Thin Plate Bending, Vibration, and Nonlinear Dynamics

Exact Analytical Solutions
Erscheinungsjahr 2026
ISBN: 978-3-032-33063-5
Verlag: Springer

Buch, Englisch, 243 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Synthesis Lectures on Mechanical Engineering

While modern engineering practice relies heavily on numerical methods such as the finite element method (FEM), these approaches require reliable benchmarks for validation. Exact solutions remain indispensable for this purpose.

This book presents a unified treatment of exact analytical solutions for the bending, vibration, and nonlinear dynamics of thin plates, including rectangular, circular, and annular geometries. It integrates classical plate theory with modern developments such as symplectic elasticity, thermoelastic vibration analysis, and electrostatic MEMS modeling, providing a rigorous framework derived from first principles.

The book systematically develops governing equations, derives exact solutions for all boundary-condition combinations, and extends the analysis to thermal loading, buckling, and nonlinear dynamic behavior. More than 80 exact solutions are presented alongside numerical benchmarks, worked examples, and engineering interpretations, making the results directly applicable to real-world problems.

Designed as both a reference and a research tool, the book serves multiple audiences: graduate students seeking a comprehensive foundation, engineers requiring validation benchmarks, and researchers developing new analytical or computational methods. It bridges the gap between classical theory and modern engineering applications, emphasizing both mathematical rigor and practical utility.

Zielgruppe

Research

Autoren/Hrsg.

Faris, Waleed

Fachgebiete

• Technische Wissenschaften Bauingenieurwesen Baukonstruktion, Baufachmaterialien
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik

Inhaltsverzeichnis

Chapter 1 – Introduction.- Chapter 2 – Governing Equations for Thin Plates.- Chapter 3 – Exact Static Bending Solutions for Rectangular Thin Plates.- Chapter 4 – Dynamic Solutions: Thermal Effects on Plate Vibrations.- Chapter 5 – Circular and Annular Plates under Thermal and Electrostatic Loadings.- Chapter 6 – Conclusions and Comparative Assessment.

Über Autor(innen)

Dr Waleed Faris is currently a faculty-in-residence at the University of Nevada, Las Vegas, USA. He was a professor in the Mechanical Engineering and Aerospace Department, College of Engineering, International Islamic University, Malaysia before this.

He received his BSc and MSc degrees from Zagazig University, Egypt and his PhD from Virginia Tech, USA. His research focuses on multidisciplinary applications of dynamics and control. He is a well-known scholar in his field, having published 130 journal papers in internationally indexed scientific journals, around 120 conference papers, six engineering books.