Fourth-order Runge-Kutta Method Research Articles

Nonlinear forced vibration of functionally graded hybrid three-phase nanocomposite toroidal shell segments reinforced by carbon nanotubes (CNTs) and graphene nanoplatelets (GPLs)

This study proposes a unique three-phase functionally graded (FG) hybrid nanocomposite material reinforcing the toroidal shell segments to investigate the nonlinear forced vibration using Reddy's higher-order shear deformation theory, von Karman geometrical nonlinearity and Stein-McElman's assumption along with the Hamilton principle. The examined toroidal shell's material consists of polymeric resin, carbon nanotubes (CNTs), and graphene platelets (GPLs) as nanocomposites. The material properties have been derived based on a modified Halpin-Tsai micromechanical model. Four distribution patterns have been studied: uniform (UD), FG-X, FG-O, and FG-V. The continuous distribution of GPLs and CNTs leads to inhomogeneous position-dependent properties throughout the shell thickness. The obtained differential equations of motion have been reduced to ordinary equations using Galerkin's technique. A multi-scales method (MSM) is used to estimate a closed-form solution representing the frequency-amplitude relation, and the state space representation is used along with numerical fourth-order Runge Kutta method (RK4) to obtain the nonlinear dynamic response of the toroidal shell. The accuracy of the current results obtained has been verified by comparing them with the relevant literature and numerical results using (RK4). In addition, the influence of both GPLs and CNTs weight fractions, nanofillers’ distribution types, longitudinal and circumferential wave numbers, elastic foundation parameters, static axial compression load, transverse excitation load, damping ratio, geometrical characteristics of the toroidal shell on the dimensionless natural frequency, nonlinear primary resonance (frequency-amplitude curve), and nonlinear dynamic response are carefully studied. The results found that combining (GPLs & CNTs) into the shell's matrix improves performance, especially in concave shells compared to convex ones. The FG-X pattern reduces peak resonance amplitude and improves natural frequency. A reduction of 12.3 % is observed for convex shells, and 21.5 % for concave shells compared to FG-O.

Heat and Mass Transfer in Unsteady Radiating MHD Flow of a Maxwell Fluid with a Porous Vertically Stretching Sheet in the Presence of Activation Energy and Thermal Diffusion Effects

The aim of this study is to analyze the effects of activation energy and thermal diffusion an unsteady MHD reactive Maxwell fluid flow past a porous stretching sheet in the presence of Brownian motion, Thermophoresis and nonlinear thermal. The non-linear partial differential equations that govern the fluid flow have been transformed into a two-point boundary value problem using similarity variables and then solved numerically by fourth order Runge–Kutta method with shooting technique. Graphical results are discussed for non-dimensional velocity, temperature and concentration profiles while numerical values of the skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system. The present study is compared with the previous literature and found to be in good agreement.

Transient MHD Darcy-Forchheimer of Williamson-Casson flow with CCS: Application of wastewater treatment

With regards to the Cattaneo-Christoph (CCS) speculation, the thermal and mass transfer of a MHD Williamson-Casson ferrofluid flow through a permeable medium obeying the Darcy-Forchmeier law through an extended chamber or slab is carefully considered. The chemical reaction and Buongiorno nanofluid model were modified in the model to describe the nanoscale properties of liquid particles. Heat sources can be divided into two categories: linear and exponential space-dependent convection heat sources. The entire governing equations are changed to common differential terms, using a reasonable similarity change. These equations and their associated boundary conditions are calculated numerically via the fourth-order Runge-Kutta method. Comparison was made with the analytical solution in a special case, and very good agreement was reached. Economic success with deeper water purification can be attained by developing models for wastewater treatment facilities, conducting experiments and calculations on them, and making predictions for their nature in order to improve their cleaning efficiency, Prevent issues from arising during construction, operation, and reconstruction. The structural parameters of the quencher were physically modeled using mathematical modeling; It is possible to establish a cost-effective and effective filter model for industry and small settlements using the calculations and vertical filter model created in the article. Furthermore, it will be feasible to produce. Our mathematical procedure assure that: the deposit’s mass will be diminished through treated water under attractive field impacts; The magnetic field openness with nanometer-sized particles modifies the physical and synthetic properties of water particles bringing about exceptional characteristics; the water concentration will be decreased with the increase in the bending modulus; This means that in wastewater treatment the sediment mass will decrease.

