Some Concepts in Structural Dynamics
This chapter recalls the main aspects of structural dynamics which will be used in the subsequent chapters, with a particular emphasis on control. The chapter begins with the eigenvalue problem of a discrete system (mode shapes and natural frequencies), discusses the modal decomposition, including in the presence of rigid body modes, and introduces the dynamic flexibility matrix. Systems with collocated actuators and sensors are treated with special attention for their remarkable property of alternating poles and zeros; the relation between the transmission zeros (anti-resonances) and the natural frequencies of the constrained system is highlighted. The vibration of the Euler–Bernoulli beam is briefly discussed as an example of distributed system. Next, the chapter discusses the reduction methods: Guyan and Craig–Bampton. The chapter concludes with a short list of references and a set of problems.
KeywordsVibration modes Modal decomposition Collocated system Anti-resonance Transmission zeros Guyan reduction Craig–Bampton reduction
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