Waves in Solids
Longitudinal and transverse shear elastic waves propagating through solid continuous media.
General idea of the topic
This topic organizes the contents of waves in solids. Its purpose is to build a structured reading that connects the main concepts, quantities, and analysis methods with the problems that can be solved.
What you will truly understand
- Relate the concepts of introduction, elastic properties of solids, types of waves in solids, longitudinal waves in bars, transverse shear waves, relationship between elastic moduli, flexural waves in beams, rayleigh surface waves, p and s seismic waves, reflection and transmission in solids, mechanical impedance in solids, dispersion and attenuation in solids, resonance and modes in bars, modes in plates and membranes, and ultrasound and testing applications to their physical context.
- Identify the relevant variables and the assumptions that allow each model to be applied.
- Recognize limiting cases and validity conditions of the approximations used.
- Organize reasoning to move from the statement to the physical interpretation.
Recommended learning route
- Introduction.
- Elastic Properties of Solids.
- Types of Waves in Solids.
- Longitudinal Waves in Bars.
- Transverse Shear Waves.
- Relationship Between Elastic Moduli.
- Flexural Waves in Beams.
- Rayleigh Surface Waves.
- P and S Seismic Waves.
- Reflection and Transmission in Solids.
- Mechanical Impedance in Solids.
- Dispersion and Attenuation in Solids.
- Resonance and Modes in Bars.
- Modes in Plates and Membranes.
- Ultrasound and Testing Applications.
Physical criterion you must acquire
You must acquire the criterion of deciding which model applies in each situation, which quantities are conserved or related, and when a simplification is valid. Physical reading must precede calculation.
Connection with real problems
These contents appear in design, simulation, data analysis, technology, and everyday problem solving. Interpreting results is as important as obtaining the numerical solution.
Final goal of the topic
The final goal is to master the topic of waves in solids with physical criterion: state the problem, choose the appropriate model, solve it with traceability, and discuss the validity of the result.
Topics in this section
- Introduction
Fundamental concepts of mechanical wave propagation in solid media. Theory, formulas, worked examples and interactive graphs.
- Elastic Properties of Solids
Fundamental elastic moduli of isotropic solids, stress-strain relationship and Lame constants.
- Types of Waves in Solids
Classification and properties of longitudinal, transverse and surface waves in solid media.
- Longitudinal Waves in Bars
Non-dispersive propagation of compression-tension waves in slender bars and their applications.
- Transverse Shear Waves
Transverse shear waves in isotropic elastic solids, velocity and polarization.
- Relationship Between Elastic Moduli
Algebraic relationships between Young, shear and bulk moduli and Poisson ratio in isotropic solids.
- Flexural Waves in Beams
Dispersive propagation of bending waves in elastic beams according to Euler-Bernoulli theory.
- Rayleigh Surface Waves
Rayleigh surface waves with retrograde elliptical trajectory on the free surface of a solid.
- P and S Seismic Waves
Longitudinal P waves and transverse S waves in elastic solid media, velocities and seismic detection.
- Reflection and Transmission in Solids
Reflection and transmission of elastic waves at interfaces between solids with different acoustic impedance.
- Mechanical Impedance in Solids
Mechanical impedance in solids as force-to-velocity ratio and its role in wave transmission.
- Dispersion and Attenuation in Solids
Amplitude loss and pulse distortion in mechanical waves traveling through real solids.
- Resonance and Modes in Bars
Natural frequencies and modal patterns of longitudinal, transverse and torsional vibration in bars with various boundary conditions.
- Modes in Plates and Membranes
Modal frequencies and nodal patterns of vibratory modes in plates and membranes.
- Ultrasound and Testing Applications
Ultrasound applications in non-destructive testing and physical diagnosis.