Numerical Investigation of Diffusion Thermo and Thermal Diffusion on MHD Convective Flow of Williamson Nanofluid on a Stretching Surface Through a Porous Medium in the Presence Chemical Reaction and Thermal Radiation

In this paper, analyze the impact of Diffusion thermo and thermal diffusion with heat and mass transfer inherent of thermally radiant Williamson nanofluid over a stretyching surface through a porous medium under the convective boundary condition in the presence of thermal radiation and chemical reaction has been studied. The coefficients of Brownian and thermophoresis diffusions are also taken into consideration. The governing partial differential equations are reduced to a couple of nonlinear ordinary differential equations by using suitable transformation equations; these equations are then solved numerically with the use of the conventional fourth-order Runge Kutta method accompanied by the shooting technique. As a result, the effects of various physical parameters on the velocity, temperature, and nanoparticle concentration profiles as well as on the skin friction coefficient and rate of heat transfer are discussed with the aid of graphs and tables. This study has been directly applied in the pharmaceutical industry, microfluidic technology, microbial improved oil recovery, modelling oil and gas-bearing sedimentary basins, and many other fields. Further, to check the accuracy and validation of the present results, satisfactory concurrence is observed with the existing literature.

Nonlinear vibration characteristics of axially moving anisotropic membrane with gas-thermal-elastic coupling

In the actual printing production process, the printing electronic motion membrane is susceptible to transverse vibration caused by interference from air drag, temperature changes, and other external conditions, resulting in membrane wrinkles, slippage, and other phenomena in the transmission process. We studied the bifurcation and chaos movement properties of anisotropic membranes under air drag and temperature. According to D’Alembert’s theory and von Kármán’s principle, the nonlinear dynamic differential formulas of axially moving anisotropic membranes with gas-thermal-elastic coupling are established. The Galerkin method is applied to discretize the formulas to obtain the state equation of the system. Finally, numerical simulations are performed by applying the fourth-order Runge–Kutta method to analyze the bifurcation and chaos of the system in terms of orthotropic coefficient, dimensionless air drags, and dimensionless temperature. The bifurcation diagrams, Lyapunov exponent diagrams, displacement time-history diagrams, phase-trajectory plane diagrams, and Poincaré diagrams of the membrane system are obtained. The results show that the anisotropic coefficient, dimensionless air drag, and dimensionless temperature significantly impact the investigated nonlinear dynamic of the anisotropic membrane, which provides a theoretical basis for production efficiency and high-quality printing equipment.

Effect of Stratified Flow on the Vibration of Anchor Cables in a Submerged Floating Tunnel

This study investigates the vertical-type submerged floating tunnel with anchor cables. Based on the characteristics of the anchor cables, the anchor cables are simplified as a nonlinear beam model with hinged ends. Disregarding the axial displacement of the tunnel body, the loads will cause displacements in the x and z directions of the tunnel body. The vibrations of the anchor cables are decomposed into three directions, and the parameter excitation at the connection point between the anchor cables and the tunnel body is taken into account. The equations of motion for the three degrees of freedom of the anchor cables are established using Hamilton’s principle, and then the three equations are solved using the Galerkin method and the fourth-order Runge–Kutta method. The basic characteristics of an internal wave stratified flow acting on the anchor cables are considered, as well as the influence of the incident angle of the ocean currents on the three degrees of freedom of the anchor cables. The results indicate that (1) stratified flow weakens the first- and third-order vortex-induced vibrations of the anchor cables while enhancing the second-order vortex-induced vibrations. When considering the parameter excitation of the anchor cables, the first- and third-order vibrations are weakened, while the second-order vibration remains significant; (2) the first-order vibration of the anchor cables reaches its maximum value when the transverse oscillation frequency of the tunnel body is twice its natural frequency, and the second-order vibration of the anchor cables reaches its maximum value when the transverse oscillation frequency of the tunnel body is twice its natural frequency; (3) the downstream vibration of the anchor cables increases with the increase in the incident angle of the ocean currents, the cross-flow vibration of the anchor cables decreases with the increase in the incident angle of the ocean currents, and the axial vibration of the anchor cables reaches its maximum value when the incident angle of the ocean currents is 60 degrees; (4) stratified flow weakens the lock-in phenomenon of the anchor cables, and the influence of the 1/2 stratified flow on the vibrations of the anchor cables is greater than the influence of the 1/2 stratified flow.

