. Analytical solution is assumed to satisfy simply supported boundary conditions and Galerkin procedure is employed to obtain a time ordinary differential equation including both quadratic and cubic nonlinear terms. This differential equation is numerically solved employing fourth-order Runge-Kutta scheme to determine the frequencies of nonlinear free vibration and nonlinear transient response. Parametric studies are executed to examine numerous influences on the nonlinear dynamical characteristics of hybrid nanocomposite beams. The study reveals that tangential constraints of ends substantially effect the frequencies and dynamic response of the beam, especially at elevated temperatures. The results also indicate that nonlinear dynamic responses can be controlled effectively by means of piezoelectric actuators and elasticity of tangential constraints of ends should be considered in design of piezo-CNTRC beams.

Strain engineering of nonlinear nanoresonators from hardening to softening

Although strain engineering and soft-clamping techniques for attaining high Q-factors in nanoresonators have received much attention, their impact on nonlinear dynamics is not fully understood. In this study, we show that nonlinearity of high-Q Si3N4 nanomechanical string resonators can be substantially tuned by support design. Through careful engineering of support geometries, we control both stress and mechanical nonlinearities, effectively tuning nonlinear stiffness of two orders of magnitude. Our approach also allows control over the sign of the Duffing constant resulting in nonlinear softening of the mechanical mode that conventionally exhibits hardening behavior. We elucidate the influence of support design on the magnitude and trend of the nonlinearity using both analytical and finite element-based reduced-order models that validate our experimental findings. Our work provides evidence of the role of soft-clamping on the nonlinear dynamic response of nanoresonators, offering an alternative pathway for nullifying or enhancing nonlinearity in a reproducible and passive manner.

Time Domain Nonlinear Dynamic Analysis of Vertically Loaded Tapered Pile in Layered Soils

A simplified model is proposed for predicting the nonlinear dynamic response of vertically loaded tapered piles in the time domain, in which the tapered pile is divided into several frustum segments and the four-spring is used for the simulation of the soil–pile interaction. The differential equations for the tapered pile are given and solved by the finite difference method. The vertical dynamic response of a typical tapered pile is investigated, and the consistency of the computational results compared with the finite element results convincingly verifies the reliability of the proposed simplified model. Then, recommended segment numbers, considering the computational efficiency and accuracy requirements for the dynamic analysis of tapered piles, are given. And parametric studies are also carried out to investigate the effect of soil and pile parameters on the nonlinear dynamic response of the tapered pile. The results show that soil nonlinearity significantly affects the vertical dynamic characteristics of the tapered pile. And the tapered pile shows better dynamic characteristics than the cylindrical pile with the same volume and pile length. In addition, the properties of the soil along the upper part of the tapered pile have a more considerable effect on the dynamic response of the tapered pile. These results help to further improve the theory of nonlinear dynamic response analysis of tapered piles and promote its widespread application in engineering practice.

Nonlinear dynamic analysis of auxetic-FGM sandwich plates resting on a Kerr elastic substrate under blast loading

This study examines the nonlinear dynamic response of sandwich plates placed on the Kerr elastic substrate under blast loading. The plate is composed of an auxetic honeycomb core and functionally graded material (FGM) coating layers. The volume fraction of FGM is determined following the power-law model (P-FGM). The equations of motion of the plate are formulated by using the first-order shear deformation theory (FSDT) in conjunction with the use of the Airy stress function. The Runge-Kutta scheme, with the assistance of the Galerkin technique, is utilized in the present study to obtain numerical results for the nonlinear dynamic response of the plate. After verifying the proposed solution, the influences of material characteristics, blast loading, elastic substrate, and geometry parameters on the free vibration and nonlinear dynamic behavior of the plate are investigated comprehensively. The results show that negative Poisson’s ratio has a significant effect on the linear and nonlinear vibration characteristics of the auxetic-FGM sandwich plate.

Large‐scale seismic soil–structure interaction analysis via efficient finite element modeling and multi‐GPU parallel explicit algorithm

AbstractAs urban population increases, integrated underground–aboveground complexes are being constructed at growing paces in major cities. The seismic analysis of such complexes is crucial for the safety and functionality in the threat of potential earthquake disasters. However, fine‐grained numerical modeling and analysis of such large and complex structures are still inefficient due to the consideration of the soil–structure interaction (SSI). To address this challenge, an efficient approach for numerical modeling of large‐scale seismic SSI analysis is presented in this paper to overcome the limitations of existing finite element analysis (FEA) software. Moreover, a multi‐graphic processing unit (GPU) parallel explicit algorithm is implemented for the nonlinear dynamic SSI problems to further increase the computational efficiency. A large underground–aboveground complex project in China is used as an example to demonstrate the capability of the integrated method. The accuracy and reliability of the multi‐GPU parallel explicit finite element algorithm for SSI analysis (GFEA‐SSIA) are verified through a comparative analysis of the linear‐elastic and nonlinear dynamic response of the building calculated by GFEA‐SSIA and common FEA software. Finally, the structural response and structural damage of the underground–aboveground complex are analyzed under multidirectional seismic motions, and the damage distributions of the structures are provided.

