Abstract
Different kinematic mathematical models of nonlinear dynamics of a contact interaction of two microbeams are derived and studied. Dynamics of one of the microbeams is governed by kinematic hypotheses of the first, second, and third approximation orders. The second beam is excited through a contact interaction with the first beam and is described by the kinematic hypothesis of the second-order approximation in both geometric linear and nonlinear frameworks. The derived nonlinear partial differential equations (PDEs) are transformed to the counterpart system of nonlinear ordinary differential equations (ODEs) by the finite difference method. Nonlinear contact interaction dynamics of the microbeam structure is analyzed with the help of time series (signals), Fourier spectra, and wavelet spectra based on various mother wavelets, Morlet wavelet spectra employed to study synchronization phenomena, Poincaré maps, phase portraits, and the Lyapunov exponents estimated with the Wolf, Kantz, and Rosenstein algorithms. We have illustrated that neglecting the shear function (Euler–Bernoulli model) yields erroneous numerical results. We have shown that the geometric nonlinearity cannot be neglected in the analysis even for small two-layer microbeam deflection. In addition, we have detected that the contact between two microbeams takes place in the vicinity of
Acknowledgments
This work has been supported the Ministry of Education and Science of the Russian Federation by the Grant Number 2.1642.2017.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Modeling the Effects of Health Education and Early Therapy on Tuberculosis Transmission Dynamics
- Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays
- Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy
- Kinetic Flux Vector Splitting Method for Numerical Study of Two-dimensional Ripa Model
- Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems
- A Riccati–Bernoulli sub-ODE Method for Some Nonlinear Evolution Equations
- New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems
- Numerical Solution of Space and Time Fractional Telegraph Equation: A Meshless Approach
- Stability and Bifurcation Analysis in a Discrete-Time SIR Epidemic Model with Fractional-Order
- A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems
- The Multiplicity of Solutions for a Class of Nonlinear Fractional Dirichlet Boundary Value Problems with p-Laplacian Type via Variational Approach
- Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses
- The Optimal Design of a Functionally Graded Corrugated Cylindrical Shell under Axisymmetric Loading
- Application of the Optimal Auxiliary Functions Method to a Permanent Magnet Synchronous Generator
- Investigation of Geometry Effect on Heat and Mass Transfer in Buoyancy Assisting with the Vertical Backward and Forward Facing Steps
- Existence of at Least One Homoclinic Solution for a Nonlinear Second-Order Difference Equation
- Some Novel Solitary Wave Characteristics for a Generalized Nonlocal Nonlinear Hirota (GNNH) Equation
- Fractional Navier–Stokes Equation from Fractional Velocity Arguments and Its Implications in Fluid Flows and Microfilaments
- Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas
- Results on Controllability of Nonlinear Hilfer Fractional Stochastic System
- Effects of Different Turbulence Models on Three-Dimensional Unsteady Cavitating Flows in the Centrifugal Pump and Performance Prediction
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Modeling the Effects of Health Education and Early Therapy on Tuberculosis Transmission Dynamics
- Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays
- Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy
- Kinetic Flux Vector Splitting Method for Numerical Study of Two-dimensional Ripa Model
- Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems
- A Riccati–Bernoulli sub-ODE Method for Some Nonlinear Evolution Equations
- New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems
- Numerical Solution of Space and Time Fractional Telegraph Equation: A Meshless Approach
- Stability and Bifurcation Analysis in a Discrete-Time SIR Epidemic Model with Fractional-Order
- A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems
- The Multiplicity of Solutions for a Class of Nonlinear Fractional Dirichlet Boundary Value Problems with p-Laplacian Type via Variational Approach
- Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses
- The Optimal Design of a Functionally Graded Corrugated Cylindrical Shell under Axisymmetric Loading
- Application of the Optimal Auxiliary Functions Method to a Permanent Magnet Synchronous Generator
- Investigation of Geometry Effect on Heat and Mass Transfer in Buoyancy Assisting with the Vertical Backward and Forward Facing Steps
- Existence of at Least One Homoclinic Solution for a Nonlinear Second-Order Difference Equation
- Some Novel Solitary Wave Characteristics for a Generalized Nonlocal Nonlinear Hirota (GNNH) Equation
- Fractional Navier–Stokes Equation from Fractional Velocity Arguments and Its Implications in Fluid Flows and Microfilaments
- Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas
- Results on Controllability of Nonlinear Hilfer Fractional Stochastic System
- Effects of Different Turbulence Models on Three-Dimensional Unsteady Cavitating Flows in the Centrifugal Pump and Performance Prediction