High-efficiency and low-hazard artillery recoil reduction technology based on barrel gas reflection

Reducing recoil as well as reducing muzzle hazards are important issues in artillery design. This paper presents a barrel gas reflection method for the artillery aiming for efficient recoil reduction while reducing muzzle hazards. The launching process is modeled by coupling the interior ballistic equations and the flow equations of the barrel gas reflection device. The fourth-order Runge–Kutta method was used to solve the model, and the LHS method as well as the Kriging model was used to establish a mapping relationship between the parameters and the effect. To validate the proposed model, shooting experiments are carried out on a 30 mm caliber artillery. The maximum error between the experiment and simulation results was 5.32%. The experiment has demonstrated that the barrel gas reflection method increases the recoil reduction efficiency of artillery by 44.54% and reduces the muzzle hazard by 52.18%. Finally, the barrel gas reflection method can produce effects with the muzzle device at the same time, and it has little effect on the velocity of the projectile muzzle velocity, and it provides a new way of thinking for the development of future artillery recoil reduction technology.

New Analytical and Numerical Solutions for Squeezing Flow between Parallel Plates under Slip

In this article, the effects of physical flow parameters on squeezed fluid between parallel plates are explored through the Darcy porous channel when fluid is moving as a result of the upper plate being squeezed towards the stretchable lower plate, such as velocity slip, thermal slip, solutal slip, thermal stratification parameter, solutal stratification parameter, squeezing number, Darcy number, Prandtl number, and Schmidt number. The governing equations are transformed into a nonlinear ordinary differential equation using the appropriate similarity transformations. The resulting equations are solved by using the perturbation iteration method (PIT) to produce a convergent analytical solution with high accuracy. The phenomena of the squeezing fluid as the plates are moving apart and when they are coming together are illustrated using the resulting analytical solutions. Plots are used to discuss the significant effects of physical parameters on velocity, temperature, and fluid concentration profiles. The skin friction coefficient and Nusselt Sherwood values have graphical interpretations that are listed. For strong velocity slip parameters, the results demonstrate the existence of a minimum velocity profile close to the plate and a growing velocity profile distant from the plate. Additionally, as the slip effects rise, the fluid temperature and concentration both considerably drop. The results of the fourth-order Runge-Kutta method (RK4M) and the presented analytical solutions provided are in excellent agreement.

Bounds for Weierstrass Elliptic Function and Jacobi Elliptic Integrals of First and Second Kinds

The Weierstrass elliptic function is presented in connection with the Jacobi elliptic integrals of first and second kinds leading to comparing coefficients appearing in the Laurent series expansion with those of Eisenstein series for the cubic polynomial in the meromorphic Weierstrass function. It is unified in the formulation the Weierstrass elliptic function with Jacobi elliptic integral by considering motion of a unit mass particle in a cubic potential in terms of bounded and unbounded velocities and the time of flight with imaginary part in the complex function playing a major role. Numerical tools box used are the Konrad-Gauss quadrature and Runge-Kutta fourth order method.

Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation

This study presents families of the fourth-order Runge–Kutta methods for solving a quadratic Riccati differential equation. From these families, the England version is more efficient than other fourth-order Runge–Kutta methods and practically well-suited for solving initial value problems in general and quadratic Riccati differential equation in particular. The stability analysis of the present method is well-established. In order to verify the accuracy, we compared the numerical solutions obtained using the England version of fourth-order Runge–Kutta method with the recently published works reported in the literature. Several counter examples are solved using the present methods to demonstrate their reliability and efficiency.

Research on NURBS Curve Interpolation Algorithm Based on Mline-Gear

Aiming at the problem of speed fluctuation caused by the large error between the ideal interpolation step and the actual interpolation step in the traditional non-uniform rational B-spline ( NURBS ) curve interpolation, a NURBS curve interpolation algorithm based on Mline-Gear is proposed. The differential and derivative definitions are derived to transform the Mline and Gear formulas respectively, and the prediction and correction formulas of the interpolation parameters are obtained. Then, it is judged whether the interpolation parameter values obtained by the correction formula meet the speed fluctuation rate requirements, and the interpolation can be continued. Otherwise, the Steffensen descent formula is used to iteratively correct the interpolation parameter values. In order to ensure the calculation accuracy and avoid solving high-order derivatives, the fourth-order Runge-Kutta method is used to solve the initial two interpolation parameters. Finally, the algorithm is simulated. The simulation results show that the algorithm reduces the feed speed fluctuation rate while ensuring a small number of iterations.

