Abstract
This chapter provides a brief overview of vibrations of lumped-parameter systems, also referred to as discrete systems. A generalized treatment of these systems using modal matrix representation is presented first, followed by decoupling strategies for the governing equations of motion. Although brief, the outcomes of this chapter are used in the subsequent chapters when the equations of motion governing the vibrations of continuous systems or vibration-control systems reduce to their respective discrete representations. We leave the more detailed discussions and treatment of these systems to standard vibration books cited in this chapter (Tse et al. 1978; Thomson and Dahleh 1998; Rao 1995; Inman 2007; Meirovitch 1986; Balachandran and Magrab 2009).
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Notes
- 1.
e jθ = cosθ + jsinθ, \(j = \sqrt{-1}\).
- 2.
These operators in continuous systems reduce to mass and stiffness matrices in discrete systems.
- 3.
The exercises denoted by asterisk (*) refer to problems that require extensive use of numerical solvers such as Matlab/Simulink.
References
Balachandran B, Magrab EB (2009) Vibrations, 2nd ed. Cengage learning, Toronto, ON, Canada
Inman DJ (2007) Engineering vibration, 3rd edn. Prentice Hall Inc
Meirovitch L (1986) Elements of vibrations analysis, 2nd edn. McGraw-Hill, Inc
Nayfeh AH, Pai PF (2004) Linear and nonlinear structural mechanics. Wiley, Hoboken, New Jersey
Rao SS (1995) Mechanical vibrations, 3rd edn. Addison-Wesley Publishing Company
Thomson WT, Dahleh M (1998) Theory of vibration with applications, 5th edn. Prentice Hall Inc
Tse F, Morse IE, Hinkle RT (1978) Mechanical vibrations, theory and applications, 2nd edn. Allyn and Bacon Inc
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Jalili, N. (2010). An Introduction to Vibrations of Lumped-Parameters Systems. In: Piezoelectric-Based Vibration Control. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0070-8_2
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DOI: https://doi.org/10.1007/978-1-4419-0070-8_2
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