Exploring Complexities and Solutions in Beam Equation Modeling

Beam equations have broad application across a range of different domains. These equations are often used to model physical phenomena such as damping, time-delay, and nonlinear source effects. However, there are ongoing debates and gaps in knowledge within the field. Recent studies have attempted to address some of the key issues through the use of generalized fractional derivatives, diffusive representation, and finite difference schemes. However, there is a need for better investigation and validation of these theoretical findings.

This Research Topic aims to explore the complexities of beam equations and systems, with a particular focus on the Euler–Bernoulli and Timoshenko beam equations. Submissions are invited that answer specific questions related to the modeling of dissipation, the well-posedness of the problems, and the exponential decay of energy. Contributors are also encouraged to test hypotheses addressing these issues, validate their theoretical findings through practical implementation, and to examine the potential of deep neural networks for efficiently dealing with computational and stability burdens.

To gather further insights into the complexities of beam equations and systems, this Research Topic welcomes articles addressing, but not limited to, the following themes:
- The use of generalized fractional derivatives in modeling dissipation
- The well-posedness of problems addressed through diffusive representation
- The exponential decay of energy associated with global solutions
- The potential of deep neural networks in dealing with computational and stability burdens
- The boundedness of the local propagation matrix
- The efficiency of finite difference schemes in addressing related issues

Article types and fees

This Research Topic accepts the following article types, unless otherwise specified in the Research Topic description:

• Brief Research Report
• Curriculum, Instruction, and Pedagogy
• Data Report
• Editorial
• FAIR² Data
• FAIR² DATA Direct Submission
• General Commentary
• Hypothesis and Theory
• Methods
• ... View all formats

Articles that are accepted for publication by our external editors following rigorous peer review incur a publishing fee charged to Authors, institutions, or funders.

Article types

This Research Topic accepts the following article types, unless otherwise specified in the Research Topic description:

• Brief Research Report
• Curriculum, Instruction, and Pedagogy
• Data Report
• Editorial
• FAIR² Data
• FAIR² DATA Direct Submission
• General Commentary
• Hypothesis and Theory
• Methods
• Mini Review
• Opinion
• Original Research
• Perspective
• Review
• Technology and Code

Keywords: Euler–Bernoulli equation, Timoshenko equation, diffusive representation, finite difference schemes, damping and dissipation modelling, time-delay effects, nonlinear source effects, exponential energy decay, local propagation matrix, problem well-posedness

Important note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.