From discrete masses to distributed systems. Covers wave equation for strings/bars/shafts, Euler-Bernoulli beam equation, boundary conditions, and Rayleigh's energy method for frequency estimation.
How do engineers find natural frequencies of systems with thousands of DOFs? This post covers five essential numerical techniques: Dunkerley's lower bound, Rayleigh's quotient, Holzer's transfer matrix, power iteration, and Jacobi's rotation method.
From coupled oscillators to real-world structures: master the matrix formulation of MDOF dynamics, solve the eigenvalue problem for natural frequencies, and harness modal analysis to decouple complex vibrations into independent modes.
Introduction to multi-DOF systems. Covers coupled equations, matrix notation, natural frequencies, mode shapes, static vs dynamic coupling, principal coordinates, and semidefinite (unrestrained) systems.
Handling non-harmonic and transient forces. Covers Fourier series for periodic forces, the Convolution Integral for arbitrary excitations, Response Spectra for earthquake design, and Laplace Transform methods for step and ramp inputs.
Exploring forced vibration with harmonic excitation. Covers resonance, phase relationships, beating phenomenon, rotating unbalance, base excitation, vibration isolation design, and frequency response analysis.
How systems vibrate naturally without external forces. Covers undamped oscillation, Rayleigh's energy method, viscous damping, the three damping regimes, logarithmic decrement, and system stability analysis.
An introduction to mechanical vibration theory. Covers the history of vibration science, basic system elements (spring, mass, damper), degrees of freedom, and the engineering workflow for translating physical systems into mathematical models.
This post provides tips on camera usage, focusing on essential aspects such as focusing techniques, depth of field control, shutter speed management, and creative tools for photography. It also covers auto exposure modes and strategies for capturing sharp photos, addressing common issues like blur caused by poor focus or camera shake.
This post explores the intricacies of film and sensor in photography, focusing on key elements such as film speed and ISO sensitivity, exposure techniques including light metering, and the concept of dynamic range. It also provides practical settings for moon photography, highlighting the importance of understanding light intensity and its impact on capturing images.