Iterated Crank–Nicolson Method for Peridynamic Models

In this paper, we explore the iterated Crank–Nicolson (ICN) algorithm for the one-dimensional peridynamic model. The peridynamic equation of motion is an integro-differential equation that governs structural deformations such as fractures. The ICN method was originally developed for hyperbolic advection equations. In peridynamics, we apply the ICN algorithm for temporal discretization and the midpoint quadrature method for spatial integration. Several numerical tests are carried out to evaluate the performance of the ICN method. In general, the ICN method demonstrates second-order accuracy, consistent with the Störmer–Verlet (SV) method. When the weight is 1/3, the ICN method behaves as a third-order Runge–Kutta method and maintains strong stability-preserving (SSP) properties for linear problems. Regarding energy conservation, the ICN algorithm maintains at least second-order accuracy, making it superior to the SV method, which converges linearly. Furthermore, selecting a weight of 0.25 results in fourth-order superconvergent energy variation for the ICN method. In this case, the ICN method exhibits energy variation similar to that of the fourth-order Runge–Kutta method but operates approximately 20% faster. Higher-order convergence for energy can also be achieved by increasing the number of iterations in the ICN method.

Study on dynamic characteristics of acceleration process of spherical hybrid sliding bearings rotor system

Purpose The transient loads on the spherical hybrid sliding bearings (SHSBs) rotor system during the process of accelerating to stable speed are related to time, which exhibits a complex transient response of the rotor dynamics. The current study of the shaft center trajectory of the SHSBs rotor system is based on the assumption that the rotational speed is constant, which cannot truly reflect the trajectory of the rotor during operation. The purpose of this paper truly reflects the trajectory of the rotor and further investigates the stability of the rotor system during acceleration of SHSBs. Design/methodology/approach The model for accelerated rotor dynamics of SHSBs is established. The model is efficiently solved based on the fourth-order Runge–Kutta method and then to obtain the shaft center trajectory of the rotor during acceleration. Findings Results show that the bearing should choose larger angular acceleration in the acceleration process from startup to the working speed; rotor system is more stable. With the target rotational speed increasing, the changes in the shaft trajectory of the acceleration process are becoming more complex, resulting in more time required for the bearing stability. When considering the stability of the rotor system during acceleration, the rotor equations of motion provide a feasible solution for the simulation of bearing rotor system. Originality/value The study can simulate the running stability of the shaft system from startup to the working speed in this process, which provides theoretical guidance for the stability of the rotor system of the SHSBs in the acceleration process.

Structural design and dynamic characteristics analysis of braided composite two-stage gear transmission system

In order to realize the lightweight design of the transmission system, the braided composite material is applied to the two-stage gear transmission system. According to the structural characteristics of the two-stage gear reducer box, the whole box is designed to be assembled with the braided base and the box wall. Woven composite materials are applied to the web parts of mixed metal composite gears to realize the design goal of lightweight gears. Then, under the assumption of ignoring the influence of friction, bearings and other factors on the system, the dynamic model of the two-stage gear transmission system considering the box is established. By normalizing and dimensionless processing of the equations, the dimensionless differential equations of motion are obtained. The fourth-order Runge–Kutta method is used to analyze the relationship between the connection parameters and the dynamic characteristics of the system under the two working conditions of rigid and flexible connection between the composite base and the box wall.Through the analytical analysis of vibration displacement of two-stage gear reducer and box, the theoretical basis is found for the numerical analysis results. Finally, the dynamic characteristics of the transmission system are studied by vibration resonance analysis through high and low frequency interference. It is found that in a certain frequency range, with the decrease of the mass and moment of inertia of the transmission parts corresponding to the mixed metal composite gear, the amplitude-frequency characteristic Q of the lightweight gear and gearbox transmission system is slightly lower than that of the common gear and gearbox system, and the stability of the system is increased, and the dynamic characteristics of the system are improved.

