Preface

In practical applications that range from outer space to the deep oceans, engineering structures such as aircraft, rockets, automobiles, turbines, architectures, vessels, and submarines often work in complex environments and can be subjected to various dynamic loads, which can lead to the vibratory behaviors of the structures. In all these applications, the engineering structures may fail and collapse because of material fatigue resulting from vibrations. Many calamitous incidents have shown the destructive nature of vibrations. For instance, the main span of the famous Tacoma Narrows Bridge suffered severe forced resonance and collapsed in 1940 due to the fact that the wind provided an external periodic frequency that matched one of the natural structural frequencies of the bridge. Furthermore, noise generated by vibrations always causes annoyance, discomfort, and loss of efficiency to human beings. Therefore, it is of particular importance to understand the structural vibrations and reduce them through proper design to ensure a reliable, safe, and lasting structural performance. An important step in the vibration design of an engineering structure is the evaluation of its vibration modal characteristics, such as natural frequencies and mode shapes. This modal information plays a key role in the design and vibration suppression of the structure when subjected to dynamics excitations. In engineering applications, a variety of possible boundary restraining cases may be encountered for a structure. In recent decades, the ability of predicting the vibration characteristics of structures with general boundary conditions is of prime interest to engineers and designers and is the mutual concern of researchers in this field as well. Beams, plates, and shells are basic structural elements of most engineering structures and machines. A thorough understanding of their vibration characteristics is of great significance for engineers to predict the vibrations of the whole structures and design suitable structures with low vibration and noise radiation characteristics. There exists many books, papers, and research reports on the vibration analysis of beams, plates, and shells. In 1969, Prof. A.W. Leissa published the excellent monograph Vibration of Plates, in which theoretical and experimental results of approximately 500 research papers and reports were presented. And in 1973, he organized and summarized approximately 1,000 references in the field of shell