Page 119 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

116 Chapter 1 Fundamentals oF Vibration
problems

section 1.4 basic Concepts of Vibration and
section 1.6 Vibration analysis procedure
1.1* A study of the response of a human body subjected to vibration/shock is important in many
applications. In a standing posture, the masses of head, upper torso, hips, and legs and
the elasticity/damping of neck, spinal column, abdomen, and legs influence the response
characteristics. Develop a sequence of three improved approximations for modeling the
human body.

1.2* Figure 1.62 shows a human body and a restraint system at the time of an automobile collision
[1.47]. Suggest a simple mathematical model by considering the elasticity, mass, and damp-
ing of the seat, human body, and restraints for a vibration analysis of the system.

Restraint Windshield
Seat belts

Instrument
panel

Slant
footboard
Impact
Floor force
FiGure 1.62 A human body and a restraint system.

1.3* A reciprocating engine is mounted on a foundation as shown in Fig. 1.63. The unbalanced
forces and moments developed in the engine are transmitted to the frame and the foundation.
An elastic pad is placed between the engine and the foundation block to reduce the transmis-
sion of vibration. Develop two mathematical models of the system using a gradual refinement
of the modeling process.
1.4* A car moving over a rough road (Fig. 1.64) can be modeled considering (a) weight
of the car body, passengers, seats, front wheels, and rear wheels; (b) elasticity of tires

*The asterisk denotes a design-type problem or a problem with no unique answer.