SPREADING PATTERN OF INFECTIOUS DISEASES: SUSCEPTIBLE INFECTED RECOVERED MODEL WITH VACCINATION AND DRUG-RESISTANT CASES (APPLICATION ON TB DATA IN INDONESIA)

Mycobacterium tuberculosis is the causative agent of the infectious illness tuberculosis (TB). Indonesia is the world's third-highest TB burden country. TB transmission is prevented by the BCG vaccination. A directly observed treatment, short-course (DOTS) treatment approach can cure TB illness. Recurrent TB may occur due to either relapse or reinfection with drug-resistant bacteria. The goals of this article are formulating the SVITR model with relapse and drug-resistant cases, applying the model to the TB data in Indonesia, determining the model accuracy, determining the spreading pattern and interpreting the result, and simulating the parameters. Literature study and application methods are used in this research. The SVITR model with relapse and drug-resistant cases is a first-order nonlinear differential equation system. The model is applied to TB in Indonesia based on annual data from Indonesian Health Profile, World Bank, and WHO. The model is solved by the fourth-order Runge-Kutta method. The model is accurate enough to explain the spread of TB in Indonesia with a MAPE value of 15,5%. The spreading pattern of tuberculosis infection is upward from 2010 to 2050. In 2050, there are still 8.115.976 TB cases in Indonesia. Hence in 2050, Indonesia's free of TB target has yet to be achieved. Simulation is conducted by increasing BCG vaccination to 95%, reducing contact with TB patients to 5%, increasing treatment to 95%, and lowering relapses and drug-resistant cases to 0.00005%, so the Indonesia free of TB target in 2050 can be achieved from 2042.

Enhancing accuracy and efficiency: A novel implicit–explicit approach for fluid dynamics simulation

This study presents an innovative implicit–explicit time-stepping algorithm based on a first-order temporal accuracy method, addressing challenges in simulating all-regimes of fluid flows. The algorithm's primary focus is on mitigating stiffness inherent in the density-based “Roe” method, pivotal in finite volume approaches employing unstructured meshes. The objective is to comprehensively evaluate the method's efficiency and robustness, contrasting it with the explicit fourth-order Runge–Kutta method. This evaluation encompasses simulations across a broad spectrum of Mach numbers, including scenarios of incompressible and compressible flow. The scenarios investigated include the Sod Riemann problem to simulate compressible Euler equations, revealing the algorithm's versatility, and the low Mach number Riemann problem to analyze system stiffness in incompressible flow. Additionally, Navier–Stokes equations are employed to study viscous and unsteady flow patterns around stationary cylinders. The study scrutinizes two time-stepping algorithms, emphasizing accuracy, stability, and computational efficiency. The results demonstrate the implicit–explicit Runge–Kutta algorithm's superior accuracy in predicting flow discontinuities in compressible flow. This advantage arises from the semi-implicit nature of the equations, reducing numerical errors. The algorithm significantly enhances accuracy and stability for low Mach number Riemann problems, addressing increasing stiffness as Mach numbers decrease. Notably, the algorithm optimizes computational efficiency for both low Mach number Riemann problems and viscous flows around cylinders, reducing computational costs by 38%–68%. The investigation extends to a two dimensional hypersonic inviscid flow over cylinder and double Mach reflection case, showcasing the method's proficiency in capturing complex and hypersonic flow behavior. Overall, this research advances the understanding of time discretization techniques in computational fluid dynamics, offering an effective approach for handling a wide range of Mach numbers while improving accuracy and efficiency.

Illustration of thermal buoyancy on the flow of MHD Casson CNT–water nanofluids over a vertical stretching surface

This study addresses the applications of non-uniform heat source/sink and viscous dissipation in the magnetohydrodynamic (MHD) flow of Casson nanoparticles toward a porous stretchable sheet. The free convective flow for the inclusion of thermal buoyancy along with dissipative heat encourages the flow phenomena. The governing equations of the flow model are presented in terms of partial differential equations and then transformed into a system of ordinary differential equations using similarity transformations. These systems of equations are solved numerically by using the Runge–Kutta fourth-order method with a very efficient shooting technique. The effects of various parameters such as the Casson parameter, elastic parameter, porosity parameter, Prandtl number, non-uniform heat source/sink constant, Eckert number, skin fraction and Nusselt number on the flow area are computed and represented graphically. The present results reflect that the velocity of nanoparticles declined effectively with the porosity parameter and nanoparticle volume fraction. The temperature profile is increased with the elastic parameter and heat source parameter while decreasing with the Eckert number and Casson fluid parameter. Moreover, it is observed that when the Hartmann number is maximum, a retardation in wall shear force against nanoparticles volume fraction is marked.

