Most scientific problems in solid mechanics are inherently nonlinear by nature, and, except for a limited number of cases, most of them do not have analytical solutions. The most nonlinear problems in solid mechanics are vibration analysis; deflection and deformation of different beams, materials, or plates. In this chapter some of these problems are presented and solved by DTM, which is categorized in the following sections:
8.1
Introduction
8.2
Deflection Prediction of a Cantilever Beam
8.3
Vibration Analysis of Stepped FGM Beams
8.4
Piezoelectric Modal Sensors for Cantilever Beams
8.5
Damped System With High Nonlinearity
8.6
Free Vibration of a Centrifugally Stiffened Beam
8.7
Deflections of Orthotropic Rectangular Plate
8.8
Free Vibration of Circular Plates
8.9
Vibration of Pipes Conveying Fluid
8.10
Piezoelectric Modal Sensor for Nonuniform Euler–Bernoulli Beams With Rectangular Cross Section
8.11
Free Vibrations of Oscillators
8.12
Composite Sandwich Beams With Viscoelastic Core
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