Transient nonlinear responses of a sandwich plate with micro-cellular auxetic core based on modified strain gradient theory under impact loads

This study investigates the nonlinear dynamic response of an auxetic sandwich structure under impact load. The core is made of a micro-cellular auxetic structure. The main point of interest is studying the micro-cellular core properties’ effects on the structure’s nonlinear dynamic response. First, the mechanical properties of the micro-cellular auxetic core are introduced based on modified strain gradient theory (MSGT), followed by experimental and numerical validation. Then, Hamilton’s principle is applied to derive the sandwich structure’s nonlinear governing partial differential equations. Lastly, Galerkin’s method paved the way to achieving the final solution. So as to perform frequency-response analysis, the four-dimensional averaged equations are obtained using the perturbation method. In order to carry out experimental validation, a nanosecond laser system is used for micro-cellular auxetic sample fabrication, and the tensile tests are carried out per ISO 6892 standard. The comparison between the experimental and the theoretical results indicates an excellent agreement among the results. It can be concluded that MSGT plays a significant role in the mechanical properties and the nonlinear dynamic response of the micro-cellular auxetic structures. The present study is applicable in the field of protective panels, sensors, and energy harvesters.

Nonlinear combined harmonic resonances of composite cylindrical shells operating in hygro-thermo-electro-magneto-mechanical fields

By considering the effects of the hygro-thermo-electro-magnetic environments, von Karman nonlinear terms, and multi-harmonic excitations, a coupled nonlinear vibration modeling of composite cylindrical shells comprising a carbon nanotube-reinforced composite (CNTRC) core and two piezoelectric/magnetic composite (PEMC) skins is developed, and the nonlinear dynamic behaviors of such cylindrical shells under primary, super/sub-harmonic, and combined resonance states are investigated. In the theoretical modeling process, the effective mechanical properties of the CNTRC core are first determined using the mixing and Schapery laws, and the hygro-thermo-electro-magneto-mechanical constitutive relations of the PEMC skins are then formulated. Within the framework of Reissner-Mindlin shell theory, the Lagrangian of the system containing Green-Lagrange and von Karman nonlinear terms is derived, and solution techniques based on the multiscale method are provided to obtain nonlinear frequencies, dynamic responses, and phases of CNTRC-PEMC cylindrical shells under multi-physics fields. Consequently, comparison studies are conducted to validate the correctness of the proposed model from different aspects. Based on this, various resonance and chaos behaviors of such structures subjected to multiple load components are revealed and compared, and the influences of environmental factors and structure composition on the amplitude-frequency curves, time-history responses, and phase planes are explored, with several recommendations and findings being drawn.

Non-Linear Blast-Induced Dynamic Responses of Graphene Platelets-Reinforced Porous Cylindrical Panels in Thermal Environments

Non-Linear Blast-Induced Dynamic Responses of Graphene Platelets-Reinforced Porous Cylindrical Panels in Thermal Environments

A semi-analytical sinusoidal shear deformation theory for nonlinear dynamic response and vibration of CNT–FGM doubly curved shallow shells

A semi-analytical sinusoidal shear deformation theory for nonlinear dynamic response and vibration of CNT–FGM doubly curved shallow shells

Nonlinear torsional vibration and dynamic post-buckling responses of spiral stiffened functionally graded porous cylindrical shells

This study employs a semi-analytical approach to investigate the nonlinear torsional vibration and dynamic torsional post-buckling (DTPB) responses of spiral stiffened functionally graded (FG) porous (SSFGP) cylindrical shells. These shells are resting on a generalized nonlinear viscoelastic foundation (GNVEF). This foundation consists of a dual-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model. The model includes nonlinear cubic stiffness and takes damping effects into consideration. Within the scope of this research, two variations of SSFGP cylindrical shells are examined: those characterized by non-uniform and uniform porosity distributions. Employing the Donnell shell theory, von-Kármán nonlinear geometric assumptions, and Galerkin’s method, a discretized nonlinear governing equation is derived to analyze the behaviors of the shells. Consequently, explicit formulations for dynamic torsional load are meticulously obtained. The findings of the present study are validated by comparing them with the outcomes documented in existing literature, as well as through alignment with the P-T method. This research delves into the system’s nonlinear behaviors, with scrutinization of the effects of diverse factors such as material and geometrical parameters. The researchers and engineers in this field may use the findings of this research as benchmarks for their design and research of SSFGP cylindrical shells.