A self-excited bistable oscillator with a light-powered liquid crystal elastomer

The nonlinearity in the dynamics of a liquid crystal elastomer-based systems plays an important role when designing and controlling a responsive LCE-based smart system. In this work, we proposed an LCE-based bistable oscillator and investigated its self-excited oscillation behavior. The oscillator consists of a lumped mass, connected by two lateral helical springs, and one liquid crystal elastomer fiber spring which is subjected to a steady light illumination. After inserting the dynamic model of the light-powered LCE fiber into that of the oscillator, the nonlinear vibration response is obtained by using a fourth-order Runge-Kutta method. Different from the reported mono-stable limit circle modes, the self-vibration has a snap-through oscillation mode owing to an opto-mechanical coupling where the light energy can overcome the potential well of the mechanical part. Since the light illumination energy compensates the dissipative energy loss in each nonlinear vibration period, the nonlinear vibration of the LCE-based bistable oscillator is sustainable. We discuss the influence of both the linear and nonlinear parameters on the self-excited vibration response of the bistable oscillator. The nonlinear parameters of the lateral spring, such as the stiffness ratio and the length ratio, as well as the linear parameters of the LCE fiber, including the damping ratio, spring stiffness, light intensity, light contraction coefficient, and gravity, are all taken into consideration in our analysis. Our results reveal that the self-excited vibration can be controlled by adequately tuning these linear and/or nonlinear parameters. The investigation may pave a way for promising applications such as intelligent structural design, energy harvesting, sensing, actuating, and bio-mimic/bio-inspired system using the LCE fiber.

New particle tracking method for 2D steady-state groundwater flow around wells: A modified algorithm using the stream function

Particle tracking is an essential process in analyzing groundwater flow and solute transport in aquifers. A drawback of existing particle tracking methods, which are based on approximate estimations of the velocity in a time step, is the accumulative errors of numerous time steps would lead to deviation of particles away from the exact streamlines, especially when pumping and injecting wells exist. In this study, to improve the accuracy of particle tracking for the two-dimensional (2D) steady-state flow around wells, we propose a stream-function-based (SFB) particle tracking method in which a particle is traced along the exact streamline with a given value of the stream function, and the branch cut effect caused by the multivalued stream function around a well is eliminated. Three synthetic cases are used to demonstrate the advantages of the SFB method over the existing Pollock method and the fourth-order Runge-Kutta method. In the cases of a single pumping well and an injecting-pumping well pair, the Pollock and Runge-Kutta methods yield pathways that may be far away from the exact streamline, but the SFB method performs much better. In the case with a pumping well and two injecting wells, the SFB method successfully delineated a narrow capture zone of the pumping well, which requires a high accuracy particle tracking process. Moreover, the accuracy of particle positions obtained by the SFB method is insensitive to the step-travel distance. The study would be useful for accurate investigation of flow fields in aquifers disturbed by wells.

Modeling of self-oscillating flexible circuits based on liquid crystal elastomers

Deformable and movable flexible circuits are characterized by simple construction, precise control, flexible and versatile morphology, and various functional forms, which can be used to build dynamic circuit systems, achieve the integration of drivers and controllers, and automated control of circuits, etc. Limited to conventional materials, challenges remain in designing novel self-oscillating flexible circuit. In this paper, a concept for a self-oscillating flexible circuit based on electrothermally responsive liquid crystal elastomers (LCEs) is presented, which is capable of generating periodic continuous oscillation under steady applied voltage. The governing equation of the self-oscillating LCE-based flexible circuit is formulated, and numerically calculated by fourth-order Runge-Kutta method with Matlab software. The numerical calculations reveal that the self-oscillating flexible circuit involves two motion patterns, i.e., static pattern and self-oscillation pattern. The self-oscillation arises from the coupling between the electrothermally driven deformation of the LCE film and its motion, and the electrothermal input compensates for the damping dissipation. Moreover, it is found that system parameters affect the self-oscillation of flexible circuit and that there are critical values of these parameters that trigger self-oscillation. Based on the self-oscillating flexible circuit, we conceptualized an automatic control device and a disturbance monitoring device, realizing automatic control of electrical appliances without human intervention and automatic monitoring of external disturbances. The proposed self-oscillating LCE-based flexible circuit features convenient operation, simple construction, flexibility, lightweight, and noiseless operation, rendering it suitable for constructing dynamic circuit systems, achieving actuator-controller integration, and facilitating circuit automation applications.